Relevant bibliographies by topics / Fermion interactions

Academic literature on the topic 'Fermion interactions'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Fermion interactions"

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SESHAVATHARAM, U. V. S., and S. LAKSHMINARAYANA. "SUPER SYMMETRY IN STRONG AND WEAK INTERACTIONS." International Journal of Modern Physics E 19, no. 02 (February 2010): 263–80. http://dx.doi.org/10.1142/s021830131001473x.

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For strong interaction two new fermion mass units 105.32 MeV and 11450 MeV are assumed. Existence of "Integral charge quark bosons", "Integral charge effective quark fermions", "Integral charge (effective) quark fermi-gluons" and "Integral charge quark boso-gluons" are assumed and their masses are estimated. It is noticed that, characteristic nuclear charged fermion is Xs · 105.32 = 938.8 MeV and corresponding charged boson is Xs(105.32/x) = 415.0 where Xs = 8.914 is the inverse of the strong coupling constant and x = 2.26234 is a new number by using which "super symmetry" can be seen in "strong and weak" interactions. 11450 MeV fermion and its boson of mass = 11450/x = 5060 MeV plays a crucial role in "sub quark physics" and "weak interaction". 938.8 MeV strong fermion seems to be the proton. 415 MeV strong boson seems to be the mother of the presently believed 493,496 and 547 MeV etc, strange mesons. With 11450 MeV fermion "effective quark-fermi-gluons" and with 5060 MeV boson "quark boso-gluon masses" are estimated. "Effective quark fermi-gluons" plays a crucial role in ground state charged baryons mass generation. Light quark bosons couple with these charged baryons to form doublets and triplets. "Quark boso-gluons" plays a crucial role in ground state neutral and charged mesons mass generation. Fine and super-fine rotational levels can be given by [I or (I/2)] power(1/4) and [I or (I/2)] power(1/12) respectively. Here, I = n(n+1) and n = 1, 2, 3, ….
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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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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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CASAS, M., A. PUENTE, A. RIGO, M. J. DAVIDSON, R. M. QUICK, M. FORTES, M. A. SOLIS, et al. "BEC-DRIVEN SUPERCONDUCTIVITY IN THE CUPRATES." International Journal of Modern Physics B 13, no. 29n31 (December 20, 1999): 3489–91. http://dx.doi.org/10.1142/s021797929900326x.

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We apply to cuprates a three-fluid ideal boson-fermion statistical model of superconductivity in two dimensions (2D) derived from three extrema of the system Helmholtz free energy (subject to constant total fermion-number) for the BCS model interaction between fermions. The same interactions absent in BCS theory are neglected here. As the ensuing bosonic Cooper pairs move not in vacuum but in a Fermi sea we employ the correct linear — as opposed to the commonly-assumed quadratic — dispersion relation in the center-of-mass momentum (CMM). More importantly, pair breakup beyond a certain (very small) CMM is accounted for. Bose–Einstein condensation (BEC) critical temperatures of about 800 K result for moderate coupling with cuprate parameters.
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SHANKAR, R., and M. SIVAKUMAR. "BOSE-FERMI TRANSMUTATION 2+1 DIMENSIONS: EFFECT OF SELF-INTERACTIONS AND THE MAXWELL TERM." Modern Physics Letters A 06, no. 26 (August 30, 1991): 2379–87. http://dx.doi.org/10.1142/s0217732391002803.

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We show the partition function of self-interacting charged scalar fields coupled with Abelian gauge fields governed by Maxwell-Chern-Simons action is equivalent in the long-wavelength approximation to that of a massive four-Fermi theory. The coupling constants and mass of the fermionic theory is explicitly related to those of the bosonic theory. The gauge invariant charged scalar current is shown to be transmuted to fermion current. The physical mass of the fermion is computed at the mean field level and shown to be finite at large self-coupling.
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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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Plastino, Angelo, Gustavo Luis Ferri, and Angel Ricardo Plastino. "Features of Fermion Dynamics Revealed by SU2 Symmetry." Symmetry 14, no. 10 (October 17, 2022): 2179. http://dx.doi.org/10.3390/sym14102179.

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We deal here with the notion of statistical order and apply it to a system of interacting fermions endowed with an SU2 × SU2 symmetry. The discussion takes place in a thermal quantum statistical scenario. Two distinct fermion–fermion interactions are at play. One of them is a well-known spin–flip interaction. The other is the pairing interaction responsible for nuclear superconductivity. We used novel statistical quantifiers that yield insights regarding changes in the statistical order produced when the values of the pertinent coupling constants vary. In particular, we show that judicious manipulation of the energy cost associated with statistical order variations with the fermion number is the key to understanding important details of the associated dynamics.
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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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Jaroszewics, T., and P. S. Kurzepa. "Intersections of fermionic paths and four-fermion interactions." Physics Letters B 303, no. 3-4 (April 1993): 323–26. http://dx.doi.org/10.1016/0370-2693(93)91439-t.

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BRANT, S., N. YOSHIDA, and L. ZUFFI. "PROTON-NEUTRON INTERACTING BOSON-FERMION-FERMION MODEL AND THE EXCHANGE INTERACTIONS." International Journal of Modern Physics E 17, supp01 (December 2008): 373–85. http://dx.doi.org/10.1142/s0218301308011999.

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The exchange interactions proper to the proton-neutron version of the interacting boson-fermion-fermion model are derived from the proton-neutron quadrupole-quadrupole interaction. The influence of the exchange interactions on the F-spin content of wave functions is analysed for a typical odd-odd nucleus.
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Dissertations / Theses on the topic "Fermion interactions"

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Thornton, Andrew M. "Studies of lattice fermion-scalar interactions." Thesis, University of Edinburgh, 1989. http://hdl.handle.net/1842/14539.

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Shively, William F. Khveshchenko D. V. "Novel behaviors in fermion systems with point-like Fermi surfaces and singular interactions." Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2006. http://dc.lib.unc.edu/u?/etd,439.

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Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2006.
Title from electronic title page (viewed Oct. 10, 2007). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics & Astronomy." Discipline: Physics and Astronomy; Department/School: Physics and Astronomy.
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Karim, Pour Farshid. "Quantum Monte Carlo studies of fermions with attractive interactions in optical traps." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-34763.

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Fraser, Louisa Mairi. "Coulomb interactions and positron annihilation in many fermion systems : a Monte Carlo approach." Thesis, Imperial College London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338685.

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Curtis, Duncan Charles. "A non-perturbative study of fermion propagators and their interactions in gauge theories." Thesis, Durham University, 1991. http://etheses.dur.ac.uk/6275/.

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In this thesis we study the non-perturbative behaviour of the fermion propagator in an Abelian gauge theory, namely four dimensional, quenched QED –where by quenched we mean that we neglect the effect of the fermion loops in the boson propagator. What is of primary interest is the dynamical generation of mass. In order to carry out this study we need to make use of the Schwinger-Dyson equations, which are the field equations of the theory. For the investigation of the fermion propagator, the form of the three point interaction is of critical importance. We study the usual ansatz, the Ball-Chiu form, for the three point function, that is obtained from the Ward-Takahashi identities, and improve upon it. This is done by making use of the powerful constraints that Multiplicative Renormalizability place upon the theory in the perturbative (high energy) region. We initially study the theory in the massless case, for simplicity, where we find that using our improved ansatz we can obtain an exact, non-perturbative solution for the renormalised wave function. Moving on, we then study the theory in the massive case -where we have a brief interlude to look at the ladder approximation. We solve the theory in the case where there is a finite cutoff and reproduce the well-known critical coupling point. We then consider the case where there is an infinite cutoff, when we find no critical coupling. We discuss and explain the differences. Returning to our improved ansatz for the fermion-boson vertex we solve the renormalised theory for both the wavefunction and mass function and find that there is no critical coupling. In doing this having a form for the fermion-boson vertex that satisfies both the Ward-Takahashi identity and Multiplicative Renormalizability is essential. These studies suggest that full QED may turn out to be a theory without a critical coupling and thus be free of phase changes.
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Pfoh, Torsten [Verfasser]. "Electroweak precision observables and effective four-fermion interactions in warped extra dimensions / Torsten Pfoh." Mainz : Universitätsbibliothek Mainz, 2011. http://d-nb.info/1026802652/34.

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Howald, Ludovic. "Interactions entre la supraconductivité et la criticité quantique, dans les composés CeCoIn5, URhGe et UCoGe." Phd thesis, Université de Grenoble, 2011. http://tel.archives-ouvertes.fr/tel-00584598.

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Le sujet de cette thèse est l'analyse du second champ critique supraconducteur (Hc2) ainsi que l'interaction entre la supraconductivité et les points critiques quantiques (PCQ), pour les composés CeCoIn5, URhGe et UCoGe. Dans le composé CeCoIn5, l'étude par résistivité du domaine de liquide de Fermi a permis la localisation précise du PCQ a pression ambiante. Cette analyse permet d'invalider l'hypothèse d'une coïncidence entre Hc2(0) et le PCQ. Dans une deuxième partie, l'évolution sous pression de Hc2 est analysée. Le dôme supraconducteur de ce composé est non-conventionnel avec deux pressions caractéristiques différentes: à ~1.6GPa, la température de transition supraconductrice est maximum alors que c'est à ~0.4GPa que la plupart des grandeurs physiques (maximum de Hc2(0), maximum de la pente dHc2/dT, maximum du saut de chaleur spécifique DC/C, ...) suggèrent la présence d'un PCQ. Nous expliquons cet antagonisme par l'importance des processus de brisure de pairs liés a la proximité du PCQ. Ces deux observations nous permettent de proposer un nouveau diagramme de phase pour CeCoIn5. Dans une troisième partie, les mesures de conduction thermique sur les composés URhGe et UCoGe sont présentées. Elles nous permettent dans un premier temps d'obtenir la transition "bulk" supraconductrice et de confirmer la forme in-habituelle de Hc2 observée en résistivité. La dépendance en températures et en champs de la conduction thermique nous permet d'identifier une contribution non-électronique au transport de chaleur jusqu'aux plus basses températures. D'autre part, nous identifions deux différents domaines supraconducteurs a bas et hauts champs appliqués selon l'axe b. Ces deux domaines sont compatibles avec un modèle de supraconductivité multigaps. Suivant ces observations et des mesures de pouvoir thermoélectrique, nous proposons un modèle de transition de Lifshitz pour ces deux composés.
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Baez, Michael Cabrera. "Fundamental electronic and magnetic interactions in the cage compounds RT2Zn20 (R = Y, Gd, Yb, T = Fe, Co)." reponame:Repositório Institucional da UFABC, 2017.

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Orientador: Prof. Dr. Marcos Abreu Avila
Tese (doutorado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2017.
The electronic correlations originated from the Coulomb interactions between electrons play a fundamental role in the establishment of the physical properties of a wide range of materials. For the case of weak correlations, the material can be described within a simplied non-interacting point of view, as in the case of standard metals. Unexpected and intriguing properties are revealed when strong correlations are involved, due to a large number of degrees of freedom in the electronic correlations. As a result of this electronic correlation, it is possible to go from conventional forms of magnetism, passing through superconducting systems and reaching heavy fermion behavior. Members within a single family of compounds can provide all those very dierent ground states, and the opportunity to study and try to understand some of the electronic and magnetic fundamental interactions involved. This thesis is a result of exploring these dierent behaviors that arise from electron-electron correlations, specically in the family of cage compounds RT2Zn20 (R=Y,Gd,Yb and T=Fe,Co). A detailed combination of quantitative macroscopic and microscopic descriptions of the electronic, thermodynamic and magnetic properties of some members of this family were developed. The rst part of this thesis presents a study on Gd3+- doped YCo2Zn20 single crystals (Y1..xGdxCo2Zn20: (0.002 . x 1.00) through a combination of temperature-dependent Electron Spin Resonance (ESR), heat capacity and dc magnetic susceptibility experiments, plus collaborative rst-principles Density Functional Theory (DFT) calculations. The combination of experimental and electronic structure data establish GdCo2Zn20 as a model Ruderman-Kittel-Kasuya-Yosida (RKKY) system by predicting a Curie-Weiss temperature C = ..1:2(2) K directly from microscopic parameters, in very good agreement with the bulk value from magnetization data. The second part involves an exploration of the unconventional ferromagnetic behaviors that have been found in GdFe2Zn20, which has a relatively high ferromagnetic ordering temperature (TC = 86 K) despite being a system with wide separation between Gd3+ ions in a matrix with strong electron-electron correlation. Taking into account those correlations and itinerant molecular eld eects, analysis of our ESR results indicate that the exchange interaction between the Gd3+ is processed via the d-type of electrons at the Fermi level and becomes an exchange interaction of covalent nature (J(0)fd < 0). Our results shows that the RKKY model cannot explain the ferromagnetic behavior of this compound, and a super-exchange-like mechanism is proposed for this magnetic interaction. Increasing a little bit the level of complexity, the third part of this thesis is on the tuning of the electronic properties of the heavy fermion compound YbFe2Zn20 by chemical substitution (Cd doping). With increasing amount of Cd, the hybridization between Yb 4f electrons and the conduction electrons is weakened, which should be accompanied by a valence shift of the Yb3+ due to the negative chemical pressure eect. The combined results demonstrate excellent complementarity between positive physical pressure and negative chemical pressure, and point to a rich playground for exploring the physics of strongly correlated electron systems. Finally, this thesis ends with a general set of conclusions of the explored quantum materials.
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Mollet, Simon. "Exploration of 6-dimensional models with non trivial topology and their predictions for fermions masses and mixings, neutrino physics, flavour changing interactions and CP violation." Doctoral thesis, Universite Libre de Bruxelles, 2016. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/230863.

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In this thesis, we study several scenarios which go beyond the Standard Model of particle physics with the aim of gaining a better understanding for the multiplication of fermion families, their masses and mixings pattern and its relation to CP violation. The common feature of the models we envisaged (and the guiding principle of the thesis) is the introduction of extra space dimensions. In a first attempt to explain the fermion mass structure, we elaborate on a model with two extra-dimensions and a Nielsen- Olesen vortex background established on it. In this framework, three families in 4D can be seen as different modes of a single generation in 6D, while their extra-dimensional wavefunctions turn out highly constrained by the dynamics, which allows to determined the mass matrices with few parameters. Moreover, with a few additional hypotheses only, it is possible to simultaneously account for the striking differences between neutrinos and charged fermions. After a summary of the model, we illustrate this with the explicit formulation of a benchmark model which reproduces convincingly all the mass and mixing parameters of the Standard Model, taking advantage of new, more precise numerical solutions of the field equations, and including the recent measurements of the Standard Model scalar boson mass and of the neutrino heta_13 mixing angle (the latter has however been correctly predicted by the model before its first measurement). We then turn to the predictions which mainly concern the neutrino and gauge sectors. In the former, we remind the Majorana nature, and the natural tendency for inverted hierarchy pattern with an almost maximally suppressed neutrinoless double beta decay. On the other hand, we predict new (neutral) gauge bosons whose couplings to fermions are not flavour-diagonal but are however constrained (in their strength and their flavour structure) by the 6D anatomy of the theory. We compare their detectability in precision low energy processes and at colliders (especially at the LHC), and show that in the simplest geometries at least, the bounds from the former exclude interesting phenomenology for the latter. Nevertheless, we turn to more phenomenological effective Lagrangians with the same overall structure and in which we are able to lower the mass scale of the new bosons to a reachable energy, and thus analyse the possible signatures for LHC.In the last part of this work, we turn to the issue of CP violation and show how in certain 6D models with non simply connected topologies, it is possible to generate a non negligible CP violation at the 4D level in a pure gauge approach. We carefully study how the 4D CP symmetry is related to particular transformations of the original 6D theory and subsequently show how an incompatibility of such transformations with the compactification scheme can lead to an effective CP breaking. As a proof of concept, we build a toy model with two extra-dimensions compactified on a flat torus and end in 4D with a light neutral fermion with a non zero electric dipole moment.Dans cette thèse, nous étudions plusieurs scénarios au-delà du Modèle Standard de la physique des particules à la recherche d'une meilleure compréhension de la multiplication des familles de fermions, de leurs masses et de leurs mélanges, ainsi que la relation à laviolation de CP.La caractéristique commune à tous les modèles envisagés (et le concept sous-jacent à toute la thèse) est l'introduction de nouvelles dimensions spatiales. Dans une première tentative pour expliquer le spectre des fermions, nous développons un modèle où une structure de vortex à la Nielsen-Olesen est établie sur deux dimensions supplémentaires. Dans ce cadre, les trois familles à 4D peuvent être vues comme différents modes d'une unique génération à 6D, tandis que leur fonctions d'onde extra-dimensionnelles s'avèrent fortement contraintes par la dynamique ;ceci permet d'établir les matrices de masses en terme d'un petit nombre de paramètres. De plus, grâce à quelques hypothèses additionnelles seulement, il est possible de justifier simultanément les différences marquées entre neutrinos et fermions chargés. Nous synthétisons le modèle et l'illustrons en en formulant une réalisation particulière qui parvient à reproduire de manière convaincante tous les paramètres de masse et de mélange du Modèle Standard. Pour l'occasion, nous exploitons de nouvelles solutions aux équations des champs, numériquement plus précises, et prenons en compte les mesures récentes de la masse du boson scalaire et de l'angle de mélange heta_13 pour les neutrinos (le modèle avait cependant prédit ce dernier avant qu'il ne soit mesuré pour la première fois). Nous nous tournons ensuite vers les prédictions du modèle et qui concernent principalement le secteur des neutrinos et celui des bosons de jauge. Pour le premier, nous rappelons la nature "Majorana" des neutrinos, ainsi que la tendance naturelle à une hiérarchie inverse avec une suppression quasi maximale de la double désintégration bêta sans neutrino. D'autre part, nous prédisons de nouveaux bosons de jauge (neutres) dont les couplages aux fermions ne sont pas diagonaux dans l'espace des saveurs mais sont contraints (autant en terme de valeurs qu'en termes de structure) par l'anatomie de la théorie à 6D. Nous comparons leurs détections potentielles dans les processus de précision à basse énergie et auprès des collisionneurs (en particulier au LHC). Nous montrons que, dans les géométries les plus simples du moins, les limites imposées par les premiers excluent toute phénoménologie intéressante du côté des seconds. Toutefois, en nous tournantvers des Lagrangiens effectifs qui conservent la même structure d'ensemble mais ouvrent à une étude plus phénoménologique, nous sommes capables de réduire l'échelle de masse de ces nouveaux bosons jusqu'à une énergie accessible, et donc d'en analyser de potentielles signatures au LHC.Dans la dernière partie de ce travail, nous nous intéressons à la question de la violation de CP et montrons comment dans certains modèles à 6D avec une topologie non-simplement connexe, il est possible de générer une violation de CP non négligeable à 4D dans une approche de "pure jauge". Nous étudions attentivement comment la symétrie CP à 4D est reliée à des transformations particulières de la théorie originale à 6D, suite à quoi nous montrons comment l'incompatibilité de ces transformations avec la façon dont sont "compactifiées" les dimensions supplémentaires peut conduire à une brisure effective de CP. Pour illustrer la faisabilité de notre approche, nous élaborons un "modèle jouet" où deux dimensions supplémentaires sont compactifiées sur un tore plat, et obtenons à 4D un fermion neutre léger et qui possède un moment électrique dipolaire non nul.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Snyman, Izak. "Analysis and applications of the generalised Dyson mapping." Thesis, Stellenbosch : Stellenbosch University, 2004. http://hdl.handle.net/10019.1/49829.

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Thesis (MSc)--Stellenbosch University, 2004.
ENGLISH ABSTRACT: In this thesis, generalized Dyson boson-fermion mappings are considered. These are techniques used in the analysis of the quantum many-body problem, and are instances of so-called boson expansion methods. A generalized Dyson boson-fermion mapping, or a Dyson mapping for short, is a one-to-one linear but non-unitary operator that can be applied to vectors representing the states of a many-fermion system. A vector representing a fermion system maps onto a vector that is most naturally interpreted as representing a state of a many-body system that contains both bosons and fermions. The motivation for doing such a mapping is the hope that the mapping will reveal some property of the system that simplifies its analysis and that was hidden in the original form. The aims of this thesis are 1. to review the theory of generalized Dyson boson-fermion mappings, 2. by considering a tutorial example, to demonstrate that it is feasible to implement the theory and 3. to find a useful application for a generalized Dyson boson-fermion mapping, by considering a non-trivial model, namely the Richardson model for superconductivity. The realization of the first two aims mainly involve the collecting together of ideas that have already appeared in the literature, into one coherent text. Some subtle points that were treated only briefly due to space restrictions in the journal publications where the theory was first expounded, are elaborated on in the present work. On the other hand, the analysis of the Richardson Hamiltonian that uses a Dyson mapping, goes beyond what has already appeared in the literature. It is the first time that a boson expansion technique is implemented for a system where the roles of both collective and non-collective fermion pairs are important. (The Dyson mapping associates bosons with Cooper pairs, while the fermions not bound in Cooper pairs result in fermions being present in the mapped system as well.) What is found is that the Dyson mapping uncovers non-trivial properties of the system. These properties aid the construction of time-independent perturbation expansions for the stationary states of the system, as well as time-dependent expansions for transition amplitudes between states. The time-independent expansions agree with results that other authors obtained through methods other than boson expansions. The time-dependent expansions, that one would be hard-pressed to develop without a Dyson mapping, might in future prove useful in understanding aspects of the dynamics of ultracold fermi gases, when time-dependent magnetic fields are used to vary the atom-atom interaction strenght.
AFRIKAANSE OPSOMMING: In hierdie tesis word veralgemeende Dyson boson-fermion-afbeeldings ondersoek. Hierdie afbeeldings word gebruik in die analise van die kwantum veeldeeltjie probleem, en is voorbeelde van sogenaamde boson-uitbreidingstegnieke. 'n Veralgemeende Dyson bosonfermion- afbeelding, of kortweg 'n Dyson afbeelding, is 'n een-tot-een, lineêre maar nie-unitêre operator wat inwerk op vektore wat toestande verteenwoordig van 'n veel-fermion sisteem. 'n Vektor wat 'n fermionsisteem verteenwoordig word so afgebeeld op 'n vektor waarvoor die mees natuurlike interpretasie is dat dit 'n toestand verteenwoordig van 'n sisteem waarin beide bosone en fermione aanwesig is. So 'n afbeelding word gewoonlik gemaak in die hoop dat eienskappe van die sisteem, wat versteek was in die oorspronklike weergawe, voor-die-hand-liggend is na die afbeelding. Hierdie tesis het ten doel 1. om die teorie van veralgemeende Dyson boson-fermion-afbeeldings te hersien, 2. om 'n eenvoudige voorbeeld deur te werk, en so te demonstreer dat die teorie sonder moeite geïmplimenteer kan word en 3. om 'n nuttige toepassing te vind vir 'n veralgemeende Dyson boson-fermion-afbeelding deur 'n nie-triviale model, naamlik die Richardson model vir supergeleiding, te ondersoek. Die eerste twee van hierdie doelwitte behels hoofsaaklik dat idees wat reeds in die literatuur verskyn het, saamgevat word in een koherente teks. Sommige subtiele punte wat, vanwee beperkte ruimte, slegs kortliks bespreek is in die joernaalartikels waarin die teorie oorspronklik verskyn het, word in hierdie tesis meer breedvoering bespreek. Daarteenoor verteenwoordig die analise van die Richardson model met behulp van 'n Dyson afbeelding 'n nuwe bydra. Dit is naamlik die eerste keer dat 'n bosonuitbreiding ingespan word vir 'n sisteem waar sowel kollektiewe as nie-kollektiewe fermionpare 'n belangrike rol speel. (Die Dyson afbeelding assosieer bosone met die oorspronklike sisteem se Cooper pare, terwyl die fermione wat in die oorspronklike sisteem nie tot Cooper pare gebind is nie, sorg dat daar ook fermione teenwoordig is in die afgebeelde sisteem.) Ons vind dat die Dyson afbeelding nie-triviale eienskappe van die sisteem aan die lig bring. Hierdie eienskappe is nuttig vir die konstruksie van beide tyd-onafhanklike steuringsreekse vir die stasionêre toestande van die sisteem en vir tyd-afhanklike steuringsreekse vir oorgangsamplitudes tussen toestande. Die tyd-onafhanklike uitbreidings stem ooreen met resultate wat ander outeurs afgelei het sonder die gebruik van 'n Dyson afbeelding. Die tyd-afhanklike uitbreidings, wat kwalik afgelei kan word sonder 'n Dyson afbeelding, mag vorentoe nuttig wees om aspekte van die dinamika van baie koue Fermi gasse te verstaan, wanneer tydafhanklike magneetvelde gebruik word om die inter-atoomwisselwerking te manipuleer.
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Books on the topic "Fermion interactions"

1

Mulay, Shashikant, John J. Quinn, and Mark Shattuck. Strong Fermion Interactions in Fractional Quantum Hall States. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00494-1.

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Iachello, F. The interacting Boson-Fermion model. Cambridge [England]: Cambridge University Press, 1991.

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Kopietz, Peter. Bosonization of interacting fermions in arbitrary dimensions. Berlin: Springer, 1997.

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Will, Sebastian. From atom optics to quantum simulation: Interacting bosons and fermions in three-dimensional optical lattice potentials. Berlin: Springer, 2013.

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Kopietz, Peter. Bosonization of Interacting Fermions in Arbitrary Dimensions. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-540-68495-4.

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Casten, R. F. Algebraic approaches to nuclear structure: Interacting boson and fermion models. Langhorne, Pa: Harwood Academic Publishers, 1993.

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R, Casten, ed. Algebraic approaches to nuclear structure: Interacting boson and fermion models. Langhorne, Pa: Harwood Academic Publishers, 1993.

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Nozières, Philippe. Theory of interacting Fermi systems. Reading, Mass: Addison-Wesley, 1997.

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Interacting boson models of nuclear structure. Oxford: Clarendon Press, 1989.

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Bonatsos, D. Interacting boson models of nuclear structure. Oxford: Clarendon, 1988.

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Book chapters on the topic "Fermion interactions"

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Ceulemans, Arnout. "Boson-Fermion Interactions." In The Theory of the Jahn-Teller Effect, 31–75. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09528-3_3.

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Ho-Kim, Quang, and Xuan-Yem Pham. "Fermion Fields." In Elementary Particles and Their Interactions, 57–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03712-6_3.

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Scheck, F. "Fermion Fields and Their Properties." In Electroweak and Strong Interactions, 1–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-662-03245-9_1.

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Knight, Walter D. "Hyperfine Interactions in Metals." In Pair Correlations in Many-Fermion Systems, 57–62. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4899-1555-9_3.

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Namsrai, Khavtgain. "Four-Fermion Weak Interactions in Stochastic Space-Time." In Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics, 134–56. Dordrecht: Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4518-0_4.

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Finster, Felix. "The Continuum Limit of a Fermion System Involving Neutrinos: Weak and Gravitational Interactions." In Fundamental Theories of Physics, 327–430. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42067-7_4.

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Finster, Felix. "The Continuum Limit of a Fermion System Involving Leptons and Quarks: Strong, Electroweak and Gravitational Interactions." In Fundamental Theories of Physics, 431–77. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42067-7_5.

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Jackson Kimball, Derek F., Leanne D. Duffy, and David J. E. Marsh. "Ultralight Bosonic Dark Matter Theory." In The Search for Ultralight Bosonic Dark Matter, 31–72. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95852-7_2.

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AbstractThe basic theoretical concepts motivating the hypothesis that dark matter may consist of ultralight spin-0 or spin-1 bosons are explored. The origin of bosons with masses ≪ 1 eV from spontaneous and explicit symmetry breaking is illustrated with examples. The origins and characteristics of nongravitational couplings or “portals” between ultralight bosons and Standard Model particles and fields are considered, with particular attention paid to the cases of the axion-photon and axion-fermion interactions. Theoretical motivations for the existence of ultralight bosons, besides as an explanation of dark matter, are examined, with particular focus on the Peccei-Quinn solution to the strong CP problem (resulting in the QCD axion) and a dynamical solution to the hierarchy problem (the “relaxion” hypothesis, based on a particular axion-Higgs coupling in the early universe). Mechanisms for non-thermal production of ultralight bosonic dark matter are examined.
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Wipf, Andreas. "Interacting Fermions." In Statistical Approach to Quantum Field Theory, 475–545. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-83263-6_17.

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Cabibbo, Nicola. "Weak interactions." In Enrico Fermi, 138–50. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-01160-7_9.

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Conference papers on the topic "Fermion interactions"

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Rantaharju, Jarno, Vincent Drach, Ari Hietanen, Claudio Pica, and Francesco Sannino. "Wilson Fermions with Four Fermion Interactions." In The 33rd International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.251.0228.

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Vrancx, Tom, Lesley De Cruz, Jan Ryckebusch, and Pieter Vancraeyveld. "Consistent interactions for high-spin fermion fields." In THE 8TH INTERNATIONAL WORKSHOP ON THE PHYSICS OF EXCITED NUCLEONS: NSTAR 2011. AIP, 2012. http://dx.doi.org/10.1063/1.3701249.

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Rantaharju, Jarno, Vincent Drach, Claudio Pica, and Francesco Sannino. "Adjoint SU(2) with Four Fermion Interactions." In 34th annual International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.256.0231.

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Ross, G. G., Pyungwon Ko, and Deog Ki Hong. "Fermion masses, flavour mixing and CP violation." In SUPERSYMMETRY AND THE UNIFICATION OF FUNDAMENTAL INTERACTIONS. AIP, 2008. http://dx.doi.org/10.1063/1.3051900.

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Bajc, Borut. "Fermion Masses and SO(10)." In SUSY06: THE 14TH INTERNATIONAL CONFERENCE ON SUPERSYMMETRY AND THE UNIFICATION OF FUNDAMENTAL INTERACTIONS. AIP, 2007. http://dx.doi.org/10.1063/1.2735203.

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Veernala, Aarti, and Simon Catterall. "Four Fermion Interactions in Non Abelian Gauge Theory." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Trieste, Italy: Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0108.

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Rowlands, Peter. "Fermion Interactions and Mass Generation in the Nilpotent Formalism." In COMPUTING ANTICIPATORY SYSTEMS: CASYS'05 - Seventh International Conference. AIP, 2006. http://dx.doi.org/10.1063/1.2216631.

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Bhattacharya, Tanmoy, Rajan Gupta, Anosh Joseph, Huey-Wen Lin, and Saul Cohen. "Theoretical Bounds on New Four-Fermion Interactions and TeV Scale Physics." In XXIX International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2012. http://dx.doi.org/10.22323/1.139.0272.

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Nandi, S., George Alverson, Pran Nath, and Brent Nelson. "Fermion Mass Hierarchy and New Physics at the TeV Scale." In SUSY09: 7th International Conference on Supersymmetry and the Unification of Fundamental Interactions. AIP, 2010. http://dx.doi.org/10.1063/1.3327768.

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Vale Silva, Luiz, Sebastian Jäger, and Kirsten Leslie. "Using dipole processes to constrain the flavour of four-fermion effective interactions." In 40th International Conference on High Energy physics. Trieste, Italy: Sissa Medialab, 2021. http://dx.doi.org/10.22323/1.390.0434.

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Reports on the topic "Fermion interactions"

1

Yarotski, Dmitry Anatolievitch, and Richard L. Sandberg. Coherent behavior in Heavy Fermion materials; Understanding and controlling competing interactions in complex oxide heterostructures. Office of Scientific and Technical Information (OSTI), February 2015. http://dx.doi.org/10.2172/1170261.

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Wilkins, J. Strongly interacting fermion systems. Office of Scientific and Technical Information (OSTI), January 1990. http://dx.doi.org/10.2172/6745929.

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Wilkins, J. W. Final Report of Strongly Interacting Fermion Systems. Office of Scientific and Technical Information (OSTI), June 2001. http://dx.doi.org/10.2172/836268.

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Wilkins, J. Strongly interacting fermion systems: Technical progress report. Office of Scientific and Technical Information (OSTI), May 1989. http://dx.doi.org/10.2172/6246658.

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Author, Not Given. (Strongly interacting fermion system): Annual performance for 1988--89. Office of Scientific and Technical Information (OSTI), May 1989. http://dx.doi.org/10.2172/6218943.

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Quinn, John. Final Report - Composite Fermion Approach to Strongly Interacting Quasi Two Dimensional Electron Gas Systems. Office of Scientific and Technical Information (OSTI), November 2009. http://dx.doi.org/10.2172/1054786.

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Thomas, John E. Strongly-Interacting Fermi Gases in Reduced Dimensions. Fort Belvoir, VA: Defense Technical Information Center, May 2009. http://dx.doi.org/10.21236/ada519063.

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Zwierlein, Martin W. Strongly Interacting Fermi Gases in Two Dimensions. Fort Belvoir, VA: Defense Technical Information Center, July 2012. http://dx.doi.org/10.21236/ada564578.

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Zwierlein, Martin W. Strongly Interacting Fermi Gases In Two Dimensions. Fort Belvoir, VA: Defense Technical Information Center, January 2012. http://dx.doi.org/10.21236/ada554942.

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Thomas, John E. Simulating strongly correlated electrons with a strongly interacting Fermi gas. Office of Scientific and Technical Information (OSTI), May 2013. http://dx.doi.org/10.2172/1080278.

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