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Journal articles on the topic 'Fermions'

Author: Grafiati

Published: 4 June 2021

Last updated: 23 November 2024

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1

Ma, Tian-Chi, Jing-Nan Hu, Yuan Chen, Lei Shao, Xian-Ru Hu, and Jian-Bo Deng. "Coexistence of type-II and type-IV Dirac fermions in SrAgBi." Modern Physics Letters B 35, no. 11 (February 9, 2021): 2150181. http://dx.doi.org/10.1142/s0217984921501815.

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Relativistic massless Weyl and Dirac fermions have isotropic and linear dispersion relations to maintain Poincaré symmetry, which is the most basic symmetry in high-energy physics. The situation in condensed matter physics is less constrained; only certain subgroups of Poincaré symmetry — the 230 space groups that exist in 3D lattices — need be respected. Then, the free fermionic excitations that have no high-energy analogues could exist in solid state systems. Here, We discovered a type of nonlinear Dirac fermion without high-energy analogue in SrAgBi and named it type-IV Dirac fermion. The type-IV Dirac fermion has a nonlinear dispersion relationship and is similar to the type-II Dirac fermion, which has electron pocket and hole pocket. The effective model for the type-IV Dirac fermion is also found. It is worth pointing out that there is a type-II Dirac fermion near this new Dirac fermion. So we used two models to describe the coexistence of these two Dirac fermions. Topological surface states of these two Dirac points are also calculated. We envision that our findings will stimulate researchers to study novel physics of type-IV Dirac fermions, as well as the interplay of type-II and type-IV Dirac fermions.

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2

GUENDELMAN, E. I., and A. B. KAGANOVICH. "DARK ENERGY, DARK MATTER AND FERMION FAMILIES IN THE TWO MEASURES THEORY." International Journal of Modern Physics A 19, no. 31 (December 20, 2004): 5325–32. http://dx.doi.org/10.1142/s0217751x04022542.

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A field theory is proposed where the regular fermionic matter and the dark fermionic matter are different states of the same "primordial" fermion fields. In regime of the fermion densities typical for normal particle physics, each of the primordial fermions splits into three generations identified with regular fermions. In a simple model, this fermion families birth effect is accompanied with the right lepton numbers conservation laws. It is possible to fit the muon to electron mass ratio without fine tuning of the Yukawa coupling constants. When fermion energy density becomes comparable with dark energy density, the theory allows new type of states - Cosmo-Low Energy Physics (CLEP) states. Neutrinos in CLEP state can be both a good candidate for dark matter and responsible for a new type of dark energy. In the latter case the total energy density of the universe is less than it would be in the universe free of fermionic matter at all. The (quintessence) scalar field is coupled to dark matter but its coupling to regular fermionic matter appears to be extremely suppressed.

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3

GUENDELMAN, E. I., and A. B. KAGANOVICH. "NEW PHYSICS AT LOW ENERGIES AND DARK MATTER-DARK ENERGY TRANSMUTATION." International Journal of Modern Physics A 20, no. 06 (March 10, 2005): 1140–47. http://dx.doi.org/10.1142/s0217751x05024018.

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A field theory is proposed where the regular fermionic matter and the dark fermionic matter can be different states of the same "primordial" fermion fields. In regime of the fermion densities typical for normal particle physics, the primordial fermions split into three families identified with regular fermions. When fermion energy density becomes comparable with dark energy density, the theory allows transition to new type of states. The possibility of such Cosmo-Low Energy Physics (CLEP) states is demonstrated by means of solutions of the field theory equations describing FRW universe filled with homogeneous scalar field and uniformly distributed nonrelativistic neutrinos. Neutrinos in CLEP state are drawn into cosmological expansion by means of dynamically changing their own parameters. One of the features of the fermions in CLEP state is that in the late time universe their masses increase as a3/2 (a=a(t) is the scale factor). The energy density of the cold dark matter consisting of neutrinos in CLEP state scales as a sort of dark energy; this cold dark matter possesses negative pressure and for the late time universe its equation of state approaches that of the cosmological constant. The total energy density of such universe is less than it would be in the universe free of fermionic matter at all.

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4

BELYAEV, V. M., and IAN I. KOGAN. "MASSLESS FERMIONS IN KALUZA-KLEIN MODELS: SU(N) GAUGE FIELDS, ZN SYMMETRY AND STABILITY OF THE METASTABLE VACUUM." Modern Physics Letters A 07, no. 02 (January 20, 1992): 117–29. http://dx.doi.org/10.1142/s0217732392000057.

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Kaluza-Klein model on M4×S1 with SU (N) gauge fields and Nf fermions in fundamental representation is considered. It is noted that on one-loop level the lowest state of this theory corresponds to effective four-dimensional theory which has no massless fermions. This statement does not depend on fermion boundary conditions. The state with mass-less four-dimensional fermions is metastable. It is shown that this metastable states can be stabilized by effects of classical gravitation. The same problem of metastability of states with zero fermionic modes can appear in more realistic superstring compactification models and these effects of classical gravitation can resolve this problem of metastability.

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5

Dajka, Jerzy. "Interference of Particles with Fermionic Internal Degrees of Freedom." Entropy 26, no. 6 (May 26, 2024): 449. http://dx.doi.org/10.3390/e26060449.

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The interference of fermionic particles, specifically molecules comprising a small number of fermions, in a Mach–Zehnder interferometer is being investigated under the influence of both classical and non-classical external controls. The aim is to identify control strategies that can elucidate the relationship between the interference pattern and the characteristics of internal fermion–fermion interactions.

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6

Lee, Cheng-Yang. "Symmetries and unitary interactions of mass dimension one fermionic dark matter." International Journal of Modern Physics A 31, no. 35 (December 18, 2016): 1650187. http://dx.doi.org/10.1142/s0217751x16501876.

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The fermionic fields constructed from Elko have several unexpected properties. They satisfy the Klein–Gordon but not the Dirac equation and are of mass dimension one instead of three-half. Starting with the Klein–Gordon Lagrangian, we initiate a careful study of the symmetries and interactions of these fermions and their higher-spin generalizations. We find, although the fermions are of mass dimension one, the four-point fermionic self-interaction violates unitarity at high-energy so it cannot be a fundamental interaction of the theory. Using the optical theorem, we derive an explicit bound on energy for the fermion–scalar interaction. It follows that for the spin-half fermions, the demand of renormalizability and unitarity forbids four-point interactions and only allows for the Yukawa interaction. For fermions with spin [Formula: see text], they have no renormalizable or unitary interactions. Since the theory is described by a Klein–Gordon Lagrangian, the interaction generated by the local [Formula: see text] gauge symmetry which contains a four-point interaction, is excluded by the demand of renormalizability. In the context of the Standard Model, these properties make the spin-half fermions natural dark matter candidates. Finally, we discuss the recent developments on the introduction of new adjoint and spinor duals which may allow us to circumvent the unitarity constraints on the interactions.

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7

CORDOVA, NICOLAS J. "FRACTIONAL CHARGE IN 1+1, 2+1 AND 3+1 DIMENSIONS." Modern Physics Letters A 06, no. 33 (October 30, 1991): 3071–77. http://dx.doi.org/10.1142/s0217732391003560.

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Fractional charge is analyzed in models containing massive fermions interacting with topologically non-trivial background fields in 1+1, 2+1 and 3+1 dimensions. It is found that the induced vacuum fermionic charge depends discontinuously on the fermion mass, when scalar interactions are involved.

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8

DOLOCAN, ANDREI, VOICU OCTAVIAN DOLOCAN, and VOICU DOLOCAN. "A NEW HAMILTONIAN OF INTERACTION FOR FERMIONS." Modern Physics Letters B 19, no. 13n14 (June 20, 2005): 669–81. http://dx.doi.org/10.1142/s0217984905008700.

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Using the Lagrangian formalism we attempt to introduce a new Hamiltonian for fermions. On this basis we have evaluated the expectation values for the interaction energy between fermions via bosons. The interaction energy between two fermions via phonons becomes attractive in a degenerate fermion-gas. The interaction energy between two fermions via photons appears to be attractive in certain conditions. The self-energy of the fermion + boson system, e.g. polaron and polariton, was evaluated.

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9

Klaric, J., A. Shkerin, and G. Vacalis. "Non-perturbative production of fermionic dark matter from fast preheating." Journal of Cosmology and Astroparticle Physics 2023, no. 02 (February 1, 2023): 034. http://dx.doi.org/10.1088/1475-7516/2023/02/034.

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Abstract We investigate non-perturbative production of fermionic dark matter in the early universe. We study analytically the gravitational production mechanism accompanied by the coupling of fermions to the background inflaton field. The latter leads to the variation of effective fermion mass during preheating and makes the resulting spectrum and abundance sensitive to its parameters. Assuming fast preheating that completes in less than the inflationary Hubble time and no oscillations of the inflaton field after inflation, we find an abundant production of particles with energies ranging from the inflationary Hubble rate to the inverse duration of preheating. The produced fermions can account for all observed dark matter in a broad range of parameters. As an application of our analysis, we study non-perturbative production of fermionic dark matter in the model of Palatini Higgs inflation.

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10

GIROTTI, H. O. "CANONICAL QUANTIZATION OF THE SELF-DUAL MODEL COUPLED TO FERMIONS." International Journal of Modern Physics A 14, no. 16 (June 30, 1999): 2495–510. http://dx.doi.org/10.1142/s0217751x99001238.

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This paper is devoted to formulating the interaction-picture dynamics of the self-dual field minimally coupled to fermions. As a preliminary, we quantize the free self-dual model by means of the Dirac-bracket quantization procedure. The free self-dual model turns out to be a relativistically invariant quantum field theory whose excitations are identical to the physical (gauge-invariant) excitations of the free Maxwell–Chern–Simons theory. The interacting model is also quantized through the Dirac-bracket quantization procedure. One of the self-dual field components is found not to commute, at equal times, with the fermionic fields. Hence, the formulation of the interaction-picture dynamics demands the elimination of that component. This procedure brings, in turn, two new interactions terms, which are local in space and time while nonrenormalizable by power counting. Relativistic invariance is tested in connection with the elastic fermion–fermion scattering amplitude. We prove that all the noncovariant pieces in the interaction Hamiltonian are equivalent to the covariant minimal interaction of the self-dual field with the fermions. The high-energy behavior of the self-dual field propagator confirms that the coupled theory is nonrenormalizable. The self-dual field minimally coupled to fermions bears no resemblance to the renormalizable model defined by the Maxwell–Chern–Simons field minimally coupled to fermions.

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11

Chiew, Mitchell, and Sergii Strelchuk. "Discovering optimal fermion-qubit mappings through algorithmic enumeration." Quantum 7 (October 18, 2023): 1145. http://dx.doi.org/10.22331/q-2023-10-18-1145.

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Simulating fermionic systems on a quantum computer requires a high-performing mapping of fermionic states to qubits. A characteristic of an efficient mapping is its ability to translate local fermionic interactions into local qubit interactions, leading to easy-to-simulate qubit Hamiltonians.All fermion-qubit mappings must use a numbering scheme for the fermionic modes in order for translation to qubit operations. We make a distinction between the unordered labelling of fermions and the ordered labelling of the qubits. This separation shines light on a new way to design fermion-qubit mappings by making use of the enumeration scheme for the fermionic modes. The purpose of this paper is to demonstrate that this concept permits notions of fermion-qubit mappings that are optimal with regard to any cost function one might choose. Our main example is the minimisation of the average number of Pauli matrices in the Jordan-Wigner transformations of Hamiltonians for fermions interacting in square lattice arrangements. In choosing the best ordering of fermionic modes for the Jordan-Wigner transformation, and unlike other popular modifications, our prescription does not cost additional resources such as ancilla qubits.We demonstrate how Mitchison and Durbin's enumeration pattern minimises the average Pauli weight of Jordan-Wigner transformations of systems interacting in square lattices. This leads to qubit Hamiltonians consisting of terms with average Pauli weights 13.9% shorter than previously known. By adding only two ancilla qubits we introduce a new class of fermion-qubit mappings, and reduce the average Pauli weight of Hamiltonian terms by 37.9% compared to previous methods. For n-mode fermionic systems in cellular arrangements, we find enumeration patterns which result in n1/4 improvement in average Pauli weight over naïve schemes.

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12

Pandey, Mahul, and Sachindeo Vaidya. "Yang–Mills matrix mechanics and quantum phases." International Journal of Geometric Methods in Modern Physics 14, no. 08 (May 11, 2017): 1740009. http://dx.doi.org/10.1142/s0219887817400096.

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The [Formula: see text] Yang–Mills matrix model coupled to fundamental fermions is studied in the adiabatic limit, and quantum critical behavior is seen at special corners of the gauge field configuration space. The quantum scalar potential for the gauge field induced by the fermions diverges at the corners, and is intimately related to points of enhanced degeneracy of the fermionic Hamiltonian. This in turn leads to superselection sectors in the Hilbert space of the gauge field, the ground states in different sectors being orthogonal to each other. The [Formula: see text] Yang–Mills matrix model coupled to two Weyl fermions has three quantum phases. When coupled to a massless Dirac fermion, the number of quantum phases is four. One of these phases is the color-spin locked phase. This paper is an extended version of the lectures given by the second author (SV) at the International Workshop on Quantum Physics: Foundations and Applications, Bangalore, in February 2016, and is based on [1].

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13

FELDMAN, JOEL, HORST KNÖRRER, and EUGENE TRUBOWITZ. "SINGLE SCALE ANALYSIS OF MANY FERMION SYSTEMS PART 1: INSULATORS." Reviews in Mathematical Physics 15, no. 09 (November 2003): 949–93. http://dx.doi.org/10.1142/s0129055x03001771.

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We construct, using fermionic functional integrals, thermodynamic Green's functions for a weakly coupled fermion gas whose Fermi energy lies in a gap. Estimates on the Green's functions are obtained that are characteristic of the size of the gap. This prepares the way for the analysis of single scale renormalization group maps for a system of fermions at temperature zero without a gap.

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14

KHOKHLACHEV, S., and YU MAKEENKO. "ADJOINT FERMIONS INDUCE QCD." Modern Physics Letters A 07, no. 39 (December 21, 1992): 3653–67. http://dx.doi.org/10.1142/s0217732392003086.

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We propose to induce QCD by fermions in the adjoint representation of the gauge group SU (Nc) on the lattice. We consider various types of lattice fermions: chiral, Kogut-Susskind and Wilson ones. Using the mean field method we show that a first order large-N phase transition occurs with decreasing fermion mass. We conclude, therefore, that adjoint fermions induce QCD. We draw the same conclusion for the adjoint scalar or fermion models at large number of flavors Nf when they induce a single-plaquette lattice gauge theory. We find an exact strong coupling solution for the adjoint fermion model and show that it is quite similar to that for the Kazakov-Migdal model with the quadratic potential. We discuss the possibility for the adjoint fermion model to be solvable as Nc→∞ in the weak coupling region where the Wilson loops obey normal area law.

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15

OIKONOMOU, V. K. "HIDDEN SUPERSYMMETRY IN DIRAC FERMION QUASINORMAL MODES OF BLACK HOLES." International Journal of Modern Physics A 28, no. 15 (June 16, 2013): 1350057. http://dx.doi.org/10.1142/s0217751x13500577.

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We connect the quasinormal modes corresponding to Dirac fermions in various curved space–time backgrounds to an N = 2 supersymmetric quantum mechanics algebra, which can be constructed from the radial part of the fermionic solutions of the Dirac equation. In the massless fermion case, the quasinormal modes are in bijective correspondence with the zero modes of the fermionic system and this results to unbroken supersymmetry. The massive case is more complicated, but as we demonstrate, supersymmetry remains unbroken even in this case.

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16

Yanagisawa, Takashi. "Zero-Energy Modes, Fractional Fermion Numbers and The Index Theorem in a Vortex-Dirac Fermion System." Symmetry 12, no. 3 (March 2, 2020): 373. http://dx.doi.org/10.3390/sym12030373.

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Physics of topological materials has attracted much attention from both physicists and mathematicians recently. The index and the fermion number of Dirac fermions play an important role in topological insulators and topological superconductors. A zero-energy mode exists when Dirac fermions couple to objects with soliton-like structure such as kinks, vortices, monopoles, strings, and branes. We discuss a system of Dirac fermions interacting with a vortex and a kink. This kind of systems will be realized on the surface of topological insulators where Dirac fermions exist. The fermion number is fractionalized and this is related to the presence of fermion zero-energy excitation modes. A zero-energy mode can be regarded as a Majorana fermion mode when the chemical potential vanishes. Our discussion includes the case where there is a half-flux quantum vortex associated with a kink in a magnetic field in a bilayer superconductor. A normalizable wave function of fermion zero-energy mode does not exist in the core of the half-flux quantum vortex. The index of Dirac operator and the fermion number have additional contributions when a soliton scalar field has a singularity.

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17

GOERBIG, M. O., P. LEDERER, and C. MORAIS SMITH. "SECOND GENERATION OF COMPOSITE FERMIONS AND THE SELF-SIMILARITY OF THE FRACTIONAL QUANTUM HALL EFFECT." International Journal of Modern Physics B 18, no. 27n29 (November 30, 2004): 3549–52. http://dx.doi.org/10.1142/s0217979204026998.

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A recently developed model of interacting composite fermions, is used to investigate different composite-fermion phases. Their interaction potential allows for the formation of both solid and new quantum-liquid phases, which are interpreted in terms of second-generation composite fermions and which may be responsible for the fractional quantum Hall states observed at unusual filling factors, such as ν=4/11. Projection of the composite-fermion dynamics to a single level, involved in the derivation of the Hamiltonian of interacting composite fermions, reveals the underlying self-similarity of the model.

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18

Wang, Juven, and Yi-Zhuang You. "Symmetric Mass Generation." Symmetry 14, no. 7 (July 19, 2022): 1475. http://dx.doi.org/10.3390/sym14071475.

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The most well-known mechanism for fermions to acquire a mass is the Nambu–Goldstone–Anderson–Higgs mechanism, i.e., after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group, also applicable to chiral fermions with anomaly-free chiral symmetries. This new mechanism is generally referred to as the symmetric mass generation (SMG). It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes the current numerical results, introduces an unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and presents an overview of various features and applications of SMG.

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19

DU, MUYUN, XIYUN DU, and YUEYING XIE. "SCALAR AND FERMION ZERO MODES ON THE THICK BRANE ARISING FROM TWO SCALAR FIELDS." Modern Physics Letters A 23, no. 37 (December 7, 2008): 3179–86. http://dx.doi.org/10.1142/s0217732308026492.

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In this note we study scalar and fermion zero modes on the brane arising from two scalar fields. The result is that there exist normalizable massless modes of scalar fields which can be localized on the brane. While, for spin 1/2 and spin 3/2 fermions, the corresponding zero modes are non-normalizable. Thus, some mechanism such as Yukawa coupling should be introduced for the localization of these fermionic fields on the thick brane.

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20

ABE, HIROYUKI, HIRONORI MIGUCHI, and TAIZO MUTA. "DYNAMICAL FERMION MASSES UNDER THE INFLUENCE OF KALUZA–KLEIN FERMIONS IN EXTRA DIMENSIONS." Modern Physics Letters A 15, no. 06 (February 28, 2000): 445–54. http://dx.doi.org/10.1142/s0217732300000438.

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The dynamical fermion mass generation in the four-dimensional brane is discussed in a model with five-dimensional Kaluza–Klein fermions in interaction with four-dimensional fermions. It is found that the dynamical fermion masses are generated beyond the critical radius of the compactified extra dimensional space and may be made small compared with the masses of the Kaluza–Klein modes.

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21

Lahiri, Amitabha. "Geometry creates inertia." International Journal of Modern Physics D 29, no. 14 (September 5, 2020): 2043020. http://dx.doi.org/10.1142/s0218271820430208.

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The dynamics of fermions in curved spacetime is governed by a spin connection, a part of which is contorsion, an auxiliary field independent of the metric, without dynamics but fully expressible in terms of the axial current density of fermions. Its effect is the appearance of a quartic interaction involving all fermions. Contorsion can couple to left- and right-handed fermions with different strengths, leading to an effective mass for fermions propagating on a background containing fermionic matter.

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22

Hartke, Thomas, Botond Oreg, Carter Turnbaugh, Ningyuan Jia, and Martin Zwierlein. "Direct observation of nonlocal fermion pairing in an attractive Fermi-Hubbard gas." Science 381, no. 6653 (July 7, 2023): 82–86. http://dx.doi.org/10.1126/science.ade4245.

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The Hubbard model of attractively interacting fermions provides a paradigmatic setting for fermion pairing. It features a crossover between Bose-Einstein condensation of tightly bound pairs and Bardeen-Cooper-Schrieffer superfluidity of long-range Cooper pairs, and a “pseudo-gap” region where pairs form above the superfluid critical temperature. We directly observe the nonlocal nature of fermion pairing in a Hubbard lattice gas, using spin- and density-resolved imaging of ∼ 1000 fermionic potassium-40 atoms under a bilayer microscope. Complete fermion pairing is revealed by the vanishing of global spin fluctuations with increasing attraction. In the strongly correlated regime, the fermion pair size is found to be on the order of the average interparticle spacing. Our study informs theories of pseudo-gap behavior in strongly correlated fermion systems.

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23

McKellar, Bruce H. J., T. J. Goldman, and G. J. Stephenson. "Effective masses in a dense fermion background — Applied to neutrinos, dark matter and dark energy." International Journal of Modern Physics A 29, no. 21 (August 20, 2014): 1444010. http://dx.doi.org/10.1142/s0217751x14440102.

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If fermions interact with a scalar field, and there are many fermions present the scalar field may develop an expectation value and generate an effective mass for the fermions. This can lead to the formation of fermion clusters, which could be relevant for neutrino astrophysics and for dark matter astrophysics. Because this system may exhibit negative pressure, it also leads to a model of dark energy.

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24

Goswami, Abhishek. "Mass gap in U(1) Higgs–Yukawa model on a unit lattice." Journal of Mathematical Physics 64, no. 3 (March 1, 2023): 032302. http://dx.doi.org/10.1063/5.0107644.

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A non-perturbative proof of the mass generation of fermions via the Higgs mechanism is given. This is done by showing an exponential decay of the two point fermionic correlation function in a weakly coupled U(1) Higgs–Yukawa theory on a unit lattice in d = 4. This decay implies that the Higgs boson, the photon, and the fermion all have a non-zero physical mass, and the theory is said to have a mass gap.

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25

NARAYANA SWAMY, P. "q-DEFORMED FERMIONS: ALGEBRA, FOCK SPACE AND THERMODYNAMICS." International Journal of Modern Physics B 20, no. 18 (July 20, 2006): 2537–50. http://dx.doi.org/10.1142/s0217979206034832.

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We investigate an algebra describing q-deformed Fermion oscillators. We establish the nature of the basic numbers which follow from this algebra, study the Fock space of these generalized Fermions and determine the Jackson Derivative appropriate for these Fermions. The statistical thermodynamics of these Fermions is examined and it is demonstrated that a consistent formulation preserving its full Legendre structure is accomplished by the use of Jackson Derivatives in place of the ordinary thermodynamic derivatives. We determine the important thermodynamic functions and illustrate the thermodynamic properties of q-Fermions.

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Nisperuza, J., J. P. Rubio, and R. Avella. "Density probabilities of a Bose-Fermi mixture in 1D double well potential." Journal of Physics Communications 6, no. 2 (February 1, 2022): 025004. http://dx.doi.org/10.1088/2399-6528/ac4faf.

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Abstract We use the two mode approximation for a interacting one-dimensional spinless soft core bosons and one half spin fermions in a double-well potential with a large central barrier. We include all the on-site boson-boson, fermion-fermion and boson-fermion repulsive contact potential represented by delta-function and considered bosonic and fermionic isotopes of ytterbium(Yb) 170 Yb and 171 Yb respectively. By means of this approximation, we find that in the regime λ BF > λ BB give rise to a immiscible phase and in the regime λ BB ≥ λ BF give rise to a miscible phase, that is characterized by a temporal overlap of the bosonic and fermionic probability densities. We also report that due to the Bose-Fermi interaction, the system presents an apparent destruction of the collapse-revival oscillation of boson density probability at least in the ranges investigated.

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SCAROLA, V. W., S. Y. LEE, and J. K. JAIN. "POSSIBLE NEW PHASES OF COMPOSITE FERMIONS." International Journal of Modern Physics B 16, no. 20n22 (August 30, 2002): 2946–51. http://dx.doi.org/10.1142/s0217979202013262.

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When the effective filling factor of composite fermions is an integer, the residual interaction between them can often be neglected because the ground state of the non-interacting model is unique and incompressible. However, at non-integer composite fermion (CF) filling factors the ground state of composite fermions is enormously degenerate if the interaction between them is neglected, and consideration of the inter composite fermion interaction is necessary for determining the true ground state. In this article, we summarize certain results regarding what new states the inter composite fermion interaction can possibly produce. More details can be found in Refs. [11] and [12].

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NARAYANA SWAMY, P. "TRANSFORMATIONS OF q-BOSON AND q-FERMION ALGEBRAS." Modern Physics Letters B 15, no. 21 (September 10, 2001): 915–20. http://dx.doi.org/10.1142/s0217984901002671.

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We investigate the algebras satisfied by q-deformed boson and fermion oscillators, in particular the transformations of the algebra from one form to another. Based on a specific algebra proposed in recent literature, we show that the algebra of deformed fermions can be transformed to that of undeformed standard fermions. Furthermore, we also show that the algebra of q-deformed fermions can be transformed to that of undeformed standard bosons.

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29

Stumpf, H., Th Borne, and H. J. Kaus. "Is the Gravitational Force Elementary?" Zeitschrift für Naturforschung A 48, no. 12 (December 1, 1993): 1151–65. http://dx.doi.org/10.1515/zna-1993-1202.

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Abstract The gravitational force is assumed to be mediated by spin 2 gravitons which are composed of four spin 1/2 (sub-) fermions. The dynamics is governed by a nonlinear spinorfield equation with nonperturbative Pauli-Villars regularization and canonical quantization. On the quantum level the fermion dynamics is expressed by a functional equation for algebraic state functionals, and the "graviton" (functional) states are defined to be solutions of the diagonal part of this equation. The effective interaction between such graviton states and fermions is studied by means of a weak mapping between the original functional equation and an effective functional equation for gravitons and fermions. In the low energy limit this mapping produces for the effective fermion dynamics (apart from selfinteractions) a Dirac equation in anholonomic coordinates coupled to the anholonomic connections of a gravitational field, i.e. the usual phenomenological expression for a gravitational force acting on spin 1 /2 fermions.

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30

Bennett, Ed, Jack Holligan, Deog Ki Hong, Ho Hsiao, Jong-Wan Lee, C. J. David Lin, Biagio Lucini, Michele Mesiti, Maurizio Piai, and Davide Vadacchino. "Sp(2N) Lattice Gauge Theories and Extensions of the Standard Model of Particle Physics." Universe 9, no. 5 (May 17, 2023): 236. http://dx.doi.org/10.3390/universe9050236.

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We review the current status of the long-term programme of numerical investigation of Sp(2N) gauge theories with and without fermionic matter content. We start by introducing the phenomenological as well as theoretical motivations for this research programme, which are related to composite Higgs models, models of partial top compositeness, dark matter models, and in general to the physics of strongly coupled theories and their approach to the large-N limit. We summarise the results of lattice studies conducted so far in the Sp(2N) Yang–Mills theories, measuring the string tension, the mass spectrum of glueballs and the topological susceptibility, and discuss their large-N extrapolation. We then focus our discussion on Sp(4), and summarise the numerical measurements of mass and decay constant of mesons in the theories with fermion matter in either the fundamental or the antisymmetric representation, first in the quenched approximation, and then with dynamical fermions. We finally discuss the case of dynamical fermions in mixed representations, and exotic composite fermion states such as the chimera baryons. We conclude by sketching the future stages of the programme. We also describe our approach to open access.

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31

Capitani, Stefano, Giulia Maria de Divitiis, Petros Dimopoulos, Roberto Frezzotti, Marco Garofalo, Bastian Knippschild, Bartosz Kostrzewa, Ferenc Pittler, Giancarlo Rossi, and Carsten Urbach. "Testing a non-perturbative mechanism for elementary fermion mass generation: lattice setup." EPJ Web of Conferences 175 (2018): 08009. http://dx.doi.org/10.1051/epjconf/201817508009.

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In this contribution we lay down a lattice setup that allows for the nonperturbative study of a field theoretical model where a SU(2) fermion doublet, subjected to non-Abelian gauge interactions, is also coupled to a complex scalar field doublet via a Yukawa and an “irrelevant” Wilson-like term. Using naive fermions in quenched approximation and based on the renormalizedWard identities induced by purely fermionic chiral transformations, lattice observables are discussed that enable: a) in theWigner phase, the determinations of the critical Yukawa coupling value where the purely fermionic chiral transformation become a symmetry up to lattice artifacts; b) in the Nambu-Goldstone phase of the resulting critical theory, a stringent test of the actual generation of a fermion mass term of non-perturbative origin. A soft twisted fermion mass term is introduced to circumvent the problem of exceptional configurations, and observables are then calculated in the limit of vanishing twisted mass.

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32

EBERT, D., V. CH ZHUKOVSKY, and A. V. TYUKOV. "DYNAMICAL FERMION MASSES UNDER THE INFLUENCE OF KALUZA–KLEIN FERMIONS AND A BULK ABELIAN GAUGE FIELD." Modern Physics Letters A 25, no. 35 (November 20, 2010): 2933–45. http://dx.doi.org/10.1142/s0217732310034249.

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The dynamical fermion mass generation on the 3-brane in the 5D spacetime is discussed in a model with bulk fermions in interaction with fermions on the branes assuming the presence of a constant Abelian gauge field A5 in the bulk. We calculate the effective potential as a function of the fermion masses and the gauge field A5. The masses can be found from the stationarity condition for the effective potential (the gap equation). We formulate the equation for the mass spectrum of the 4D-fermions. The phases with finite and vanishing fermion masses are studied and the dependence of the masses on the radius of the fifth dimension is analyzed. The influence of the A5-gauge field on the symmetry breaking is considered both when this field is a background parameter and a dynamical variable. The critical values of the A5 field, the coupling constant and the radius are examined.

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33

KHVIENGIA, Z., and V. F. TOKAREV. "CIRCUMSTANCES OF FERMION FRACTIONIZATION IN HIGH DENSITY FERMI GAS." Modern Physics Letters A 07, no. 23 (July 30, 1992): 2143–51. http://dx.doi.org/10.1142/s0217732392001889.

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We consider a (3 + 1)-dimensional SU(2)-gauge theory which is known to possess the fractional fermions. These are the monopoles. We compute the fermion number of a monopole in the dense Fermi gas and find the conditions under which fermions decay into the monopoles.

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34

Butt, Nouman, Simon Catterall, and Goksu Can Toga. "Symmetric Mass Generation in Lattice Gauge Theory." Symmetry 13, no. 12 (November 30, 2021): 2276. http://dx.doi.org/10.3390/sym13122276.

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We construct a four-dimensional lattice gauge theory in which fermions acquire mass without breaking symmetries as a result of gauge interactions. Our model consists of reduced staggered fermions transforming in the bifundamental representation of an SU(2)×SU(2) gauge symmetry. This fermion representation ensures that single-site bilinear mass terms vanish identically. A symmetric four-fermion operator is however allowed, and we give numerical results that show that a condensate of this operator develops in the vacuum.

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35

Jakovác, Antal, and András Patkós. "Bound states in functional renormalization group." International Journal of Modern Physics A 34, no. 27 (September 27, 2019): 1950154. http://dx.doi.org/10.1142/s0217751x19501549.

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Equivalence criteria are established for an effective Yukawa-type theory of composite fields representing two-particle fermion bound states with the original “microscopic” theory of interacting fermions based on the spectral decomposition of the 2-to-2 fermion scattering amplitude. Functional renormalization group equations of the effective theory are derived exploiting relations expressing the equivalence. The effect of truncating the spectral decomposition is investigated quantitatively on the example of the nonrelativistic bound states of two oppositely charged fermions.

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36

KOLEY, RATNA, and SAYAN KAR. "BULK PHANTOM FIELDS, INCREASING WARP FACTORS AND FERMION LOCALIZATION." Modern Physics Letters A 20, no. 05 (February 20, 2005): 363–71. http://dx.doi.org/10.1142/s0217732305015586.

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A bulk phantom scalar field (with negative kinetic energy) in a sine–Gordon type potential is used to generate an exact thick brane solution with an increasing warp factor. It is shown that the growing nature of the warp factor allows the localization of massive as well as massless spin-1/2 fermions on the brane even without any additional non-gravitational interactions. The exact solutions for the localized massive fermionic modes are presented and discussed. The inclusion of a fermion–scalar Yukawa coupling appears to change the mass spectrum and wave functions of the localized fermion though it does not play the crucial role it did in the case of a decreasing warp factor.

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37

Huang, Bo-Jie, and Chyh-Hong Chern. "Nonrelativistic fermionic energy gap in the nonabelian gauge systems." International Journal of Modern Physics B 31, no. 15 (March 27, 2017): 1750126. http://dx.doi.org/10.1142/s0217979217501260.

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We demonstrate that the nonrelativistic fermions open the energy gap when the SU([Formula: see text]) gauge bosons, mediating the interaction between fermions, acquire the mass. Surprisingly, even though there is the SU([Formula: see text]) gauge symmetry, there is always one fermionic energy gap which is not degenerate to the rest of the [Formula: see text] fermions for [Formula: see text] in the fundamental representation.

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38

RAEDT, H. DE, and W. VON DER LINDEN. "MONTE CARLO DIAGONALIZATION OF VERY LARGE MATRICES: APPLICATION TO FERMION SYSTEMS." International Journal of Modern Physics C 03, no. 01 (February 1992): 97–104. http://dx.doi.org/10.1142/s0129183192000087.

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All known Quantum-Monte-Carlo algorithms for fermions suffer from the so-called “minus-sign-problem” which is detrimental to the application of these simulation methods to fermion systems at very low temperatures and/or of very many lattice sites. We identify the origin of this fundamental problem, demonstrate that it is a very general feature, not necessarily related to the presence of fermionic degrees of freedom. We describe an novel algorithm which does not suffer from the minus-sign problem. Illustrative results for the two-dimensional Hubbard model are presented

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39

Dajka, Jerzy. "Currents in a Quantum Nanoring Controlled by Non-Classical Electromagnetic Field." Entropy 23, no. 6 (May 23, 2021): 652. http://dx.doi.org/10.3390/e23060652.

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Quantum ring accommodating interacting spin-less fermions threaded by magnetic flux with a non-classical component added to a static, inducing persistent current, is considered. It is investigated how current flowing in the ring becomes affected by a state of non-classical flux and how Coulomb interaction between fermions influences entanglement of quantum ring and the driving field. In particular it is shown that in an absence of decoherence and under certain conditions fermion–fermion interaction is necessary for a ring–field entanglement to occur.

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40

ROMBOUTS, S., D. VAN NECK, K. PEIRS, and L. POLLET. "MAXIMUM OCCUPATION NUMBER FOR COMPOSITE BOSON STATES." Modern Physics Letters A 17, no. 29 (September 21, 2002): 1899–907. http://dx.doi.org/10.1142/s0217732302008411.

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One of the major differences between fermions and bosons is that fermionic states have a maximum occupation number of one, whereas the occupation number for bosonic states is in principle unlimited. For bosons that are made up of fermions, one could ask the question to what extent the Pauli principle for the constituent fermions would limit the boson occupation number. Intuitively one can expect the maximum occupation number to be proportional to the available volume for the bosons divided by the volume occupied by the fermions inside one boson, though a rigorous derivation of this result has not been given before. In this letter we show how the maximum occupation number can be calculated from the ground-state energy of a fermionic generalized pairing problem. A very accurate analytical estimate of this eigenvalue is derived. From that a general expression is obtained for the maximum occupation number of a composite boson state, based solely on the intrinsic fermionic structure of the bosons. The consequences for Bose–Einstein condensates of excitons in semiconductors and ultra cold trapped atoms are discussed.

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41

GAMBOA SARAVÍ, R. E., G. L. ROSSINI, and F. A. SCHAPOSNIK. "THE ζ FUNCTION ANSWER TO PARITY VIOLATION IN THREE-DIMENSIONAL GAUGE THEORIES." International Journal of Modern Physics A 11, no. 15 (June 20, 1996): 2643–60. http://dx.doi.org/10.1142/s0217751x96001279.

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We study parity violation in (2+1)-dimensional gauge theories coupled to massive fermions. Using the ζ function regularization approach we evaluate the ground state fermion current in an arbitrary gauge field background, showing that it gets two different contributions which violate parity invariance and induce a Chern–Simons term in the gauge field effective action. One is related to the well-known classical parity breaking produced by a fermion mass term in three dimensions; the other, already present for massless fermions, is related to peculiarities of gauge-invariant regularization in odd-dimensional spaces.

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Lian, Biao, Xiao-Qi Sun, Abolhassan Vaezi, Xiao-Liang Qi, and Shou-Cheng Zhang. "Topological quantum computation based on chiral Majorana fermions." Proceedings of the National Academy of Sciences 115, no. 43 (October 8, 2018): 10938–42. http://dx.doi.org/10.1073/pnas.1810003115.

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The chiral Majorana fermion is a massless self-conjugate fermion which can arise as the edge state of certain 2D topological matters. It has been theoretically predicted and experimentally observed in a hybrid device of a quantum anomalous Hall insulator and a conventional superconductor. Its closely related cousin, the Majorana zero mode in the bulk of the corresponding topological matter, is known to be applicable in topological quantum computations. Here we show that the propagation of chiral Majorana fermions leads to the same unitary transformation as that in the braiding of Majorana zero modes and propose a platform to perform quantum computation with chiral Majorana fermions. A Corbino ring junction of the hybrid device can use quantum coherent chiral Majorana fermions to implement the Hadamard gate and the phase gate, and the junction conductance yields a natural readout for the qubit state.

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43

Jain, J. K., and R. K. Kamilla. "Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level." International Journal of Modern Physics B 11, no. 22 (September 10, 1997): 2621–60. http://dx.doi.org/10.1142/s0217979297001301.

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Single particle basis functions for composite fermions are obtained from which many-composite fermion states confined to the lowest electronic Landau level can be constructed in the standard manner, i.e. by building Slater determinants. This representation enables a Monte Carlo study of systems containing a large number of composite fermions, yielding new quantitative and qualitative information. The ground state energy and the gaps to charged and neutral excitations are computed for a number of fractional quantum Hall effect (FQHE) states, earlier off-limits to a quantitative investigation. The ground state energies are estimated to be accurate to ~0.1% and the gaps at the level of a few percent. It is also shown that at Landau level fillings smaller than or equal to 1/9 the FQHE is unstable to a spontaneous creation of excitons of composite fermions. In addition, this approach provides new conceptual insight into the structure of the composite fermion wave functions, resolving in the affirmative the question of whether it is possible to motivate the composite fermion theory entirely within the lowest Landau level, without appealing to higher Landau levels.

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44

Adler, Stephen L. "SU(8) family unification with boson–fermion balance." International Journal of Modern Physics A 29, no. 22 (August 29, 2014): 1450130. http://dx.doi.org/10.1142/s0217751x14501309.

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We formulate an SU(8) family unification model motivated by requiring that the theory should incorporate the graviton, gravitinos, and the fermions and gauge fields of the standard model, with boson–fermion balance. Gauge field SU(8) anomalies cancel between the gravitinos and spin ½ fermions. The 56 of scalars breaks SU(8) to SU(3) family × SU(5) × U(1)/Z5, with the fermion representation content needed for "flipped" SU(5) with three families, and with residual scalars in the 10 and [Formula: see text] representations that break flipped SU(5) to the standard model. Dynamical symmetry breaking can account for the generation of 5 representation scalars needed to break the electroweak group. Yukawa couplings of the 56 scalars to the fermions are forbidden by chiral and gauge symmetries, so in the first stage of SU(8) breaking fermions remain massless. In the limit of vanishing gauge coupling, there are N = 1 and N = 8 supersymmetries relating the scalars to the fermions, which restrict the form of scalar self-couplings and should improve the convergence of perturbation theory, if not making the theory finite and "calculable." In an Appendix we give an analysis of symmetry breaking by a Higgs component, such as the (1, 1)(-15) of the SU(8) 56 under SU(8) ⊃ SU(3) × SU(5) × U(1), which has nonzero U(1) generator.

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45

Luo, Yu-Chen, and Xiao-Peng Li. "Quantum simulation of interacting fermions." Acta Physica Sinica 71, no. 22 (2022): 226701. http://dx.doi.org/10.7498/aps.71.20221756.

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Fermions are basic building blocks in the standard model. Interactions among these elementary particles determine how they assemble and consequently form various states of matter in our nature. Simulating fermionic degrees of freedom is also a central problem in condensed matter physics and quantum chemistry, which is crucial to understanding high-temperature superconductivity, quantum magnetism and molecular structure and functionality. However, simulating interacting fermions by classical computing generically face the minus sign problem, encountering the exponential computation complexity. Ultracold atoms provide an ideal experimental platform for quantum simulation of interacting fermions. This highly-controllable system enables the realizing of nontrivial fermionic models, by which the physical properties of the models can be obtained by measurements in experiment. This deepens our understanding of related physical mechanisms and help determine the key parameters. In recent years, there have been versatile experimental studies on quantum ground state physics, finite temperature thermal equilibrium, and quantum many-body dynamics, in fermionic quantum simulation systems. Quantum simulation offers an access to the physical problems that are intractable on the classical computer, including studying macroscopic quantum phenomena and microscopic physical mechanisms, which demonstrates the quantum advantages of controllable quantum systems. This paper briefly introduces the model of interacting fermions describing the quantum states of matter in such a system. Then we discuss various states of matter, which can arise in interacting fermionic quantum systems, including Cooper pair superfluids and density-wave orders. These exotic quantum states play important roles in describing high-temperature superconductivity and quantum magnetism, but their simulations on the classical computers have exponentially computational cost. Related researches on quantum simulation of interacting fermions in determining the phase diagrams and equation of states reflect the quantum advantage of such systems.

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46

KIKUKAWA, YOSHIO. "CHIRAL SYMMETRY AND OPERATOR MIXING IN LATTICE SU(N) THIRRING MODEL WITH SHIFT SYMMETRY." Modern Physics Letters A 07, no. 10 (March 28, 1992): 871–80. http://dx.doi.org/10.1142/s0217732392003517.

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We formulate lattice SU (N) Thirring model in which two Wilson fermions describe the respective left- and right-handed components of the Dirac fermion in the continuum model. Only chirally projected half components of the Wilson fermions have four-fermion interaction. As to their non-interacting components, there exist shift symmetries discussed by Golterman and Petcher. Axial U (1) Ward-Takahashi identity is examined by weak coupling expansion. It is shown in all orders of the weak coupling expansion that the chiral limit is achieved by simply setting fermion bare mass equal to zero, and that a lattice operator has no mixing due to the Wilson masses with the operators of wrong chiral representation and of lower dimensionality.

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47

Cotăescu, Ion I. "Propagators of the Dirac fermions on spatially flat FLRW space–times." International Journal of Modern Physics A 34, no. 05 (February 20, 2019): 1950024. http://dx.doi.org/10.1142/s0217751x19500246.

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The general formalism of the free Dirac fermions on spatially flat (1[Formula: see text]+[Formula: see text]3)-dimensional Friedmann-Lemaître–Robertson–Walker (FLRW) space–times is developed in momentum representation. The mode expansions in terms of the fundamental spinors satisfying the charge conjugation and normalization conditions are used for deriving the structure of the anticommutator matrix-functions and, implicitly, of the retarded, advanced, and Feynman fermion propagators. The principal result is that the new type of integral representation we proposed recently in the de Sitter case can be applied to the Dirac fermions in any spatially flat FLRW geometry. Moreover, the Dirac equation of the left-handed massless fermions can be analytically solved finding a general spinor solution and deriving the integral representations of the neutrino propagators. It is shown that in the Minkowski flat space–time our new integral representation is up to a change of variable just like the usual Fourier representation of the fermion propagators. The form of the Feynman propagator of the massive fermions on a spatially flat FLRW space–time with a scale factor of Milne-type is also outlined.

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48

Shifman, M., and A. Yung. "Index theorem for non-supersymmetric fermions coupled to a non-Abelian string and electric charge quantization." Modern Physics Letters A 33, no. 09 (March 21, 2018): 1850053. http://dx.doi.org/10.1142/s0217732318500530.

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Non-Abelian strings are considered in non-supersymmetric theories with fermions in various appropriate representations of the gauge group U[Formula: see text]. We derive the electric charge quantization conditions and the index theorems counting fermion zero modes in the string background both for the left-handed and right-handed fermions. In both cases we observe a non-trivial [Formula: see text] dependence.

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49

KISELEV, M. N. "SEMI-FERMIONIC REPRESENTATION FOR SPIN SYSTEMS UNDER EQUILIBRIUM AND NON-EQUILIBRIUM CONDITIONS." International Journal of Modern Physics B 20, no. 04 (February 10, 2006): 381–421. http://dx.doi.org/10.1142/s0217979206033310.

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We present a general derivation of semi-fermionic representation for spin operators in terms of a bilinear combination of fermions in real and imaginary time formalisms. The constraint on fermionic occupation numbers is fulfilled by means of imaginary Lagrange multipliers resulting in special shape of quasiparticle distribution functions. We show how Schwinger–Keldysh technique for spin operators is constructed with the help of semi-fermions. We demonstrate how the idea of semi-fermionic representation might be extended to the groups possessing dynamic symmetries. We illustrate the application of semi-fermionic representations for various problems of strongly correlated and mesoscopic physics.

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50

ZÁVADA, PETR. "SPIN STRUCTURE FUNCTIONS AND INTRINSIC MOTION OF THE CONSTITUENTS." International Journal of Modern Physics A 18, no. 08 (March 30, 2003): 1397–402. http://dx.doi.org/10.1142/s0217751x03014769.

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The spin structure functions of the system of quasifree fermions on mass shell are studied in a consistently covariant approach. Comparison with the basic formulas following from the quark-parton model reveals the importance of the fermion motion inside the target for the correct evaluation of the spin structure functions. In particular it is shown, that regarding the moment Γ1, both the approaches are equivalent for the static fermions, but differ by the factor 1/3 in the limit of massles fermions (m ≪ p0, in target rest frame). Some other sum rules are discussed as well.

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