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Journal articles on the topic 'Fermion familie'

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Author: Grafiati

Published: 11 March 2023

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1

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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2

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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3

GUENDELMAN, E. I., and A. B. KAGANOVICH. "GEOMETRICAL ORIGIN OF FERMION FAMILIES IN SU(2) × U(1) GAUGE THEORY." Modern Physics Letters A 17, no. 19 (June 21, 2002): 1227–37. http://dx.doi.org/10.1142/s0217732302007351.

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A spontaneously broken SU (2) × U (1) gauge theory with just one "primordial" generation of fermions is formulated in the context of generally covariant theory which contains two measures of integration in the action: the standard [Formula: see text] and a new Φd4x, where Φ is a density built out of degrees of freedom independent of the metric. Such type of models are known to produce a satisfactory answer to the cosmological constant problem. Global scale invariance is implemented. After SSB of scale invariance and gauge symmetry it is found that with the conditions appropriate to laboratory particle physics experiments, to each primordial fermion field corresponds three physical fermionic states. Two of them correspond to particles with different constant masses and they are identified with the first two generations of the electroweak theory. The third fermionic states at the classical level get nonpolynomial interactions which indicate the existence of fermionic condensate and fermionic mass generation.

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4

Bernardini, Alex E., and Roldão da Rocha. "Matter Localization on Brane-Worlds Generated by Deformed Defects." Advances in High Energy Physics 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/3650632.

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Localization and mass spectrum of bosonic and fermionic matter fields of some novel families of asymmetric thick brane configurations generated by deformed defects are investigated. The localization profiles of spin 0, spin 1/2, and spin 1 bulk fields are identified for novel matter field potentials supported by thick branes with internal structures. The condition for localization is constrained by the brane thickness of each model such that thickest branes strongly induce matter localization. The bulk mass terms for both fermion and boson fields are included in the global action as to produce some imprints on mass-independent potentials of the Kaluza-Klein modes associated with the corresponding Schrödinger equations. In particular, for spin 1/2 fermions, a complete analytical profile of localization is obtained for the four classes of superpotentials here discussed. Regarding the localization of fermion fields, our overall conclusion indicates that thick branes produce aleft-right asymmetric chirallocalization of spin 1/2 particles.

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5

GUENDELMAN, E. I., and A. B. KAGANOVICH. "FERMION FAMILIES AND LONG-RANGE FORCE PROBLEMS: INTERRELATION AND RESOLUTION." International Journal of Modern Physics D 11, no. 10 (December 2002): 1591–95. http://dx.doi.org/10.1142/s0218271802002943.

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We study a generally covariant model with SSB of scale invariance where two measures of integration in the action enter: the standard [Formula: see text] and a new Φd4x, where Φ is a density built out of degrees of freedom independent of the metric. Under normal laboratory conditions where the fermionic matter dominates, it is found that starting from a single fermionic field we obtain exactly three different types of spin 1/2 particles which can be identified with known fermion families. It is automatically achieved that for two of them, fermion masses are constants, the energy-momentum tensor is canonical and the "fifth force" is absent. For the third family, a self-interaction appears as a result of SSB of scale invariance.

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6

DOFF, A., and F. PISANO. "CHARGE QUANTIZATION IN THE LARGEST LEPTOQUARK–BILEPTON CHIRAL ELECTROWEAK SCHEME." Modern Physics Letters A 14, no. 17 (June 7, 1999): 1133–42. http://dx.doi.org/10.1142/s0217732399001218.

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The uniqueness of the hypercharge assignments in the three-fermion families leptoquark–bilepton SU (3)C× SU (4)L× U (1)N model is established. Although the gauge group contains an explicit U(1) factor, freedom from triangle anomalies combined with the requirement of nonvanishing charged fermion masses uniquely fix the electric charges of all fermions independently of the neutrinos being massless or not. The electric-charge quantization, flavor family replication, and the existence of three colors are interwoven.

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7

Delbourgo, R., PD Jarvis, and RC Warner. "Models for Fermion Generations based on Five Fermionic Coordinates." Australian Journal of Physics 44, no. 3 (1991): 135. http://dx.doi.org/10.1071/ph910135.

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We show that a limited range of options for fermion families may be neatly encompassed in a spacetime augmented by five Grassmann internal coordinates if we require that the superfields are self-dual in an 5U(5) sense. Amongst the possibilities is a family of just three standard model generations. We consider the nature of Higgs fields in this formalism and the form of possible gauge symmetries.

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8

GUENDELMAN, E. I., and A. B. KAGANOVICH. "QUINTESSENTIAL POTENTIAL, FERMION FAMILIES AND SPONTANEOUS BREAKING OF SCALE SYMMETRY." International Journal of Modern Physics A 17, no. 29 (November 20, 2002): 4419–24. http://dx.doi.org/10.1142/s0217751x02013496.

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We study a generally covariant model with SSB of scale invariance where two measures of integration in the action enter: the standard [Formula: see text] and a new Φd4x, where Φ is a density built out of degrees of freedom independent of the metric. The theory demonstrates a new mechanism for generation of the exponential potential: in the conformal Einstein frame, after SSB of scale invariance, the theory develops the exponential potential and, in general, non-linear kinetic term is generated as well. The scale symmetry does not allow the appearance of terms breaking the exponential shape of the potential that solves the problem of the flatness of the scalar field potential in the context of quintessential scenarios. Under normal laboratory conditions where the fermionic matter dominates, it is found that starting from a single fermionic field we obtain exactly three different types of spin 1/2 particles which can be identified with known fermion families. It is automatically achieved that for two of them, fermion masses are constants, the energy-momentum tensor is canonical and the "fifth force" is absent. For the third family, a self-interaction appears as a result of SSB of scale invariance.

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9

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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10

Abbas, Gauhar. "Solving the fermionic mass hierarchy of the Standard Model." International Journal of Modern Physics A 34, no. 20 (July 20, 2019): 1950104. http://dx.doi.org/10.1142/s0217751x19501045.

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We show that a simultaneous explanation for fermionic mass hierarchy among and within the fermionic families, quark-mixing, can be obtained in an extension of the Standard Model, with real singlet scalar fields, which are UV completed by vector-like fermions and a strongly interacting sector.

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11

Semenoff, Gordon W., and Richard J. Szabo. "Fermionic Matrix Models." International Journal of Modern Physics A 12, no. 12 (May 10, 1997): 2135–291. http://dx.doi.org/10.1142/s0217751x97001328.

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We review a class of matrix models whose degrees of freedom are matrices with anti-commuting elements. We discuss the properties of the adjoint fermion one-matrix, two-matrix and gauge-invariant D-dimensional matrix models at large N and compare them with their bosonic counterparts, which are the more familiar Hermitian matrix models. We derive and solve the complete sets of loop equations for the correlators of these models and use these equations to examine critical behavior. The topological large N expansions are also constructed and their relation to other aspects of modern string theory, such as integrable hierarchies, is discussed. We use these connections to discuss the applications of these matrix models to string theory and induced gauge theories. We argue that as such the fermionic matrix models may provide a novel generalization of the discretized random surface representation of quantum gravity in which the genus sum alternates and the sums over genera for correlators have better convergence properties than their Hermitian counterparts. We discuss the use of adjoint fermions instead of adjoint scalars to study induced gauge theories. We also discuss two classes of dimensionally reduced models, a fermionic vector model and a supersymmetric matrix model, and discuss their applications to the branched polymer phase of string theories in target space dimensions D > 1 and also to the meander problem.

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12

OKUN, L. B. "Fermion Families: Conference Summary." Annals of the New York Academy of Sciences 578, no. 1 The Fourth Fa (December 1989): 306–8. http://dx.doi.org/10.1111/j.1749-6632.1989.tb50622.x.

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13

PALCU, ADRIAN. "NEUTRAL CURRENTS IN ASU(4)L⊗U(1)YGAUGE MODEL WITH EXOTIC ELECTRIC CHARGES." Modern Physics Letters A 24, no. 27 (September 7, 2009): 2175–80. http://dx.doi.org/10.1142/s0217732309031508.

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The weak currents with respect to the diagonal neutral bosons Z, Z′ and Z′′of a specific SU (4)L⊗ U (1)Ygauge model are computed in detail for all the fermion families involved therein. Our algebraical approach, which is based on the general method of solving gauge models with high symmetries proposed several years ago by Cotăescu, recovers in a nontrivial way all the Standard Model values for current couplings of the traditional leptons and quarks, and predicts plausible values for those of the exotic fermions in the model.

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14

GRETHER, M., M. de LLANO, S. RAMÍREZ, and O. ROJO. "INTRIGUING ROLE OF HOLE-COOPER-PAIRS IN SUPERCONDUCTORS AND SUPERFLUIDS." International Journal of Modern Physics B 22, no. 25n26 (October 20, 2008): 4367–78. http://dx.doi.org/10.1142/s0217979208050127.

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The role in superconductors of hole-Cooper-pairs (CPs) are examined and contrasted with the more familiar electron-CPs, with special emphasis on their “background” effect in enhancing superconducting transition temperatures Tc — even when electron-CPs drive the transition. Both kinds of CPs are, of course, present at all temperatures. An analogy is drawn between the hole CPs in any many-fermion system with the antibosons in a relativistic ideal Bose gas that appear in substantial numbers only at higher and higher temperatures. Their indispensable role in yielding a lower Helmholtz free energy equilibrium state is established. For superconductors, the problem is viewed in terms of a generalized Bose-Einstein condensation (GBEC) theory that is an extension of the Friedberg-T.D. Lee 1989 boson-fermion BEC theory of high-Tc superconductors in that the GBEC theory includes hole CPs as well as electron-CPs — thereby containing as well as further extending BCS theory to higher temperatures with the same weak-coupling electron-phonon interaction parameters. We show that the Helmholtz free energy of both 2e- and 2h-CP pure condensates has a positive second derivative, and are thus stable equilibrium states. Finally, it is conjectured that the role of hole pairs in ultra-cold fermionic atom gases will likely be negligible because the very low densities involved imply a “shallow” Fermi sea.

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15

Daas, Jesse, Wouter Oosters, Frank Saueressig, and Jian Wang. "Asymptotically Safe Gravity-Fermion Systems on Curved Backgrounds." Universe 7, no. 8 (August 19, 2021): 306. http://dx.doi.org/10.3390/universe7080306.

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We set up a consistent background field formalism for studying the renormalization group (RG) flow of gravity coupled to Nf Dirac fermions on maximally symmetric backgrounds. Based on Wetterich’s equation, we perform a detailed study of the resulting fixed point structure in a projection including the Einstein–Hilbert action, the fermion anomalous dimension, and a specific coupling of the fermion bilinears to the spacetime curvature. The latter constitutes a mass-type term that breaks chiral symmetry explicitly. Our analysis identified two infinite families of interacting RG fixed points, which are viable candidates to provide a high-energy completion through the asymptotic safety mechanism. The fixed points exist for all values of Nf outside of a small window situated at low values Nf and become weakly coupled in the large Nf-limit. Symmetry-wise, they correspond to “quasi-chiral” and “non-chiral” fixed points. The former come with enhanced predictive power, fixing one of the couplings via the asymptotic safety condition. Moreover, the interplay of the fixed points allows for cross-overs from the non-chiral to the chiral fixed point, giving a dynamical mechanism for restoring the symmetry approximately at intermediate scales. Our discussion of chiral symmetry breaking effects provides strong indications that the topology of spacetime plays a crucial role when analyzing whether quantum gravity admits light chiral fermions.

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16

Roque, Armando A., and L. Arturo Ureña-López. "Horndeski fermion–boson stars." Classical and Quantum Gravity 39, no. 4 (January 21, 2022): 044001. http://dx.doi.org/10.1088/1361-6382/ac4614.

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Abstract We establish the existence of static and spherically symmetric fermion–boson stars, in a low energy effective model of (beyond) Horndeski theories. These stars are in equilibrium, and are composed by a mixing of scalar and fermionic matters that only interact gravitationally one with each other. Properties such as mass, radius, and compactness are studied, highlighting the existence of two families of configurations defined by the parameter c 4. These families have distinctive properties, although in certain limits both are reduced to their counterparts in general relativity (GR). Finally, by assuming the same conditions used in GR, we find the maximum compactness of these hybrid stars and determine that it remains below the so-called Buchdahl’s limit.

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17

Montvay, I. "Three mirror pairs of fermion families." Physics Letters B 205, no. 2-3 (April 1988): 315–20. http://dx.doi.org/10.1016/0370-2693(88)91671-1.

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18

MASLIKOV, A. A., S. M. SERGEEV, and G. G. VOLKOV. "STRING-MOTIVATED GRAND UNIFIED THEORIES WITH HORIZONTAL GAUGE SYMMETRY." International Journal of Modern Physics A 09, no. 30 (December 10, 1994): 5369–85. http://dx.doi.org/10.1142/s0217751x94002156.

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In the framework of four-dimensional heterotic superstring with free fermions, we investigate the rank 8 grand unified string theories (GUST’s) which contain the SU(3) H gauge family symmetry. GUST’s of this type accommodate naturally the three fermion families presently observed and, moreover, can describe the fermion mass spectrum without high-dimensional representations of conventional unification groups. We explicitly construct GUST’s with gauge symmetry G= SU(5) × U(1) ×[ SU(3) × U(1) ]H ⊂ SO (16) in free complex fermion formulation. As the GUST’s originating from Kac-Moody algebras (KMA’s) contain only low-dimensional representations, it is usually difficult to break the gauge symmetry. We solve this problem by taking for the observable gauge symmetry the diagonal subgroup G sym of the rank 16 group G×G ⊂ SO(16) × SO(16) ⊂ E(8)×E(8). Such a construction effectively corresponds to a level 2 KMA, and therefore some higher-dimensional representations of the diagonal subgroup appear. This (due to G×G tensor Higgs fields) allows one to break GUST symmetry down to SU (3c)× U(1) em . In this approach the observed electromagnetic charge Q em can be viewed as a sum of two Q I and Q II charges of each G group. In this case, below the scale where G×G breaks down to G sym the spectrum does not contain particles with exotic fractional charges.

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19

JOHNSON, CLIFFORD V. "HETEROTIC COSET MODELS." Modern Physics Letters A 10, no. 07 (March 7, 1995): 549–59. http://dx.doi.org/10.1142/s0217732395000582.

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A description is given on how to construct (0, 2) supersymmetric conformal field theories as coset models. These models may be used as non-trivial backgrounds for heterotic string theory. They are realized as a combination of an anomalously gauged Wess–Zumino–Witten model, right-moving supersymmetric fermions, and left-moving current algebra fermions. Requiring the sum of the gauge anomalies from the bosonic and fermionic sectors to cancel yields the final model. Applications discussed include exact models of extremal four-dimensional charged black holes and Taub–NUT solutions of string theory. These coset models may also be used to construct important families of (0, 2) supersymmetric heterotic string compactifications. The Kazama–Suzuki models are the left-right symmetric special case of these models.

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20

Erdem, R. "Fermion families and chirality through extra dimensions." European Physical Journal C 25, no. 4 (November 2002): 623–28. http://dx.doi.org/10.1140/epjc/s2002-01037-x.

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21

Evans, Nick. "Additional fermion families and precision electroweak data." Physics Letters B 340, no. 1-2 (December 1994): 81–85. http://dx.doi.org/10.1016/0370-2693(94)91301-3.

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22

BABU, K. S., and JOGESH C. PATI. "PROBING VECTORLIKE FAMILIES IN ESSM/SO(10) THROUGH NEUTRINO COUNTING, HIGGS MASS AND ν–N SCATTERING." International Journal of Modern Physics A 20, no. 28 (November 10, 2005): 6403–36. http://dx.doi.org/10.1142/s0217751x05019981.

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The Extended Supersymmetric Standard Model (ESSM), motivated on several grounds, introduces two vectorlike families [[Formula: see text] of SO (10)] with masses of order 1 TeV. In an earlier work, a successful pattern for fermion masses and mixings (to be called pattern I) has been proposed within a unified SO (10)-framework, based on MSSM, which makes seven predictions, in good accord with observations, including Vcb ≈ 0.04, and sin 2 2θνμντ ≈ 1. Extension of this framework to ESSM, preserving the successes of pattern I, has recently been proposed, where it was noted that ESSM can provide a simple explanation of a possible anomaly in (g-2)μ. To exhibit new phenomenological possibilities which may arise within ESSM, we present here a variant pattern (to be called pattern II) for fermion masses and mixings, within the SO (10)/ESSM framework, which possesses the same degree of success as pattern I as regards the masses and mixings of all fermions including neutrinos. We first note that either one of these two patterns, embedded in ESSM, would lead to a reduction in the LEP neutrino-counting from Nν = 3 (in good agreement with the data) and also provide a simple explanation of a possible (g-2)μ-anomaly. They can, however, be distinguished from each other by (a) a sharpening of our understanding of the true magnitude of the anomaly in νμ-nucleon scattering recently reported by the NuTeV group, (b) improved measurements of mt, mH and mW, (c) improved tests of e–μ lepton-universality in charged current processes, and (d) improvements in the measurements of Vud and Vus. Both patterns would predict some departure from the SM as regards tau lifetime. The probes listed above, and, of course, direct searches for the vectorlike families at the LHC and a future NLC can clearly test ESSM, and even distinguish between certain variants.

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23

GUENDELMAN, E. I., and A. B. KAGANOVICH. "SSB OF SCALE SYMMETRY, FERMION FAMILIES AND QUINTESSENCE WITHOUT THE LONG-RANGE FORCE PROBLEM." International Journal of Modern Physics A 17, no. 03 (January 30, 2002): 417–33. http://dx.doi.org/10.1142/s0217751x02005736.

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We study a scale-invariant two measures theory where a dilaton field ϕ has no explicit potentials. The scale transformations include the translation of a dilaton ϕ→ϕ+ const . The theory demonstrates a new mechanism for generation of the exponential potential: in the conformal Einstein frame (CEF), after SSB of scale invariance, the theory develops the exponential potential and, in general, the nonlinear kinetic term is generated as well. The scale symmetry does not allow the appearance of terms breaking the exponential shape of the potential that solves the problem of the flatness of the scalar field potential in the context of quintessential scenarios. As examples, two different possibilities for the choice of the dimensionless parameters are presented where the theory permits to get interesting cosmological results. For the first choice, the theory has standard scaling solutions for ϕ usually used in the context of the quintessential scenario. For the second choice, the theory allows three different solutions, one of which is a scaling solution with equation of state pϕ=wρϕ where w is predicted to be restricted by -1<w<-0.82. The regime where the fermionic matter dominates (as compared to the dilatonic contribution) is analyzed. There it is found that starting from a single fermionic field we obtain exactly three different types of spin 1/2 particles in CEF that appears to suggest a new approach to the family problem of particle physics. It is automatically achieved that for two of them, fermion masses are constants, the energy–momentum tensor is canonical and the "fifth force" is absent. For the third type of particles, a fermionic self-interaction appears as a result of SSB of scale invariance.

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24

MUÑOZ, CARLOS. "A KIND OF PREDICTION FROM STRING PHENOMENOLOGY: EXTRA MATTER AT LOW ENERGY." Modern Physics Letters A 22, no. 14 (May 10, 2007): 989–1003. http://dx.doi.org/10.1142/s021773230702347x.

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We review the possibility that the Supersymmetric Standard Model arises from orbifold constructions of the E8×E8 Heterotic Superstring, and the phenomenological properties that such a model should have. In particular, trying to solve the discrepancy between the unification scale predicted by the Heterotic Superstring (≈g GUT × 5.27 × 1017 GeV ) and the value deduced from LEP experiments (≈2 × 1016 GeV ), we will predict the presence at low energies of three families of Higgses and vector-like colour triplets. Our approach relies on the Fayet–Iliopoulos breaking, and this is also a crucial ingredient, together with having three Higgs families, to obtain in these models an interesting pattern of fermion masses and mixing angles at the renormalizable level. Namely, after the gauge breaking some physical particles appear combined with other states, and the Yukawa couplings are modified in a well-controlled way. On the other hand, dangerous flavour-changing neutral currents may appear when fermions of a given charge receive their mass through couplings with several Higgs doublets. We will address this potential problem, finding that viable scenarios can be obtained for a reasonable light Higgs spectrum.

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25

Guo, Zhi-qiang, and Bo-Qiang Ma. "Fermion families from two layer warped extra dimensions." Journal of High Energy Physics 2008, no. 08 (August 20, 2008): 065. http://dx.doi.org/10.1088/1126-6708/2008/08/065.

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26

Bars, Itzhak, and Matt Visser. "Number of massless fermion families in superstring theory." Physics Letters B 163, no. 1-4 (November 1985): 118–22. http://dx.doi.org/10.1016/0370-2693(85)90204-7.

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27

Kauffman, L., and H. Saleur. "FERMIONS AND LINK INVARIANTS." International Journal of Modern Physics A 07, supp01a (April 1992): 493–532. http://dx.doi.org/10.1142/s0217751x92003914.

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This paper deals with various aspects of knot theory when fermionic degrees of freedom are taken into account in the braid group representations and in the state models. We discuss how the Ř matrix for the Alexander polynomial arises from the Fox differential calculus, and how it is related to the quantum group Uqgl(1,1). We investigate new families of solutions of the Yang Baxter equation obtained from "linear" representations of the braid group and exterior algebra. We study state models associated with Uqsl(n,m), and in the case n=m=1 a state model for the multivariable Alexander polynomial. We consider invariants of links in solid handlebodies and show how the non trivial topology lifts the boson fermion degeneracy that is present in S3. We use "gauge like" changes of basis to obtain invariants in thickened surfaces Σ×[0,1].

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KLASSEN, TIMOTHY R., and EZER MELZER. "SINE-GORDON VS. MASSIVE THIRRING." International Journal of Modern Physics A 08, no. 23 (September 20, 1993): 4131–74. http://dx.doi.org/10.1142/s0217751x93001703.

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By viewing the sine-Gordon and massive Thirring models as perturbed conformal field theories, one sees that they are different (the difference being observable, for instance, in finite-volume energy levels). The UV limit of the former (SGM) is a Gaussian model, that of the latter (MTM) a so-called fermionic Gaussian model, the compactification radius of the boson underlying both theories depending on the SG/MT coupling. (These two families of conformal field theories are related by a “twist”.) Corresponding SG and MT models contain a subset of fields with identical correlation functions, but each model also has fields the other one does not have; for example, the fermion fields of MTM are not contained in SGM, and the bosonic soliton fields of SGM are not in MTM. Our results imply, in particular, that the SGM at the so-called “free-Dirac point” β2=4π is actually a theory of two interacting bosons with diagonal S-matrix S=−1, and that for arbitrary couplings the overall sign of the accepted SG S-matrix in the soliton sector should be reversed. More generally, we draw attention to the existence of new classes of quantum field theories, analogs of the (perturbed) fermionic Gaussians models, whose partition functions are invariant only under a subgroup of the modular group. One such class comprises “fermionic versions” of the Virasoro minimal models.

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29

CARAVAGLIOS, FRANCESCO, and STEFANO MORISI. "GAUGE BOSON FAMILIES IN GRAND UNIFIED THEORIES OF FERMION MASSES: $E_6^4 \rtimes S_4$." International Journal of Modern Physics A 22, no. 14n15 (June 20, 2007): 2469–91. http://dx.doi.org/10.1142/s0217751x07036646.

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In third quantization the origin of fermion families is easy to understand: the electron field, the muon field and the tau field are identical fields in precisely the same sense as three electrons are identical and indistinguishable particles of a theory of second quantization. In both cases, the permutation of these fields or particles leaves the Lagrangian invariant. One can also extend the concept of family to gauge bosons. This can be obtained through the semidirect product of the gauge group with the group of permutations of n objects. In this paper we have studied the group [Formula: see text]. We explain why we have chosen E6 as fundamental gauge group factor and why we start with a model with four gauge boson/fermion families to accommodate and to fit the Standard Model with only three fermion families. We suggest a possible symmetry breaking pattern of [Formula: see text] that could explain quark, lepton and neutrino masses and mixings.

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30

Fukaya, Hidenori, Tetsuya Onogi, and Satoshi Yamaguchi. "Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator." EPJ Web of Conferences 175 (2018): 11009. http://dx.doi.org/10.1051/epjconf/201817511009.

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Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.

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31

Tiezhong, Li. "Extra z bosons, families and heavy fermions." Chinese Physics Letters 6, no. 9 (September 1989): 385–88. http://dx.doi.org/10.1088/0256-307x/6/9/001.

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32

LI, Da-xi. "String Theory with Three Families of Chiral Fermions." Communications in Theoretical Physics 7, no. 3 (April 1987): 245–52. http://dx.doi.org/10.1088/0253-6102/7/3/245.

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33

Kim, Jihn E. "Grand unification models from SO(32) heterotic string." International Journal of Modern Physics A 35, no. 32 (November 20, 2020): 2050198. http://dx.doi.org/10.1142/s0217751x20501985.

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Grand unification groups (GUTs) are constructed from SO(32) heterotic string via [Formula: see text] orbifold compactification. So far, most phenomenological studies from string compactification relied on [Formula: see text] heterotic string, and this invites the SO(32) heterotic string very useful for future phenomenological studies. Here, spontaneous symmetry breaking is achieved by Higgsing of the antisymmetric tensor representations of SU[Formula: see text]. The anti-SU[Formula: see text] presented in this paper is a completely different class from the flipped-SU[Formula: see text]’s from the spinor representations of SO[Formula: see text]. Here, we realize chiral representations: [Formula: see text] for a SU(9) GUT and [Formula: see text] for a SU(5)[Formula: see text] GUT. In particular, we confirm that the non-Abelian anomalies of SU(9) gauge group vanish and hence our compactification scheme achieves the key requirement. We also present the Yukawa couplings, in particular for the heaviest fermion, [Formula: see text], and lightest fermions, neutrinos. In the supersymmetric version, we present a scenario how supersymmetry can be broken dynamically via the confining gauge group SU(9). Three families in the visible sector are interpreted as the chiral spectra of SU[Formula: see text] GUT.

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34

DOFF, A., and F. PISANO. "MINIMAL EXTENDED FLAVOR GROUPS, MATTER FIELDS CHIRAL REPRESENTATIONS, AND THE FLAVOR QUESTION." Modern Physics Letters A 15, no. 22n23 (July 30, 2000): 1471–80. http://dx.doi.org/10.1142/s021773230000178x.

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We show the specific unusual features on chiral gauge anomalies cancellation in the minimal, necessarily 3-3-1, and the largest 3-4-1 weak isospin chiral gauge semisimple group leptoquark–bilepton extensions of the 3-2-1 conventional standard model of nuclear and electromagnetic interactions. In such models a natural answer for the fundamental question of fermion generation replication arises directly from the self-consistency of a local gauge quantum field theory, which constrains the number of the QFD fermion families to the QCD color charges.

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35

DU, DONGSHENG, and CHUN LIU. "CYCLIC FAMILY SYMMETRY AND LEPTON HIERARCHY IN SUPERSYMMETRY." Modern Physics Letters A 10, no. 25 (August 20, 1995): 1837–41. http://dx.doi.org/10.1142/s0217732395001976.

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A cyclic symmetry among the left-handed doublets of the three families is proposed. This symmetry can naturally result in a realistic hierarchical pattern of the fermion masses within the framework of supersymmetry with nonvanishing sneutrino vacuum expectation values.

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36

GRETHER, M., M. DE LLANO, and M. HOWARD LEE. "ANOMALOUS BEHAVIOR OF IDEAL FERMI GAS BELOW 2D: THE "IDEAL QUANTUM DOT" AND THE PAUL EXCLUSION PRINCIPLE." International Journal of Modern Physics B 23, no. 20n21 (August 20, 2009): 4121–28. http://dx.doi.org/10.1142/s0217979209063304.

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A physical interpretation is given to a curious "hump" that develops in the chemical potential as a function of absolute temperature in an ideal Fermi gas for any spatial dimensionality d < 2, integer or not, in contrast with the more familiar monotonic decrease for all d ≥ 2. The hump height increases without limit as d decreases to zero. The divergence at d = 0 is shown to be a clear manifestation of the Pauli Exclusion Principle whereby two spinless fermions cannot sit on top of each other in configuration space. The hump itself is thus an obvious precursor of this manifestation, otherwise well understood in momentum space. It also constitutes an "ideal quantum dot" when d = 0.

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37

Frampton, Paul H., and Y. Jack Ng. "Families in confining theory of quarks, leptons, and additional fermions." Physical Review D 42, no. 9 (November 1, 1990): 3242–45. http://dx.doi.org/10.1103/physrevd.42.3242.

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38

KHALILOV, V. R., and K. E. LEE. "BOUND FERMION STATES IN A VECTOR 1/r AND AHARONOV–BOHM POTENTIAL IN (2+1) DIMENSIONS." Modern Physics Letters A 26, no. 12 (April 20, 2011): 865–83. http://dx.doi.org/10.1142/s0217732311035419.

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We construct systematically all the self-adjoint Dirac Hamiltonians with a vector 1/r and Aharonov–Bohm potential in (2+1) dimensions with taking into account the fermion spin. Then we find spectra of these self-adjoint Dirac Hamiltonians. There are one-parameter families of the self-adjoint Dirac Hamiltonians selected by physically acceptable boundary conditions. Equations determining spectra of the self-adjoint radial Dirac Hamiltonians are derived for various values of parameters. We show that the lowest fermion state in the considered potential becomes unstable when the effective charge is greater than the so-called critical charge, and that the effective charge is influenced by the magnetic flux and spin particle.

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39

ADLER, STEPHEN L. "FERMION-SECTOR FRUSTRATED SU(4) AS A PREONIC PRECURSOR OF THE STANDARD MODEL." International Journal of Modern Physics A 14, no. 12 (May 10, 1999): 1911–34. http://dx.doi.org/10.1142/s0217751x99000968.

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We give a model for composite quarks and leptons based on the semisimple gauge group SU(4), with the preons in the 10 representation; this choice of gauge gluon and preon multiplets is motivated by the possibility of embedding them in an N=6 supergravity multiplet, with the preons and antipreons both in the 20 of SU(6). Hypercolor singlets are forbidden in the fermionic sector of this theory; we propose that the SU(4) symmetry spontaneously breaks to SU (3)× U (1), with the binding of triality nonzero preons and gluons into composites, and with the formation of a color singlet condensate that breaks the initial Z12 vacuum symmetry to Z6. The spin ½ fermionic composites have the triality structure of a quark–lepton family, and the initial Z12 symmetry implies that there are six massless families, which mix to give three distinct families below the scale of the condensate. The spin 1 triality zero composites of the color triplet SU(4) gluons, when coupled to the condensate and with the color singlet representation of the 10 acting as a doorway state, lead to weak interactions of the fermionic composites through an SU(2) gauge algebra. The initial Z12 symmetry implies that this SU(2) gauge algebra structure is doubled, which in turn permits the corresponding independent gauge bosons to couple to chiral components of the composite fermions. Since the U(1) couples to the 10 representation as B-L, an effective SU (2)L× SU (2)R × U (1)B-L electroweak theory arises at the condensate scale, with all composites having the correct electric charge structure. Assuming a mechanism for forming composite Higgs bosons, the Z12→ Z6 symmetry breaking chain implies that below the condensate scale there can be two sets of discrete chiral Z6 triplets of Higgs doublets, as required by a phenomenological model for the CKM matrix that we have analyzed in detail elsewhere. A renormalization group analysis of the SU(4) model shows that the conversion by binding of one 10 of SU(4) to 12 triplets of SU(3) can give a very large, calculable hierarchy ratio between the SU(4) and the hadronic mass scales.

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40

FINKELSTEIN, ROBERT J. "A KNOT MODEL SUGGESTED BY THE STANDARD ELECTROWEAK THEORY." International Journal of Modern Physics A 20, no. 28 (November 10, 2005): 6487–94. http://dx.doi.org/10.1142/s0217751x05028545.

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We attempt to go beyond the standard electroweak theory by replacing SU (2) with its q-deformation: SU q(2). This step introduces new degrees of freedom that we interpret as indicative of nonlocality and as a possible basis for a solitonic model of the elementary particles. The solitons are conjectured to be knotted flux tubes labeled by the irreducible representations of SU q(2), an algebra which is not only closely related to the standard theory but also plays an underlying role in the description of knots. Each of the four families of elementary fermions is conjectured to be represented by one of the four possible trefoils. The three individual fermions belonging to any family are then assumed to occupy the three lowest states in the excitation spectrum of the trefoil for that family. One finds a not unreasonable variation of q among the lepton and quark families. The model in its present form predicts a fourth generation of fermions as well as a neutrino mass spectrum. The model may be refined depending on whether or not the fourth generation is found.

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41

Quinn, John J., Arkadiusz Wojs, and Kyung-Soo Yi. "Novel families of fractional quantum Hall states: pairing of composite fermions." Physics Letters A 318, no. 1-2 (November 2003): 152–55. http://dx.doi.org/10.1016/j.physleta.2003.09.031.

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42

Gao, Yun. "Fermionic and Bosonic Representations of the Extended Affine Lie Algebra." Canadian Mathematical Bulletin 45, no. 4 (December 1, 2002): 623–33. http://dx.doi.org/10.4153/cmb-2002-057-3.

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AbstractWe construct a class of fermions (or bosons) by using a Clifford (or Weyl) algebra to get two families of irreducible representations for the extended affine Lie algebra of level (1, 0) (or (−1, 0)).

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43

Robinson, P. L. "Fermionic Gaussians." Mathematical Proceedings of the Cambridge Philosophical Society 118, no. 3 (November 1995): 543–54. http://dx.doi.org/10.1017/s0305004100073850.

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The notion of a Gaussian as the exponential of a quadratic is rather familiar. Such functions are of considerable importance in a number of contexts, for example within quantum theory. Thus, in the Schrödinger representation of the canonical commutation relations they alone minimize uncertainty and they appear as ground states for harmonic oscillators. Also in the complex-wave representation of a free boson field they arise as transforms of the Fock vacuum under certain Bogoliubov automorphisms.

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44

Adams, David H. "Fermionic topological charge of families of lattice gauge fields." Nuclear Physics B - Proceedings Supplements 119 (May 2003): 775–77. http://dx.doi.org/10.1016/s0920-5632(03)80464-4.

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45

PISANO, FELICE. "A SIMPLE SOLUTION FOR THE FLAVOR QUESTION." Modern Physics Letters A 11, no. 32n33 (October 30, 1996): 2639–47. http://dx.doi.org/10.1142/s0217732396002630.

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We consider a simple way of solving the flavor question by embedding the three-family standard model in a semisimple gauge group extending minimally the weak isospin factor. Quantum chiral anomalies between families of fermions cancel with a matching of the number of families and the number of color degrees of freedom. Our demonstration shows how the theory leads to determination of families structure when the standard model is the input at low energies. The new physics is limited to start below a few TeVs within the reach of the next generation colliders.

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46

BRANDOW, B. H. "VALENCE-FLUCTUATION MECHANISM FOR CUPRATE SUPERCONDUCTIVITY." International Journal of Modern Physics B 08, no. 19 (August 30, 1994): 2667–719. http://dx.doi.org/10.1142/s021797929400107x.

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We explore the concept that the above-T c state is a normal Fermi liquid with strong correlations of the type found in valence-fluctuation and heavy-fermion materials. Experimental evidence and theoretical arguments for this phase are presented. Using an Anderson lattice model Hamiltonian, and a variational many-body formalism, the finite-U mechanism for s-like (full point-group symmetry) pairing is examined in detail. At the mean field or (1/N)0 level of approximation, the pairing tendency is strongly opposed by a magnetic tendency arising from a Gutzwiller version of hybridization renormalization. Pairing does not seem possible for realistic Hamiltonian parameters. This finite-U treatment has, however, now been extended to the (1/N)1 level of approximation. The lattice aspect is found to play a major and unexpected role here, leading to strong suppression of the magnetic tendency. This refined treatment is now found to provide adequate pairing attraction, for reasonable Hamiltonian parameters. Superconductivity is found only when the charge transfer energy Δ CT is quite large, Δ CT ≳ U, but there is evidence that Δ CT is indeed of this magnitude in the cuprate materials. Adequate band narrowing (mass enhancement or heaviness) and a very short coherence length are also obtained, in reasonable agreement with experiment. The quasiparticle interaction at the Fermi surface is strongly repulsive. This provides a reasonable source for the large and linear resistivity, as well as for other aspects of marginal-Fermi-liquid phenomenology. Evidence is found for a strong reduction of T c due to pair-breaking by the quasiparticle scattering. The main (fully self-consistent) calculations assume in-plane isotropy. However, a simplified calculation with a more realistic (anisotropic) band structure for the CuO 2 plane is found to provide a highly anisotropic gap, which may or may not have nodes. There is considerable evidence for such types of gap structure. Because a connection is found here between anomalously short coherence length and anomalously high resistivity, we suggest that this mechanism is also operating within other families of "exotic" superconductors.

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47

Rim, Seog-Hoon, Jeong-Hee Jin, Eun-Jung Moon, and Sun-Jung Lee. "Some Identities on the -Genocchi Polynomials of Higher-Order and -Stirling Numbers by the Fermionic -Adic Integral on." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–14. http://dx.doi.org/10.1155/2010/860280.

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A systemic study of some families of -Genocchi numbers and families of polynomials of Nörlund type is presented by using the multivariate fermionic -adic integral on . The study of these higher-order -Genocchi numbers and polynomials yields an interesting -analog of identities for Stirling numbers.

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48

FINKELSTEIN, ROBERT J., and A. C. CADAVID. "MASSES AND INTERACTIONS OF q-FERMIONIC KNOTS." International Journal of Modern Physics A 21, no. 21 (August 20, 2006): 4269–302. http://dx.doi.org/10.1142/s0217751x06032496.

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The q-electroweak theory suggests a description of elementary particles as solitons labeled by the irreducible representations of SU q(2). Since knots may also be labeled by the irreducible representations of SU q(2), we study a model of elementary particles based on a one-to-one correspondence between the four families of fermions (leptons, neutrinos, (-1/3) quarks, (2/3) quarks) and the four simplest knots (trefoils). In this model the three particles of each family are identified with the ground and first two excited states of their common trefoil. Guided by the standard electroweak theory, we calculate conditions restricting the masses of the fermions and the interactions between them. In its present form the model predicts a fourth generation of fermions as well as a neutrino spectrum. The same model with q ≅ 1 is compatible with the Kobayashi–Maskawa matrix. Depending on the test of these predictions, the model may be refined.

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49

Berezhiani, Zurab, and Enrico Nardi. "Realistic SUSY model with four fermion families, natural R parity and ντ in the eV range." Physics Letters B 355, no. 1-2 (July 1995): 199–208. http://dx.doi.org/10.1016/0370-2693(95)00729-5.

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50

Ming-gao, Gu, Li Xin-zhou, and Lu Ji-zong. "Neutral Fermion Masses in an E 6 Model with Three Families and the Solar Neutrino Problem." Communications in Theoretical Physics 11, no. 1 (January 1989): 103–6. http://dx.doi.org/10.1088/0253-6102/11/1/103.

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