Baby Skyrme model and fermionic zero modes
Queiruga, J. M.
2016-09-01
In this work we investigate some features of the fermionic sector of the supersymmetric version of the baby Skyrme model. We find that, in the background of Bogomol'nyi-Prasad-Sommerfield compact baby Skyrmions, fermionic zero modes are confined to the defect core. Further, we show that, while three Supersymmetry (SUSY) generators are broken in the defect core, SUSY is completely restored outside. We study also the effect of a D-term deformation of the model. Such a deformation allows for the existence of fermionic zero modes and broken SUSY outside the compact defect.
The Role of Zero-Modes in the Canonical Quantization of Heavy-Fermion QED in Light-Cone Coordinates
Brown, Robert W.; Jun, Jin Woo; Shvartsman, Shmaryu M.; Taylor, Cyrus C.
1993-01-01
Four-dimensional heavy-fermion QED is studied in light-cone coordinates with (anti-)periodic field boundary conditions. We carry out a consistent light-cone canonical quantization of this model using the Dirac algorithm for a system with first- and second-class constraints. To examine the role of the zero modes, we consider the quantization procedure in {the }zero-mode {and the non-zero-mode} sectors separately. In both sectors we obtain the physical variables and their canonical commutation ...
Role of zero modes in the canonical quantization of heavy-fermion QED in light-cone coordinates
Brown, R.W.; Jun, J.W.; Shvartsman, S.M.; Taylor, C.C.
1993-01-01
Four-dimensional heavy-fermion QED is studied in light-cone coordinates with (anti)periodic field boundary conditions. We carry out a consistent light-cone canonical quantization of this model using the Dirac algorithm for a system with first- and second-class constraints. To examine the role of the zero modes, we consider the quantization procedure in the zero-mode and the nonzero-mode sectors separately. In both sectors we obtain the physical variables and their canonical commutation relations. The physical Hamiltonian is constructed via a step-by-step exclusion of the unphysical degrees of freedom. An example using this Hamiltonian in which the zero modes play a role is the verification of the correct Coulomb potential between two heavy fermions
Fermion zero modes in the vortex background of a Chern-Simons-Higgs theory with a hidden sector
Lozano, Gustavo [Departamento de Física, FCEYN Universidad de Buenos Aires & IFIBA CONICET,Pabellón 1 Ciudad Universitaria, 1428 Buenos Aires (Argentina); Mohammadi, Azadeh [Departamento de Física, Universidade Federal da Paraíba,58.059-970, Caixa Postal 5.008, João Pessoa, PB (Brazil); Schaposnik, Fidel A. [Departamento de Física, Universidad Nacional de La Plata/IFLP/CICBA,CC 67, 1900 La Plata (Argentina)
2015-11-06
In this paper we study a 2+1 dimensional system in which fermions are coupled to the self-dual topological vortex in U(1)×U(1) Chern-Simons theory, where both U(1) gauge symmetries are spontaneously broken. We consider two Abelian Higgs scalars with visible and hidden sectors coupled to a fermionic field through three interaction Lagrangians, where one of them violates the fermion number. Using a fine tuning procedure, we could obtain the number of the fermionic zero modes which is equal to the absolute value of the sum of the vortex numbers in the visible and hidden sectors.
Fermion zero modes and the black-hole hypermultiplet with rigid supersymmetry
Brooks, R.; Kallosh, R.; Ortin, T.
1995-01-01
The gravitini zero modes riding on top of the extreme Reissner-Nordstroem black-hole solution of N=2 supergravity are shown to be normalizable. The gravitini and dilatini zero modes of axion-dilaton extreme black-hole solutions of N=4 supergravity are also given and found to have finite norms. These norms are duality invariant. The finiteness and positivity of the norms in both cases are found to be correlated with the Witten-Israel-Nester construction; however, we have replaced the Witten condition by the pure-spin-3/2 constraint on the gravitini. We compare our calculation of the norms with the calculations which provide the moduli space metric for extreme black holes. The action of the N=2 hypermultiplet with an off-shell central charge describes the solitons of N=2 supergravity. This action, in the Majumdar-Papapetrou multi-black-hole background, is shown to be N=2 rigidly supersymmetric
Minkowski, P.
1986-01-01
The metric and contorsion tensors are constructed which yield a combined Riemann curvature tensor of the form Rsup(+-)sub(μνsigmatau)=(1/2a 2 )(gsub(μsigma)gsub(νtau) - gsub(μtau)gsub(νsigma)+-√g epsilonsub(μνsigmatau)). The metric with euclidean signature (++++) describes a sphere S 4 with radius a, i.e. admits the isometry group O5. For selfdual (antiselfdual) curvature tensor the contorsion tensor is given by the antiselfdual (selfdual) instanton configuration with respect to the spin gauge group SU2sub(R) (SU2sub(L)). The selfdual (antiselfdual) Riemann tensor admits two covariantly constant right-handed (left-handed) spin 1/2 fermion zero modes, one J=1/2 and one J=3/2 right-handed (left-handed) multiplet corresponding to L=1, transforming as a pseudoreal representation of O4 (SU2sub(R(L))). The hermitean Dirac equation retains only the two constant chiral modes. (orig.)
Torsten Karzig
2013-11-01
Full Text Available One-dimensional topological superconductors are known to host Majorana zero modes at domain walls terminating the topological phase. Their non-Abelian nature allows for processing quantum information by braiding operations that are insensitive to local perturbations, making Majorana zero modes a promising platform for topological quantum computation. Motivated by the ultimate goal of executing quantum-information processing on a finite time scale, we study domain walls moving at a constant velocity. We exploit an effective Lorentz invariance of the Hamiltonian to obtain an exact solution of the associated quasiparticle spectrum and wave functions for arbitrary velocities. Essential features of the solution have a natural interpretation in terms of the familiar relativistic effects of Lorentz contraction and time dilation. We find that the Majorana zero modes remain stable as long as the domain wall moves at subluminal velocities with respect to the effective speed of light of the system. However, the Majorana bound state dissolves into a continuous quasiparticle spectrum after the domain wall propagates at luminal or even superluminal velocities. This relativistic catastrophe implies that there is an upper limit for possible braiding frequencies even in a perfectly clean system with an arbitrarily large topological gap. We also exploit our exact solution to consider domain walls moving past static impurities present in the system.
Topological zero modes in Monte Carlo simulations
Dilger, H.
1994-08-01
We present an improvement of global Metropolis updating steps, the instanton hits, used in a hybrid Monte Carlo simulation of the two-flavor Schwinger model with staggered fermions. These hits are designed to change the topological sector of the gauge field. In order to match these hits to an unquenched simulation with pseudofermions, the approximate zero mode structure of the lattice Dirac operator has to be considered explicitly. (orig.)
Zero modes and entanglement entropy
Yazdi, Yasaman K. [Perimeter Institute for Theoretical Physics,31 Caroline St. N., Waterloo, ON, N2L 2Y5 (Canada); Department of Physics and Astronomy, University of Waterloo,200 University Avenue West, Waterloo, ON, N2L 3G1 (Canada)
2017-04-26
Ultraviolet divergences are widely discussed in studies of entanglement entropy. Also present, but much less understood, are infrared divergences due to zero modes in the field theory. In this note, we discuss the importance of carefully handling zero modes in entanglement entropy. We give an explicit example for a chain of harmonic oscillators in 1D, where a mass regulator is necessary to avoid an infrared divergence due to a zero mode. We also comment on a surprising contribution of the zero mode to the UV-scaling of the entanglement entropy.
Topological field theory: zero-modes and renormalization
Ouvry, S.; Thompson, G.
1989-09-01
We address the issue of the non-triviality of the observables in various Topological Field Theories by means of the explicit introduction of the zero-modes into the BRST algebra. Supersymmetric quantum mechanics and Topological Yang-Mills theory are dealt with in detail. It is shown that due to the presence of fermionic zero-modes the BRST algebra may be dynamically broken leading to non trivial observables albeit the local cohomology being trivial. However the metric and coupling constant independence of the observables are still valid. A renormalization procedure is given that correctly incorporates the zero-modes. Particular attention is given to the conventional gauge fixing in Topological Yang-Mills theories, with emphasis on the geometrical character of the fields and their role in the non-triviality of the observables
Majorana Zero Modes in Graphene
P. San-Jose
2015-12-01
Full Text Available A clear demonstration of topological superconductivity (TS and Majorana zero modes remains one of the major pending goals in the field of topological materials. One common strategy to generate TS is through the coupling of an s-wave superconductor to a helical half-metallic system. Numerous proposals for the latter have been put forward in the literature, most of them based on semiconductors or topological insulators with strong spin-orbit coupling. Here, we demonstrate an alternative approach for the creation of TS in graphene-superconductor junctions without the need for spin-orbit coupling. Our prediction stems from the helicity of graphene’s zero-Landau-level edge states in the presence of interactions and from the possibility, experimentally demonstrated, of tuning their magnetic properties with in-plane magnetic fields. We show how canted antiferromagnetic ordering in the graphene bulk close to neutrality induces TS along the junction and gives rise to isolated, topologically protected Majorana bound states at either end. We also discuss possible strategies to detect their presence in graphene Josephson junctions through Fraunhofer pattern anomalies and Andreev spectroscopy. The latter, in particular, exhibits strong unambiguous signatures of the presence of the Majorana states in the form of universal zero-bias anomalies. Remarkable progress has recently been reported in the fabrication of the proposed type of junctions, which offers a promising outlook for Majorana physics in graphene systems.
The Hamiltonian of QED. Zero mode
Zastavenko, L.G.
1990-01-01
We start with the standard QED Lagrangian. New derivation of the spinor QED Hamiltonian is given. We have taken into account the zero mode. Our derivation is faultless from the point of view of gauge invariance. It gives important corrections to the standard QED Hamiltonian. Our derivation of the Hamiltonian can be generalized to the case of QCD. 5 refs
Universal Nonequilibrium Signatures of Majorana Zero Modes in Quench Dynamics
R. Vasseur
2014-10-01
Full Text Available The quantum evolution that occurs after a metallic lead is suddenly connected to an electron system contains information about the excitation spectrum of the combined system. We exploit this type of “quantum quench” to probe the presence of Majorana fermions at the ends of a topological superconducting wire. We obtain an algebraically decaying overlap (Loschmidt echo L(t=|⟨ψ(0|ψ(t⟩|^{2}∼t^{-α} for large times after the quench, with a universal critical exponent α=1/4 that is found to be remarkably robust against details of the setup, such as interactions in the normal lead, the existence of additional lead channels, or the presence of bound levels between the lead and the superconductor. As in recent quantum-dot experiments, this exponent could be measured by optical absorption, offering a new signature of Majorana zero modes that is distinct from interferometry and tunneling spectroscopy.
Curvature, zero modes and quantum statistics
Calixto, M [Departamento de Matematica Aplicada y EstadIstica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de AstrofIsica de AndalucIa, Apartado Postal 3004, 18080 Granada (Spain)
2006-08-18
We explore an intriguing connection between the Fermi-Dirac and Bose-Einstein statistics and the thermal baths obtained from a vacuum radiation of coherent states of zero modes in a second quantized (many-particle) theory on the compact O(3) and noncompact O(2, 1) isometry subgroups of the de Sitter and anti-de Sitter spaces, respectively. The high frequency limit is retrieved as a (zero-curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the vacuum energy density and the cosmological constant problem. (letter to the editor)
Zero modes in de Sitter background
Einhorn, Martin B. [Kavli Institute for Theoretical Physics, University of California,Santa Barbara, CA 93106-4030 (United States); Jones, D.R. Timothy [Kavli Institute for Theoretical Physics, University of California,Santa Barbara, CA 93106-4030 (United States); Dept. of Mathematical Sciences, University of Liverpool,Liverpool L69 3BX (United Kingdom)
2017-03-28
There are five well-known zero modes among the fluctuations of the metric of de Sitter (dS) spacetime. For Euclidean signature, they can be associated with certain spherical harmonics on the S{sup 4} sphere, viz., the vector representation 5 of the global SO(5) isometry. They appear, for example, in the perturbative calculation of the on-shell effective action of dS space, as well as in models containing matter fields. These modes are shown to be associated with collective modes of S{sup 4} corresponding to certain coherent fluctuations. When dS space is embedded in flat five dimensions E{sup 5}, they may be seen as a legacy of translation of the center of the S{sup 4} sphere. Rigid translations of the S{sup 4}-sphere on E{sup 5} leave the classical action invariant but are unobservable displacements from the point of view of gravitational dynamics on S{sup 4}. Thus, unlike similar moduli, the center of the sphere is not promoted to a dynamical degree of freedom. As a result, these zero modes do not signify the possibility of physically realizable fluctuations or flat directions for the metric of dS space. They are not associated with Killing vectors on S{sup 4} but can be identified with certain non-isometric, conformal Killing forms that locally correspond to a rescaling of the volume element dV{sub 4}. We frame much of our discussion in the context of renormalizable gravity, but, to the extent that they only depend upon the global symmetry of the background, the conclusions should apply equally to the corresponding zero modes found in Einstein gravity. Although their existence has only been demonstrated at one-loop, we expect that these zero modes will be present to all orders in perturbation theory. They will occur for Lorentzian signature as well, so long as the hyperboloid H{sup 4} is locally stable, but there remain certain infrared issues that need to be clarified. We conjecture that they will appear in any gravitational theory having dS background as a
Mode regularization of the supersymmetric sphaleron and kink: Zero modes and discrete gauge symmetry
Goldhaber, Alfred Scharff; Litvintsev, Andrei; Nieuwenhuizen, Peter van
2001-01-01
To obtain the one-loop corrections to the mass of a kink by mode regularization, one may take one-half the result for the mass of a widely separated kink-antikink (or sphaleron) system, where the two bosonic zero modes count as two degrees of freedom, but the two fermionic zero modes as only one degree of freedom in the sums over modes. For a single kink, there is one bosonic zero mode degree of freedom, but it is necessary to average over four sets of fermionic boundary conditions in order (i) to preserve the fermionic Z 2 gauge invariance ψ→-ψ, (ii) to satisfy the basic principle of mode regularization that the boundary conditions in the trivial and the kink sector should be the same, (iii) that the energy stored at the boundaries cancels and (iv) to avoid obtaining a finite, uniformly distributed energy which would violate cluster decomposition. The average number of fermionic zero-energy degrees of freedom in the presence of the kink is then indeed 1/2. For boundary conditions leading to only one fermionic zero-energy solution, the Z 2 gauge invariance identifies two seemingly distinct 'vacua' as the same physical ground state, and the single fermionic zero-energy solution does not correspond to a degree of freedom. Other boundary conditions lead to two spatially separated ω∼0 solutions, corresponding to one (spatially delocalized) degree of freedom. This nonlocality is consistent with the principle of cluster decomposition for correlators of observables
Boyle Peter
2018-01-01
Full Text Available We present results for the QED and strong isospin breaking corrections to the hadronic vacuum polarization using Nf = 2 + 1 Domain Wall fermions. QED is included in an electro-quenched setup using two different methods, a stochastic and a perturbative approach. Results and statistical errors from both methods are directly compared with each other.
Instantons and quark zero modes in AdS/QCD
Bechi, Jacopo
2009-01-01
In this paper the quark zero modes creation effect is studied in the context of the AdS/QCD approach. This effect is generated, in presence of instantons, by a new that can be added in the bulk.......In this paper the quark zero modes creation effect is studied in the context of the AdS/QCD approach. This effect is generated, in presence of instantons, by a new that can be added in the bulk....
Zero modes in discretized light-front quantization
Martinovic, E.
1997-01-01
The current understanding of the role of bosonic zero modes in field-theoretical models quantized at the equal light-front time is reviewed. After a brief discussion of the main features of the light-front field theories - in particular the simplicity of the physical vacuum - the light-front canonical formalism for the quantum electrodynamics and the Yukawa model is sketched. The zero mode of Maskawa and Yamawaki is reviewed. Reasons for the appearance of the constrained and/or dynamical zero modes are explained along with the subtleties of the gauge fixing in presence of boundary conditions. Perturbative treatment of the corresponding constraint equations in the Yukawa model and quantum electrodynamics (3+1) is outlined. The next topic is the manifestation of the symmetry breaking in the light-front field theory. A pattern of multiple solutions to the zero-mode constraint equations replacing physical picture of multiple vacua of the conventionally quantized field theories is illustrated on an example of 2-dimensional theory. The importance of a (regularized) constrained zero mode of the pion field for the consistency of the Nambu-Goldstone phase of the discretized light-front linear a/model is demonstrated. Finally, a non-trivial physical vacuum based on the dynamical zero mode is constructed for the two-dimensional light-front quantum electrodynamics. (authors)
Majorana zero modes in superconductor-semiconductor heterostructures
Lutchyn, R. M.; Bakkers, E. P. A. M.; Kouwenhoven, L. P.; Krogstrup, P.; Marcus, C. M.; Oreg, Y.
2018-05-01
Realizing topological superconductivity and Majorana zero modes in the laboratory is a major goal in condensed-matter physics. In this Review, we survey the current status of this rapidly developing field, focusing on proposals for the realization of topological superconductivity in semiconductor-superconductor heterostructures. We examine materials science progress in growing InAs and InSb semiconductor nanowires and characterizing these systems. We then discuss the observation of robust signatures of Majorana zero modes in recent experiments, paying particular attention to zero-bias tunnelling conduction measurements and Coulomb blockade experiments. We also outline several next-generation experiments probing exotic properties of Majorana zero modes, including fusion rules and non-Abelian exchange statistics. Finally, we discuss prospects for implementing Majorana-based topological quantum computation.
Majorana zero modes in Dirac semimetal Josephson junctions
Li, Chuan; de Boer, Jorrit; de Ronde, Bob; Huang, Yingkai; Golden, Mark; Brinkman, Alexander
We have realized proximity-induced superconductivity in a Dirac semimetal and revealed the topological nature of the superconductivity by the observation of Majorana zero modes. As a Dirac semimetal, Bi0.97Sb0.03 is used, where a three-dimensional Dirac cone exists in the bulk due to an accidental touching between conduction and valence bands. Electronic transport measurements on Hall-bars fabricated out of Bi0.97Sb0.03 flakes consistently show negative magnetoresistance for magnetic fields parallel to the current, which is associated with the chiral anomaly. In perpendicular magnetic fields, we see Shubnikov-de Haas oscillations that indicate very low carrier densities. The low Fermi energy and protection against backscattering in our Dirac semimetal Josephson junctions provide favorable conditions for a large contribution of Majorana zero modes to the supercurrent. In radiofrequency irradiation experiments, we indeed observe these Majorana zero modes in Nb-Bi0.97Sb0.03-Nb Josephson junctions as a 4 π periodic contribution to the current-phase relation.
On the zero mode of the Poisson gauge theory
Saidi, E.H.
1990-09-01
The fundamentals of the Diff(S 2 ) and the SDiff(S 2 ) gauge theories are developed. It is shown that the adjoint representation of SU(∞) is described by a divergentless two dimensional vector field defined on the sphere. The SU(∞) Yang-Mills gauge action obtained earlier by Floratos et al. is reviewed. The problem of the zero modes is solved without need of any constraint. The fundamental representations of SU(∞) and the gauge matter couplings are discussed. (author). 6 refs
Zero-energy modes, charge conjugation, and fermion number
Sudarshan, E.C.G.; Yajnik, U.A.
1986-01-01
States with a half-integer fermion number occur when a fermionic field coupled to a soliton possesses a zero mode. This paper spells out the circumstances under which one can retain an integer fermion number as also a charge-conjugation-invariant ground state. It is necessary to make the representation reducible but it is kept irreducible by introducing an additional operator
Fermions on the electroweak string
Moreno, J M; Quirós, Mariano; Moreno, J M; Oaknin, D H; Quiros, M
1995-01-01
We construct a simple class of exact solutions of the electroweak theory including the naked Z--string and fermion fields. It consists in the Z--string configuration (\\phi,Z_\\theta), the {\\it time} and z components of the neutral gauge bosons (Z_{0,3},A_{0,3}) and a fermion condensate (lepton or quark) zero mode. The Z--string is not altered (no feed back from the rest of fields on the Z--string) while fermion condensates are zero modes of the Dirac equation in the presence of the Z--string background (no feed back from the {\\it time} and z components of the neutral gauge bosons on the fermion fields). For the case of the n--vortex Z--string the number of zero modes found for charged leptons and quarks is (according to previous results by Jackiw and Rossi) equal to |n|, while for (massless) neutrinos is |n|-1. The presence of fermion fields in its core make the obtained configuration a superconducting string, but their presence (as well as that of Z_{0,3},A_{0,3}) does not enhance the stability of the Z--stri...
Zero-mode waveguide nanophotonic structures for single molecule characterization
Crouch, Garrison M.; Han, Donghoon; Bohn, Paul W.
2018-05-01
Single-molecule characterization has become a crucial research tool in the chemical and life sciences, but limitations, such as limited concentration range, inability to control molecular distributions in space, and intrinsic phenomena, such as photobleaching, present significant challenges. Recent developments in non-classical optics and nanophotonics offer promising routes to mitigating these restrictions, such that even low affinity (K D ~ mM) biomolecular interactions can be studied. Here we introduce and review specific nanophotonic devices used to support single molecule studies. Optical nanostructures, such as zero-mode waveguides (ZMWs), are usually fabricated in thin gold or aluminum films and serve to confine the observation volume of optical microspectroscopy to attoliter to zeptoliter volumes. These simple nanostructures allow individual molecules to be isolated for optical and electrochemical analysis, even when the molecules of interest are present at high concentration (µM–mM) in bulk solution. Arrays of ZMWs may be combined with optical probes such as single molecule fluorescence, single molecule fluorescence resonance energy transfer, and fluorescence correlation spectroscopy for distributed analysis of large numbers of single-molecule reactions or binding events in parallel. Furthermore, ZMWs may be used as multifunctional devices, for example by combining optical and electrochemical functions in a single discrete architecture to achieve electrochemical ZMWs. In this review, we will describe the optical properties, fabrication, and applications of ZMWs for single-molecule studies, as well as the integration of ZMWs into systems for chemical and biochemical analysis.
Symmetry-protected zero-mode laser with a tunable spatial profile
Ge, Li
Majorana zero modes in condense matter systems have attracted considerable interest in topological quantum computation. In contrast, while robust zero modes have been observed in various photonic lattices, it remains an open question whether they can be used for the same purpose. To advance significantly the state-of-the-art in zero-mode photonics, new inspirations are needed for a better design and control of photonic systems. Using the zero modes protected by non-Hermitian particle-hole symmetry in a photonic lattice and the spatial degrees of freedom they offer, we propose a single-mode, fixed-frequency, and spatially tunable zero-mode laser. The system does not need to have zero modes before a localized pump is applied; they are created by the spontaneous restoration of particle-hole symmetry. By modifying this process using different pump configurations, we present a versatile way to tune the spatial profile of our zero-mode laser, with its lasing frequency pinned at the zero energy. Such a zero-mode laser may find applications in telecommunication, where spatial encoding is held by some to be last frontier of signal processing. This project is supported by the NSF under Grant No. DMR-1506987.
Defect States Emerging from a Non-Hermitian Flatband of Photonic Zero Modes
Qi, Bingkun; Zhang, Lingxuan; Ge, Li
2018-03-01
We show the existence of a flatband consisting of photonic zero modes in a gain and loss modulated lattice system as a result of the underlying non-Hermitian particle-hole symmetry. This general finding explains the previous observation in parity-time symmetric systems where non-Hermitian particle-hole symmetry is hidden. We further discuss the defect states in these systems, whose emergence can be viewed as an unconventional alignment of a pseudospin under the influence of a complex-valued pseudomagnetic field. These defect states also behave as a chain with two types of links, one rigid in a unit cell and one soft between unit cells, as the defect states become increasingly localized with the gain and loss strength.
Fermion structures of state vectors of the Schwinger model with multi-fermions
Nakawaki, Yuji
1983-01-01
Coulomb-gauge Schwinger model with multi-fermions is formulated consistently in a box [-L, L] by introducing true dynamical degrees of freedom of electromagnetic fields, namely zero-mode part A 1 sup((0)) of A 1 and its canonical conjugate momentum π 1 sup((0)). State vectors are constructed of free massless fermion operators and zero-mode operators A 1 sup((0)) and π 1 sup((0)) and it is clarified how and why multifermion condensations become degenerate ground states and chiral invariance is spontaneously broken. It is also examined that physical space of covariant gauge Schwinger model is isomorphic to that of Coulomb-gauge Schwinger model. (author)
Fermions in the 5D Gravity-Scalar Standing Wave Braneworld
Gogberashvili, Merab; Midodashvili, Pavle
2014-01-01
In the article we investigate localization problem for spinor fields within the 5D standing wave braneworld with the bulk real scalar field and show that there exist normalizable fermion field zero modes on the brane.
Fermionic green function and functional determinant in QCD2
Nielsen, N.K.; Rothe, K.D.; Schroer, B.
1979-01-01
We obtain a closed representation for the QCD 2 fermion determinant, euclidean Green functions and induced current in generic external fields. In the absence of zero modes the results are representable as sums over tree diagrams which as we show, can also be obtained from the original Feynman perturbation series via resummation and integration over loop variables. We also investigate the modifications due to the presence of zero modes. (orig.)
Yukawa couplings and the nature of zero modes in the Skyrme model
Kawarabayashi, K.
1989-01-01
Several issues related, directly or indirectly, to the Yukawa coupling in the Skyrme model are discussed. The authors try to shed a new light on the physical nature of the zero modes associated with translation (rotation) invariance of the model
Dynamical instability induced by the zero mode under symmetry breaking external perturbation
Takahashi, J.; Nakamura, Y.; Yamanaka, Y.
2014-01-01
A complex eigenvalue in the Bogoliubov–de Gennes equations for a stationary Bose-Einstein condensate in the ultracold atomic system indicates the dynamical instability of the system. We also have the modes with zero eigenvalues for the condensate, called the zero modes, which originate from the spontaneous breakdown of symmetries. Although the zero modes are suppressed in many theoretical analyses, we take account of them in this paper and argue that a zero mode can change into one with a pure imaginary eigenvalue by applying a symmetry breaking external perturbation potential. This emergence of a pure imaginary mode adds a new type of scenario of dynamical instability to that characterized by the complex eigenvalue of the usual excitation modes. For illustration, we deal with two one-dimensional homogeneous Bose–Einstein condensate systems with a single dark soliton under a respective perturbation potential, breaking the invariance under translation, to derive pure imaginary modes. - Highlights: • Zero modes are important but ignored in many theories for the cold atomic system. • We discuss the zero mode under symmetry breaking potential in this system. • We consider the zero mode of translational invariance for a single dark soliton. • We show that it turns into an anomalous or pure imaginary mode
Theory of quantum dynamics in fermionic environment: an influence functional approach
Chen, Y.
1987-01-01
Quantum dynamics of a particle coupled to a fermionic environment is considered, with particular emphasis on the formulation of macroscopic quantum phenomena. The framework is based on a path integral formalism for the real-time density matrix. After integrating out of the fermion variables of the environment, they embed the whole environmental effects on the particle into the so-called influence functional in analogy to Feynman and Vernon's initial work. They then show that to the second order of the coupling constant, the exponent of the influence functional is in exact agreement with that due to a linear dissipative environment (boson bath). Having obtained this, they turn to a specific model in which the influence functional can be exactly evaluated in a long-term limit (long compared to the inverse of the cutoff frequency of the environmental spectrum). In this circumstance, they mainly address their attention to the quantum mechanical representation of the system-plus-environment from the known classical properties of the particle. It is shown that, in particular, the equivalence between the fermion bath and the boson bath is generally correct for a single-channel coupling provided they make a simple mapping between the nonlinear interaction functions of the baths. Finally, generalizations of the model to more complicated situations are discussed and significant applications and connections to certain practically interesting problems are mentioned
Extended Majorana zero modes in a topological superconducting-normal T-junction
Spånslätt, Christian; Ardonne, Eddy
2017-03-01
We investigate the sub gap properties of a three terminal Josephson T-junction composed of topologically superconducting wires connected by a normal metal region. This system naturally hosts zero energy Andreev bound states which are of self-conjugate Majorana nature and we show that they are, in contrast to ordinary Majorana zero modes, spatially extended in the normal metal region. If the T-junction respects time-reversal symmetry, we show that a zero mode is distributed only in two out of three arms in the junction and tuning the superconducting phases allows for transfer of the mode between the junction arms. We further provide tunneling conductance calculations showing that these features can be detected in experiments. Our findings suggest an experimental platform for studying the nature of spatially extended Majorana zero modes.
Study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge
Capri, M.A.L.; Guimaraes, M.S.; Lemes, V.E.R.; Sorella, S.P.; Tedesco, D.G.
2014-01-01
A study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge is presented in the case of the gauge group SU(2) and for different Euclidean space–time dimensions. Explicit examples of classes of normalizable zero modes and corresponding gauge field configurations are constructed by taking into account two boundary conditions, namely: (i) the finite Euclidean Yang–Mills action, (ii) the finite Hilbert norm. -- Highlights: •We study the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge. •For d=2 we obtain solutions with finite action but not finite Hilbert norm. •For d=3,4 we obtain solutions with finite action and finite Hilbert norm. •These results can be compared with those previously obtained in the Landau gauge
New (1+1)-dimension scalar field theories using supersymmetric zeros modes
Lima Rodrigues, R. de
1994-01-01
New non-liner models are constructed for (1+1)-dimension field theories from supersymmetric zero mode associated to the soliton. The kink simplest case is considered which is the double well potential of the λ φ 4 theory. (author). 3 refs
Zhang, Ya-Jing; Zhang, Lian-Lian; Jiang, Cui; Gong, Wei-Jiang
2018-02-01
We theoretically investigate the electronic transport through a parallel-coupled multi-quantum-dot system, in which the terminal dots of a one-dimensional quantum-dot chain are embodied in the two arms of an Aharonov-Bohm interferometer. It is found that in the structures of odd(even) dots, all their even(odd) molecular states have opportunities to decouple from the leads, and in this process antiresonance occurs which are accordant with the odd(even)-numbered eigenenergies of the sub-molecule without terminal dots. Next when Majorana zero modes are introduced to couple laterally to the terminal dots, the antiresonance and decoupling phenomena still co-exist in the quantum transport process. Such a result can be helpful in understanding the special influence of Majorana zero mode on the electronic transport through quantum-dot systems.
Canfora, Fabrizio; Giacomini, Alex; Oliva, Julio
2010-08-01
It is shown that on curved backgrounds, the Coulomb gauge Faddeev-Popov operator can have zero modes even in the Abelian case. These zero modes cannot be eliminated by restricting the path integral over a certain region in the space of gauge potentials. The conditions for the existence of these zero modes are studied for static spherically symmetric spacetimes in arbitrary dimensions. For this class of metrics, the general analytic expression of the metric components in terms of the zero modes is constructed. Such expression allows one to find the asymptotic behavior of background metrics, which induce zero modes in the Coulomb gauge, an interesting example being the three-dimensional anti-de Sitter spacetime. Some of the implications for quantum field theory on curved spacetimes are discussed.
Path-integral quantization of solitons using the zero-mode Feynman rule
Sung Sheng Chang
1978-01-01
We propose a direct expansion treatment to quantize solitons without collective coordinates. Feynman's path integral for a free particle subject to an external force is directly used as the generating functional for the zero-frequency mode. The generating functional has no infrared singularity and defines a zero-mode Feynman rule which also gives a correct perturbative expansion for the harmonic-oscillator Green's function by treating the quadratic potential as a perturbation. We use the zero-mode Feynman rule to calculate the energy shift due to the second-order quantum corrections for solitons. Our result agrees with previous predictions using the collective-coordinate method or the method of Goldstone and Jackiw
Dissecting zero modes and bound states on BPS vortices in Ginzburg-Landau superconductors
Izquierdo, A. Alonso [Departamento de Matematica Aplicada, Universidad de Salamanca,Facultad de Ciencias Agrarias y Ambientales,Av. Filiberto Villalobos 119, E-37008 Salamanca (Spain); Fuertes, W. Garcia [Departamento de Fisica, Universidad de Oviedo, Facultad de Ciencias,Calle Calvo Sotelo s/n, E-33007 Oviedo (Spain); Guilarte, J. Mateos [Departamento de Fisica Fundamental, Universidad de Salamanca, Facultad de Ciencias,Plaza de la Merced, E-37008 Salamanca (Spain)
2016-05-12
In this paper the zero modes of fluctuation of cylindrically symmetric self-dual vortices are analyzed and described in full detail. These BPS topological defects arise at the critical point between Type II and Type I superconductors, or, equivalently, when the masses of the Higgs particle and the vector boson in the Abelian Higgs model are equal. In addition, novel bound states of Higss and vector bosons trapped by the self-dual vortices at their core are found and investigated.
6d Dirac fermion on a rectangle; scrutinizing boundary conditions, mode functions and spectrum
Yukihiro Fujimoto
2017-09-01
Full Text Available We classify possible boundary conditions of a 6d Dirac fermion Ψ on a rectangle under the requirement that the 4d Lorentz structure is maintained, and derive the profiles and spectrum of the zero modes and nonzero KK modes under the two specific boundary conditions, (i 4d-chirality positive components being zero at the boundaries and (ii internal chirality positive components being zero at the boundaries. In the case of (i, twofold degenerated chiral zero modes appear which are localized towards specific directions of the rectangle pointed by an angle parameter θ. This leads to an implication for a new direction of pursuing the origin of three generations in the matter fields of the standard model, even though triple-degenerated zero modes are not realized in the six dimensions. When such 6d fermions couple with a 6d scalar with a vacuum expectation value, θ contributes to a mass matrix of zero-mode fermions consisting of Yukawa interactions. The emergence of the angle parameter θ originates from a rotational symmetry in the degenerated chiral zero modes on the rectangle extra dimensions since they do not feel the boundaries. In the case of (ii, this rotational symmetry is promoted to the two-dimensional conformal symmetry though no chiral massless zero mode appears. We also discuss the correspondence between our model on a rectangle and orbifold models in some details.
Majorana zero modes in the hopping-modulated one-dimensional p-wave superconducting model.
Gao, Yi; Zhou, Tao; Huang, Huaixiang; Huang, Ran
2015-11-20
We investigate the one-dimensional p-wave superconducting model with periodically modulated hopping and show that under time-reversal symmetry, the number of the Majorana zero modes (MZMs) strongly depends on the modulation period. If the modulation period is odd, there can be at most one MZM. However if the period is even, the number of the MZMs can be zero, one and two. In addition, the MZMs will disappear as the chemical potential varies. We derive the condition for the existence of the MZMs and show that the topological properties in this model are dramatically different from the one with periodically modulated potential.
Paul, Ganesh C.; Saha, Arijit; Das, Sourin
2018-05-01
We theoretically investigate the transport properties of a quasi-one-dimensional ferromagnet-superconductor junction where the superconductor consists of mixed singlet and triplet pairings. We show that the relative orientation of the Stoner field (h ˜) in the ferromagnetic lead and the d vector of the superconductor acts like a on-off switch for the zero bias conductance of the device. In the regime, where triplet pairing amplitude dominates over the singlet counterpart (topological phase), a pair of Majorana zero modes appear at each end of the superconducting part of the nanowire. When h ˜ is parallel or antiparallel to the d vector, transport gets completely blocked due to blockage in pairing while, when h ˜ and d are perpendicular to each other, the zero energy two terminal differential conductance spectra exhibits sharp transition from 4 e2/h to 2 e2/h as the magnetization strength in the lead becomes larger than the chemical potential indicating the spin-selective coupling of a pair of Majorana zero modes to the lead.
Zero-modes of non-Abelian solitons in three-dimensional gauge theories
Eto, Minoru; Gudnason, Sven Bjarke
2011-01-01
We study non-Abelian solitons of the Bogomol'nyi type in N=2 (d = 2 + 1) supersymmetric Chern-Simons (CS) and Yang-Mills (YM) theory with a generic gauge group. In CS theory, we find topological, non-topological and semi-local (non-)topological vortices of non-Abelian kinds in unbroken, broken and partially broken vacua. We calculate the number of zero-modes using an index theorem and then we apply the moduli matrix formalism to realize the moduli parameters. For the topological solitons we exhaust all the moduli while we study several examples of the non-topological and semi-local solitons. We find that the zero-modes of the topological solitons are governed by the moduli matrix H 0 only and those of the non-topological solitons are governed by both H 0 and the gauge invariant field Ω. We prove local uniqueness of the master equation in the YM case and finally compare all results between the CS and YM theories.
Shifman, M.; Yung, A.
2018-03-01
Non-Abelian strings are considered in non-supersymmetric theories with fermions in various appropriate representations of the gauge group U(N). We derive the electric charge quantization conditions and the index theorems counting fermion zero modes in the string background both for the left-handed and right-handed fermions. In both cases we observe a non-trivial N dependence.
Jackiw, R.; Massachusetts Inst. of Tech., Cambridge; Massachusetts Inst. of Tech., Cambridge
1984-01-01
The theory of fermion fractionization due to topologically generated fermion ground states is presented. Applications to one-dimensional conductors, to the MIT bag, and to the Hall effect are reviewed. (author)
arXiv Gauge Backgrounds and Zero-Mode Counting in F-Theory
Bies, Martin; Weigand, Timo
2017-11-14
Computing the exact spectrum of charged massless matter is a crucial step towards understanding the effective field theory describing F-theory vacua in four dimensions. In this work we further develop a coherent framework to determine the charged massless matter in F-theory compactified on elliptic fourfolds, and demonstrate its application in a concrete example. The gauge background is represented, via duality with M-theory, by algebraic cycles modulo rational equivalence. Intersection theory within the Chow ring allows us to extract coherent sheaves on the base of the elliptic fibration whose cohomology groups encode the charged zero-mode spectrum. The dimensions of these cohomology groups are computed with the help of modern techniques from algebraic geometry, which we implement in the software gap. We exemplify this approach in models with an Abelian and non-Abelian gauge group and observe jumps in the exact massless spectrum as the complex structure moduli are varied. An extended mathematical appendix gi...
Hadron spectrum in quenched lattice QCD and distribution of zero modes
Iwasaki, Yoichi
1989-01-01
I report the results of the calculation of the hadron spectrum with the standard one-plaquette gauge action on a 16 3 x48 lattice at β=5.85 in the quenched lattice QCD. The result remarkably agrees with that of quark potential models for the case where the quark mass is equal to or is larger than the strange quark mass, even when one uses the standard one-plaquette gauge action. This is contrary to what is stated in the literature. We clarify the reason of the discrepancy, paying close attention to systematic errors in numerical calculations. Further, I show the distribution of zero modes of quark matrix, both in the cases of a RG improved gauge action and the standard action, and discuss the difference between the two cases. (orig.)
On the zero mode problem of the light-cone quantization
Huang, Suzhou; Lin, Wei
1993-01-01
The light-cone quantization for theories involving arbitrarily interacting scalars is studied systematically. The zero mode, which plays a special role in the light-cone quantization, is treated explicitly. The arguments utilize a lattice regularization and the constrained path-integral method. It is shown, to all orders in coupling constants or the loop expansion, that the ghost fields, introduced to enforce the constraints, decouple from all the virtual processes in the infinite-volume limit. The only possibility for the light-cone quantization to deviate from the equal-time quantization is when the interaction is such that the bosonic ghost fields develop expectation values and consequently alter the location of the minimum point of the effective potential. 24 refs
Braids and phase gates through high-frequency virtual tunneling of Majorana zero modes
Gorantla, Pranay; Sensarma, Rajdeep
2018-05-01
Braiding of non-Abelian Majorana anyons is a first step towards using them in quantum computing. We propose a protocol for braiding Majorana zero modes formed at the edges of nanowires with strong spin-orbit coupling and proximity-induced superconductivity. Our protocol uses high-frequency virtual tunneling between the ends of the nanowires in a trijunction, which leads to an effective low-frequency coarse-grained dynamics for the system, to perform the braid. The braiding operation is immune to amplitude noise in the drives and depends only on relative phase between the drives, which can be controlled by the usual phase-locking techniques. We also show how a phase gate, which is necessary for universal quantum computation, can be implemented with our protocol.
Majorana fermion exchange in strictly one dimensional structures
Chiu, Ching-Kai; Vazifeh, M. M.; Franz, M.
2014-01-01
It is generally thought that adiabatic exchange of two identical particles is impossible in one spatial dimension. Here we describe a simple protocol that permits adiabatic exchange of two Majorana fermions in a one-dimensional topological superconductor wire. The exchange relies on the concept of "Majorana shuttle" whereby a $\\pi$ domain wall in the superconducting order parameter which hosts a pair of ancillary Majoranas delivers one zero mode across the wire while the other one tunnels in ...
Monopole-fermion systems in the complex isotropic tetrad formalism
Gal'tsov, D.V.; Ershov, A.A.
1988-01-01
The interaction of fermions of arbitrary isospin with regular magnetic monopoles and dyons of the group SU(2) and also with point gravitating monopoles and dyons of the Wu-Yang type described by the Reissner-Nordstrom metric are studied using the Newman-Penrose complex isotropic tetrad formalism. Formulas for the bound-state spectrum and explicit expressions for the zero modes are obtained and the Rubakov-Callan effect for black holes is discussed
Instanton induced compactification and fermion chirality
Randjbar-Daemi, S.; Strathdee, J.
1983-07-01
The question of fermion chirality in Kaluza-Klein theories with coupling to Yang-Mills fields is discussed. The argument is illustrated in eight dimensions where an SU(2) Yang-Mills field assumes the 1-instanton form on the internal space. This serves not only to trigger spontaneous compactification of the internal space but will ensure the emergence of nsub(L)-nsub(R)=2/3t(t+1) (2t+1) zero modes in an irreducible 8-spinor belonging to the (2t+1)-dimensional representation of SU(2). (author)
Gauge backgrounds and zero-mode counting in F-theory
Bies, Martin; Mayrhofer, Christoph; Weigand, Timo
2017-11-01
Computing the exact spectrum of charged massless matter is a crucial step towards understanding the effective field theory describing F-theory vacua in four dimensions. In this work we further develop a coherent framework to determine the charged massless matter in F-theory compactified on elliptic fourfolds, and demonstrate its application in a concrete example. The gauge background is represented, via duality with M-theory, by algebraic cycles modulo rational equivalence. Intersection theory within the Chow ring allows us to extract coherent sheaves on the base of the elliptic fibration whose cohomology groups encode the charged zero-mode spectrum. The dimensions of these cohomology groups are computed with the help of modern techniques from algebraic geometry, which we implement in the software gap. We exemplify this approach in models with an Abelian and non-Abelian gauge group and observe jumps in the exact massless spectrum as the complex structure moduli are varied. An extended mathematical appendix gives a self-contained introduction to the algebro-geometric concepts underlying our framework.
The fate of the zero mode of the five-dimensional kink in the presence of gravity
Shaposhnikov, Mikhail; Tinyakov, Petr; Zuleta, Katarzyna
2005-01-01
We investigate what becomes of the translational zero-mode of a five-dimensional domain wall in the presence of gravity, studying the scalar perturbations of a thick gravitating domain wall with AdS asymptotics and a well-defined zero-gravity limit. Our analysis reveals the presence of a wide resonance which can be seen as a remnant of the translational zero-mode present in the domain wall in the absence of gravity and which ensures a continuous change of the physical quantities (such as e.g. static potential between sources) when the Planck mass is sent to infinity. Provided that the thickness of the wall is much smaller than the AdS radius of the space-time, the parameters of this resonance do not depend on details of the domain wall's structure, but solely on the geometry of the space-time
Light-front zero-mode contribution to the Ward Identity
Sales, J.H.O.; Suzuki, A.T.
2010-01-01
In a covariant gauge we implicitly assume that the Green's function propagates information from one point of the space-time to another, so that the Green's function is responsible for the dynamics of the relativistic particle. In the light front form one would naively expect that this feature would be preserved. In this manner, the fermionic field propagator can be split into a propagating piece and a non-propagating ('contact') term. Since the latter ('contact') one does not propagate information, and therefore, supposedly can be discarded with no harm to the field dynamics we wanted to know what would be the impact of dropping it off. To do that, we investigated its role in the Ward identity in the light front. Here we use the terminology Ward identity to identify the limiting case of photon's zero momentum transfer in the vertex from the more general Ward-Takahashi identity with nonzero momentum transfer.
Chimento, L P; Forte, M; Devecchi, F P; Kremer, G M; Ribas, M O; Samojeden, L L
2011-01-01
In this work we review if fermionic sources could be responsible for accelerated periods during the evolution of a FRW universe. In a first attempt, besides the fermionic source, a matter constituent would answer for the decelerated periods. The coupled differential equations that emerge from the field equations are integrated numerically. The self-interaction potential of the fermionic field is considered as a function of the scalar and pseudo-scalar invariants. It is shown that the fermionic field could behave like an inflaton field in the early universe, giving place to a transition to a matter dominated (decelerated) period. In a second formulation we turn our attention to analytical results, specifically using the idea of form-invariance transformations. These transformations can be used for obtaining accelerated cosmologies starting with conventional cosmological models. Here we reconsider the scalar field case and extend the discussion to fermionic fields. Finally we investigate the role of a Dirac field in a Brans-Dicke (BD) context. The results show that this source, in combination with the BD scalar, promote a final eternal accelerated era, after a matter dominated period.
AdS5 black holes with fermionic hair
Burrington, Benjamin A.; Liu, James T.; Sabra, W. A.
2005-01-01
The study of new Bogomol'nyi-Prasad-Sommerfield (BPS) objects in AdS 5 has led to a deeper understanding of AdS/CFT. To help complete this picture, and to fully explore the consequences of the supersymmetry algebra, it is also important to obtain new solutions with bulk fermions turned on. In this paper we construct superpartners of the 1/2 BPS black hole in AdS 5 using a natural set of fermion zero modes. We demonstrate that these superpartners, carrying fermionic hair, have conserved charges differing from the original bosonic counterpart. To do so, we find the R-charge and dipole moment of the new system, as well as the mass and angular momentum, defined through the boundary stress tensor. The complete set of superpartners fits nicely into a chiral representation of AdS 5 supersymmetry, and the spinning solutions have the expected gyromagnetic ratio, g=1
Mizushima, T.; Machida, K.
2010-01-01
We investigate how the vortex-vortex separation changes Majorana zero modes in the vicinity of the BCS-BEC (Bose-Einstein condensation) topological phase transition of p-wave resonant Fermi gases. By analytically and numerically solving the Bogoliubov-de Gennes equation for spinless p-wave superfluids with plural vortices, it is demonstrated that the quasiparticle tunneling between neighboring vortices gives rise to the quantum oscillation of the low-lying spectra on the scale of the Fermi wavelength in addition to the exponential splitting. This rapid oscillation, which appears in the weak-coupling regime as a consequence of quantum oscillations of quasiparticle wave functions, disappears in the vicinity of the BCS-BEC topological phase transition. This is understandable from that the wave function of the Majorana zero modes is described by the modified Bessel function in the strong-coupling regime, and thus it becomes spread over the vortex core region. Due to the exponential divergence of the modified Bessel function, the concrete realization of the Majorana zero modes near the topological phase transition requires the neighboring vortices to be separated beyond the length scale defined by the coherence length and the dimensionless coupling constant. All these behaviors are also confirmed by carrying out the full numerical diagonalization of the nonlocal Bogoliubov-de Gennes equation in a two-dimensional geometry. Furthermore, this argument is expanded into the case of three-vortex systems, where a pair of core-bound and edge-bound Majorana states survive at zero-energy state regardless of the vortex separation.
Boudjema, F.; Djouadi, A.; Kneur, J.L.
1992-01-01
The production of excited fermions with mass above 100 GeV is considered. f→Vf (1) decay widths are calculated where V=γ, Z or W. Excited fermion pair production in e + e - annihilation and in γγ collisions, and single production in e + e - annihilation, eγ and γγ collisions is also discussed. Cross sections are calculated for all these cases. The discovery potential of the NLC at 500 GeV is compared with that of other colliders. (K.A.) 15 refs., 5 figs., 2 tabs
Randjbar-Daemi, S.
1995-12-01
The so-called doubling problem in the lattice description of fermions led to a proof that under certain circumstances chiral gauge theories cannot be defined on the lattice. This is called the no-go theorem. It implies that if Γ/sub/A is defined on a lattice then its infrared limit, which should correspond to the quantum description of the classical action for the slowly varying fields on lattice scale, is inevitably a vector like theory. In particular, if not circumvented, the no-go theorem implies that there is no lattice formulation of the Standard Weinberg-Salam theory or SU(5) GUT, even though the fermions belong to anomaly-free representations of the gauge group. This talk aims to explain one possible attempt at bypassing the no-go theorem. 20 refs
Randjbar-Daemi, S
1995-12-01
The so-called doubling problem in the lattice description of fermions led to a proof that under certain circumstances chiral gauge theories cannot be defined on the lattice. This is called the no-go theorem. It implies that if {Gamma}/sub/A is defined on a lattice then its infrared limit, which should correspond to the quantum description of the classical action for the slowly varying fields on lattice scale, is inevitably a vector like theory. In particular, if not circumvented, the no-go theorem implies that there is no lattice formulation of the Standard Weinberg-Salam theory or SU(5) GUT, even though the fermions belong to anomaly-free representations of the gauge group. This talk aims to explain one possible attempt at bypassing the no-go theorem. 20 refs.
Instantons, fermions and Chern-Simons terms
Collie, Benjamin; Tong, David
2008-01-01
In five spacetime dimensions, instantons are finite energy, solitonic particles. We describe the dynamics of these objects in the presence of a Chern-Simons interaction. For U(N) instantons, we show that the 5d Chern-Simons term induces a corresponding Chern-Simons term in the ADHM quantum mechanics. For SU(N) instantons, we provide a description in terms of geodesic motion on the instanton moduli space, modified by the presence of a magnetic field. We show that this magnetic field is equal to the first Chern character of an index bundle. All of these results are derived by a simple method which follows the fate of zero modes as fermions are introduced, made heavy, and subsequently integrated out.
Fermion masses through four-fermion condensates
Ayyar, Venkitesh [Department of Physics, Duke University,Science Drive, Durham, NC 27708 (United States); Chandrasekharan, Shailesh [Department of Physics, Duke University,Science Drive, Durham, NC 27708 (United States); Center for High Energy Physics, Indian Institute of Science,C.V. Raman Avenue, Bangalore, 560012 (India)
2016-10-12
Fermion masses can be generated through four-fermion condensates when symmetries prevent fermion bilinear condensates from forming. This less explored mechanism of fermion mass generation is responsible for making four reduced staggered lattice fermions massive at strong couplings in a lattice model with a local four-fermion coupling. The model has a massless fermion phase at weak couplings and a massive fermion phase at strong couplings. In particular there is no spontaneous symmetry breaking of any lattice symmetries in both these phases. Recently it was discovered that in three space-time dimensions there is a direct second order phase transition between the two phases. Here we study the same model in four space-time dimensions and find results consistent with the existence of a narrow intermediate phase with fermion bilinear condensates, that separates the two asymptotic phases by continuous phase transitions.
Higgs Phase in a Gauge U(1 Non-Linear CP1-Model. Two Species of BPS Vortices and Their Zero Modes
Alberto Alonso-Izquierdo
2016-09-01
Full Text Available In this paper, zero modes of fluctuation are dissected around the two species of BPS vortices existing in the critical Higgs phase, where the scalar and vector meson masses are equal, of a gauged U ( 1 nonlinear CP 1 -model. If 2 π n , n ∈ Z , is the quantized magnetic flux of the two species of BPS vortex solutions, 2 n linearly-independent vortex zero modes for each species are found and described. The existence of two species of moduli spaces of dimension 2 n of these stringy topological defects is thus locally shown.
Wilson Fermions with Four Fermion Interactions
Rantaharju, Jarno; Drach, Vincent; Hietanen, Ari
2015-01-01
We present a lattice study of a four fermion theory, known as Nambu Jona-Lasinio (NJL) theory, via Wilson fermions. Four fermion interactions naturally occur in several extensions of the Standard Model as a low energy parameterisation of a more fundamental theory. In models of dynamical electroweak...
Coupled fermion-kink system in Jackiw-Rebbi model
Amado, A.; Mohammadi, A.
2017-01-01
In this paper, we study Jackiw-Rebbi model, in which a massless fermion is coupled to the kink of λφ"4 theory through a Yukawa interaction. In the original Jackiw-Rebbi model, the soliton is prescribed. However, we are interested in the back-reaction of the fermion on the soliton besides the effect of the soliton on the fermion. Also, as a particular example, we consider a minimal supersymmetric kink model in (1 + 1) dimensions. In this case, the bosonic self-coupling, λ, and the Yukawa coupling between fermion and soliton, g, have a specific relation, g = √(λ/2). As the set of coupled equations of motion of the system is not analytically solvable, we use a numerical method to solve it self-consistently. We obtain the bound energy spectrum, bound states of the system and the corresponding shape of the soliton using a relaxation method, except for the zero mode fermionic state and threshold energies which are analytically solvable. With the aid of these results, we are able to show how the soliton is affected in general and supersymmetric cases. The results we obtain are consistent with the ones in the literature, considering the soliton as background. (orig.)
Self-dual gauge field, its quantum fluctuations, and interacting fermions
Flory, C.A.
1983-01-01
The quantum fluctuations about a self-dual background field in SU(2) are computed. The background field consists of parallel and equal uniform chromomagnetic and chromoelectric fields. Determination of the gluon fluctuations about this field yields zero modes, which are naturally regularized by the introduction of massless fermions. This regularization makes the integrals over all fluctuations convergent, and allows a simple computation of the vacuum energy which is shown to be lower than the energy of the configuration of zero field strength. The regularization of the zero modes also facilitates the introduction of heavy test charges which can interact with the classical background field and also exchange virtual quanta. The formalism for introducing these heavy test charges could be a good starting point for investigating the relevant physics of the self-dual background field beyond the classical level
Senjanovic, G.; Virginia Polytechnic Inst. and State Univ., Blacksburg
1984-07-01
Extended supersymmetry, Kaluza-Klein theory and family unification all suggest the existence of mirror fermions, with same quantum numbers but opposite helicities from ordinary fermions. The laboratory and especially cosmological implications of such particles are reviewed and summarized. (author)
Fermion flavor in the soft-wall AdS model
Gherghetta, Tony; Sword, Daniel
2009-01-01
The formalism for modeling multiple fermion generations in a warped extra dimension with a soft wall is presented. A bulk Higgs condensate is responsible for generating mass for the zero-mode fermions but leads to additional complexity from large mixing between different flavors. We extend existing single-generation analyses by considering new special cases in which analytical solutions can be derived. The general three-generation case is then treated using a simple numerical routine. Assuming anarchic 5D parameters, we find a fermion mass spectrum resembling the standard model quarks and leptons with highly degenerate couplings to Kaluza-Klein gauge bosons. This confirms that the soft-wall model has similar attractive features as that found in hard-wall models, providing a framework to generalize existing phenomenological analyses.
Moore, Christopher; Stanescu, Tudor D.; Tewari, Sumanta
2018-04-01
We show that a pair of overlapping Majorana bound states (MBSs) forming a partially separated Andreev bound state (ps-ABS) represents a generic low-energy feature in spin-orbit-coupled semiconductor-superconductor (SM-SC) hybrid nanowire in the presence of a Zeeman field. The ps-ABS interpolates continuously between the "garden variety" ABS, which consists of two MBSs sitting on top of each other, and the topologically protected Majorana zero modes (MZMs), which are separated by a distance given by the length of the wire. The really problematic ps-ABSs consist of component MBSs separated by a distance of the order of the characteristic Majorana decay length ξ , and have nearly zero energy in a significant range of control parameters, such as the Zeeman field and chemical potential, within the topologically trivial phase. Despite being topologically trivial, such ps-ABSs can generate signatures identical to MZMs in local charge tunneling experiments. In particular, the height of the zero-bias conductance peak (ZBCP) generated by ps-ABSs has the quantized value 2 e2/h , and it can remain unchanged in an extended range of experimental parameters, such as Zeeman field and the tunnel barrier height. We illustrate the formation of such low-energy robust ps-ABSs in two experimentally relevant situations: a hybrid SM-SC system consisting of a proximitized nanowire coupled to a quantum dot and the SM-SC system in the presence of a spatially varying inhomogeneous potential. We then show that, unlike local measurements, a two-terminal experiment involving charge tunneling at both ends of the wire is capable of distinguishing between the generic ps-ABSs and the non-Abelian MZMs. While the MZMs localized at the opposite ends of the wire generate correlated differential conduction spectra, including correlations in energy splittings and critical Zeeman fields associated with the emergence of the ZBCPs, such correlations are absent if the ZBCPs are due to ps-ABSs emerging in the
Classification of compactified su( N c ) gauge theories with fermions in all representations
Anber, Mohamed M.; Vincent-Genod, Loïc
2017-12-01
We classify su( N c ) gauge theories on R^3× S^1 with massless fermions in higher representations obeying periodic boundary conditions along S^1 . In particular, we single out the class of theories that is asymptotically free and weakly coupled in the infrared, and therefore, is amenable to semi-classical treatment. Our study is conducted by carefully identifying the vacua inside the affine Weyl chamber using Verma bases and Frobenius formula techniques. Theories with fermions in pure representations are generally strongly coupled. The only exceptions are the four-index symmetric representation of su(2) and adjoint representation of su( N c ). However, we find a plethora of admissible theories with fermions in mixed representations. A sub-class of these theories have degenerate perturbative vacua separated by domain walls. In particular, su( N c ) theories with fermions in the mixed representations adjoint⊕fundamental and adjoint⊕two-index symmetric admit degenerate vacua that spontaneously break the parity P , charge conjugation C , and time reversal T symmetries. These are the first examples of strictly weakly coupled gauge theories on R^3× S^1 with spontaneously broken C , P , and T symmetries. We also compute the fermion zero modes in the background of monopole-instantons. The monopoles and their composites (topological molecules) proliferate in the vacuum leading to the confinement of electric charges. Interestingly enough, some theories have also accidental degenerate vacua, which are not related by any symmetry. These vacua admit different numbers of fermionic zero modes, and hence, different kinds of topological molecules. The lack of symmetry, however, indicates that such degeneracy might be lifted by higher order corrections. Finally, we study the general phase structure of adjoint⊕fundamental theories in the small circle and decompactification limits.
Fermion production despite fermion number conservation
Bock, W.; Hetrick, J.E.; Smit, J.
1995-01-01
Lattice proposals for a nonperturbative formulation of the Standard Model easily lead to a global U(1) symmetry corresponding to exactly conserved fermion number. The absence of an anomaly in the fermion current would then appear to inhibit anomalous processes, such as electroweak baryogenesis in the early universe. One way to circumvent this problem is to formulate the theory such that this U(1) symmetry is explicitly broken. However we argue that in the framework of spectral flow, fermion creation and annihilation still in fact occurs, despite the exact fermion number conservation. The crucial observation is that fermions are excitations relative to the vacuum, at the surface of the Dirac sea. The exact global U(1) symmetry prohibits a state from changing its fermion number during time evolution, however nothing prevents the fermionic ground state from doing so. We illustrate our reasoning with a model in two dimensions which has axial-vector couplings, first using a sharp momentum cutoff, then using the lattice regulator with staggered fermions. The difference in fermion number between the time evolved state and the ground state is indeed in agreement with the anomaly. Both the sharp momentum cutoff and the lattice regulator break gauge invariance. In the case of the lattice model a mass counterterm for the gauge field is sufficient to restore gauge invariance in the perturbative regime. A study of the vacuum energy shows however that the perturbative counterterm is insufficient in a nonperturbative setting and that further quartic counterterms are needed. For reference we also study a closely related model with vector couplings, the Schwinger model, and we examine the emergence of the θ-vacuum structure of both theories. ((orig.))
Bravyi, Sergey; Terhal, Barbara M; Leemhuis, Bernhard
2010-01-01
We initiate the study of Majorana fermion codes (MFCs). These codes can be viewed as extensions of Kitaev's one-dimensional (1D) model of unpaired Majorana fermions in quantum wires to higher spatial dimensions and interacting fermions. The purpose of MFCs is to protect quantum information against low-weight fermionic errors, that is, operators acting on sufficiently small subsets of fermionic modes. We examine to what extent MFCs can surpass qubit stabilizer codes in terms of their stability properties. A general construction of 2D MFCs is proposed that combines topological protection based on a macroscopic code distance with protection based on fermionic parity conservation. Finally, we use MFCs to show how to transform any qubit stabilizer code to a weakly self-dual CSS code.
Chandrasekharan, Shailesh
2000-01-01
Cluster algorithms have been recently used to eliminate sign problems that plague Monte-Carlo methods in a variety of systems. In particular such algorithms can also be used to solve sign problems associated with the permutation of fermion world lines. This solution leads to the possibility of designing fermion cluster algorithms in certain cases. Using the example of free non-relativistic fermions we discuss the ideas underlying the algorithm
Lattice degeneracies of fermions
Raszillier, H.
1983-10-01
We present a detailed description of the minimal degeneracies of geometric (Kaehler) fermions on all the lattices of maximal symmetries in n = 1, ..., 4 dimensions. We also determine the isolated orbits of the maximal symmetry groups, which are related to the minimal numbers of ''naive'' fermions on the reciprocals of these lattices. It turns out that on the self-reciprocal lattices the minimal numbers of naive fermions are equal to the minimal numbers of degrees of freedom of geometric fermions. The description we give relies on the close connection of the maximal lattice symmetry groups with (affine) Weyl groups of root systems of (semi-) simple Lie algebras. (orig.)
Chiral fermions in asymptotically safe quantum gravity.
Meibohm, J; Pawlowski, J M
2016-01-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
Phantom cosmologies and fermions
Chimento, Luis P; Forte, Monica; Devecchi, Fernando P; Kremer, Gilberto M
2008-01-01
Form invariance transformations can be used for constructing phantom cosmologies starting with conventional cosmological models. In this work we reconsider the scalar field case and extend the discussion to fermionic fields, where the 'phantomization' process exhibits a new class of possible accelerated regimes. As an application we analyze the cosmological constant group for a fermionic seed fluid
Dynamical triangulated fermionic surfaces
Ambjoern, J.; Varsted, S.
1990-12-01
We perform Monte Carlo simulations of randomly triangulated random surfaces which have fermionic world-sheet scalars θ i associated with each vertex i in addition to the usual bosonic world-sheet scalar χ i μ . The fermionic degrees of freedom force the internal metrics of the string to be less singular than the internal metric of the pure bosonic string. (orig.)
Fermionic one-loop corrections to soliton energies in 1+1 dimensions
Graham, N.; Jaffe, R.L.
1999-01-01
We demonstrate an unambiguous and robust method for computing fermionic corrections to the energies of classical background field configurations. We consider the particular case of a sequence of background field configurations that interpolates continuously between the trivial vacuum and a widely separated soliton/antisoliton pair in 1+1 dimensions. Working in the continuum, we use phase shifts, the Born approximation, and Levinson's theorem to avoid ambiguities of renormalization procedure and boundary conditions. We carry out the calculation analytically at both ends of the interpolation and numerically in between, and show how the relevant physical quantities very continuously. In the process, we elucidate properties of the fermionic phase shifts and zero-modes
Transport properties of chiral fermions
Puhr, Matthias
2017-04-26
Anomalous transport phenomena have their origin in the chiral anomaly, the anomalous non-conservation of the axial charge, and can arise in systems with chiral fermions. The anomalous transport properties of free fermions are well understood, but little is known about possible corrections to the anomalous transport coefficients that can occur if the fermions are strongly interacting. The main goal of this thesis is to study anomalous transport effects in media with strongly interacting fermions. In particular, we investigate the Chiral Magnetic Effect (CME) in a Weyl Semimetal (WSM) and the Chiral Separation Effect (CSE) in finite-density Quantum Chromodynamics (QCD). The recently discovered WSMs are solid state crystals with low-energy excitations that behave like Weyl fermions. The inter-electron interaction in WSMs is typically very strong and non-perturbative calculations are needed to connect theory and experiment. To realistically model an interacting, parity-breaking WSM we use a tight-binding lattice Hamiltonian with Wilson-Dirac fermions. This model features a non-trivial phase diagram and has a phase (Aoki phase/axionic insulator phase) with spontaneously broken CP symmetry, corresponding to the phase with spontaneously broken chiral symmetry for interacting continuum Dirac fermions. We use a mean-field ansatz to study the CME in spatially modulated magnetic fields and find that it vanishes in the Aoki phase. Moreover, our calculations show that outside of the Aoki phase the electron interaction has only a minor influence on the CME. We observe no enhancement of the magnitude of the CME current. For our non-perturbative study of the CSE in QCD we use the framework of lattice QCD with overlap fermions. We work in the quenched approximation to avoid the sign problem that comes with introducing a finite chemical potential on the lattice. The overlap operator calls for the evaluation of the sign function of a matrix with a dimension proportional to the volume
Ozkendir, Osman Murat
2017-11-01
The influence of heavy fermion Ytterbium substitution was investigated on the crystal, electronic, and magnetic properties of CuFeO2 with the general formula Yb x Cu1- x FeO2. The results of the crystal structure study revealed polycrystalline formations in the sample. The electronic and magnetic properties of the samples were studied using X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) techniques. Both XAS and XMCD revealed that the substituted Yb atoms govern the entire phenomena with their narrow 4 f levels by forming broader molecular bonds with the 3 d levels of the transition metals. Owing to the prominent changes caused by the activity of the 4 f electrons in the crystal structures, Yb atoms were determined to be the main "role player" in the phase transitions. XMCD measurements were performed at room temperature 300 K (27 °C) to determine the magnetic properties of the samples and, except for CuFeO2 ( x = 0.0), the samples were observed to be ordered magnetically (mainly ferrimagnetic) in the bulk.
Fermion masses and multiplicity
Ramond, P.
1986-01-01
A general survey and analysis of fermion masses is presented in terms of both the known low energy gauge structure and of the simplest GUT structure. The replication of fermion families is discussed in the context of possible family group structures. Sample family gauge groups are presented in the cases of three and four chiral families, using ABJ and Witten anomalies to restrict the maximal gauged family group. The possible relevance of the family group to the fermion mass hierarchy is discussed in the context of various models. (author)
Iliesiu, Luca [Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (United States); Kos, Filip; Poland, David [Department of Physics, Yale University, New Haven, CT 06520 (United States); Pufu, Silviu S. [Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (United States); Simmons-Duffin, David [School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540 (United States); Yacoby, Ran [Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (United States)
2016-03-17
We study the conformal bootstrap for a 4-point function of fermions 〈ψψψψ〉 in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ×ψ OPE, and also on the central charge C{sub T}. We observe features in our bounds that coincide with scaling dimensions in the Gross-Neveu models at large N. We also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.
Fermion number in supersymmetric models
Mainland, G.B.; Tanaka, K.
1975-01-01
The two known methods for introducing a conserved fermion number into supersymmetric models are discussed. While the introduction of a conserved fermion number often requires that the Lagrangian be massless or that bosons carry fermion number, a model is discussed in which masses can be introduced via spontaneous symmetry breaking and fermion number is conserved at all stages without assigning fermion number to bosons. (U.S.)
Fermions from classical statistics
Wetterich, C.
2010-01-01
We describe fermions in terms of a classical statistical ensemble. The states τ of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability distribution can be associated to a quantum state for fermions. If the time evolution of the classical probabilities p τ amounts to a rotation of the wave function q τ (t)=±√(p τ (t)), we infer the unitary time evolution of a quantum system of fermions according to a Schroedinger equation. We establish how such classical statistical ensembles can be mapped to Grassmann functional integrals. Quantum field theories for fermions arise for a suitable time evolution of classical probabilities for generalized Ising models.
Superstrings fermionic solutions
Rausch de Traubenberg, M.
1990-06-01
The solutions proposed by the superstring theory are classified and compared. In order to obtain some of the equivalences, the demonstration is based on the coincidence of the excitation spectrum and the quantum numbers from different states. The fermionic representation of the heterotical strings is discussed. The conformal invariance and the supersymmetric results extended to two dimensions are investigated. Concerning the fermionic strings, the formalism and a phenomenological solution involving three families of quarks, chiral leptons and leptons from the E 6 gauge group are presented. The equivalence between real and complex fermions is discussed. The similarity between some of the solutions of the Wess-Zumino-Witten model and the orbifolds is considered. The formal calculation program developed for reproducing the theory's low energy spectra, in the fermionic string formalism is given [fr
Kamleh, W.; Leinweber, D.B.; Williams, A.G.
2004-01-01
The use of APE smearing or other blocking techniques in fermion actions can provide many advantages. There are many variants of these fat link actions in lattice QCD currently, such as FLIC fermions. The FLIC fermion formalism makes use of the APE blocking technique in combination with a projection of the blocked links back into the special unitary group. This reunitarisation is often performed using an iterative maximisation of a gauge invariant measure. This technique is not differentiable with respect to the gauge field and thus prevents the use of standard. Hybrid Monte Carlo simulation algorithms. The use of an alternative projection technique circumvents this difficulty and allows the simulation of dynamical fat link fermions with standard HMC and its variants
Fannes, Mark; Wouters, Jeroen
2012-01-01
We study a quantum process that can be considered as a quantum analogue for the classical Markov process. We specifically construct a version of these processes for free Fermions. For such free Fermionic processes we calculate the entropy density. This can be done either directly using Szeg\\"o's theorem for asymptotic densities of functions of Toeplitz matrices, or through an extension of said theorem to rates of functions, which we present in this article.
On the magnetoresistance of heavy fermion compounds
Lee Chengchung; Chen Chung
1992-09-01
Starting from two-conduction-band Anderson lattice model, the magneto-transport properties of heavy fermion systems are studied in the slave boson mean field theory. The residual magnetoresistivity induced by different kinds of impurities is calculated, and the experimentally detected positive maximum structure in the residual magnetoresistance of heavy fermion systems is reproduced. The transition of field-dependent resistivity from nonmonotonic to monotonic behaviour with increasing temperature can be explained naturally by including the charge fluctuation effect. The influence of applied pressure is also investigated. (author). 22 refs, 5 figs
Fermion masses from dimensional reduction
Kapetanakis, D.; Zoupanos, G.
1990-01-01
We consider the fermion masses in gauge theories obtained from ten dimensions through dimensional reduction on coset spaces. We calculate the general fermion mass matrix and we apply the mass formula in illustrative examples. (orig.)
Fermion masses from dimensional reduction
Kapetanakis, D. (National Research Centre for the Physical Sciences Democritos, Athens (Greece)); Zoupanos, G. (European Organization for Nuclear Research, Geneva (Switzerland))
1990-10-11
We consider the fermion masses in gauge theories obtained from ten dimensions through dimensional reduction on coset spaces. We calculate the general fermion mass matrix and we apply the mass formula in illustrative examples. (orig.).
Smith, J.L.; Cooke, D.W.
1986-01-01
The heavy-fermion ground state occurs in a few select metallic compounds as a result of interactions between f-electron and conduction-electron spins. A characteristically large electronic heat capacity at low temperature indicates that the effective electron mass of these materials is more than two orders of magnitude greater than that expected for a free-electron metal. This heavy-fermion ground state can become superconducting or antiferromagnetic, exhibiting very unusual properties. These materials and the role of muon spin rotation in their study are briefly discussed
Moessner, Roderich
Condensed matter systems provide emergent mini-universes in which quasiparticles may exist which do not correspond to any experimentally detected elementary particle. Topological quantum materials have been particularly productive in this regard, with the present search focussing on Majorana fermions, known theoretically already for decades. Here, we discuss manifestations of magnetic Majorana fermions in the Kitaev model. We place particular emphasis on their fate when perturbations, such as Heisenberg terms, are added to the ideal model system, and address experimental signatures of their vestiges in phases adjacent to the spin liquid.
Kalloniatis, A.C.
1996-01-01
SU(2) Yang-Mills theory coupled to massive adjoint scalar matter is studied in 1+1 dimensions using discretized light-cone quantization. This theory can be obtained from pure Yang-Mills theory in 2+1 dimensions via dimensional reduction. On the light cone, the vacuum structure of this theory is encoded in the dynamical zero mode of a gluon and a constrained mode of the scalar field. The latter satisfies a linear constraint, suggesting no nontrivial vacua in the present paradigm for symmetry breaking on the light cone. I develop a diagrammatic method to solve the constraint equation. In the adiabatic approximation I compute the quantum-mechanical potential governing the dynamical gauge mode. Because of a condensation of the lowest momentum modes of the dynamical gluons, a centrifugal barrier is generated in the adiabatic potential. In the present theory, however, the barrier height appears too small to make any impact in this model. Although the theory is superrenormalizable on naive power-counting grounds, the removal of ultraviolet divergences is nontrivial when the constrained mode is taken into account. The solution of this problem is discussed. copyright 1996 The American Physical Society
Molecular dynamics for fermions
Feldmeier, H.; Schnack, J.
2000-02-01
The time-dependent variational principle for many-body trial states is used to discuss the relation between the approaches of different molecular dynamics models to describe indistinguishable fermions. Early attempts to include effects of the Pauli principle by means of nonlocal potentials as well as more recent models which work with antisymmetrized many-body states are reviewed under these premises. (orig.)
Renormalization of fermion mixing
Schiopu, R.
2007-01-01
Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by
Renormalization of fermion mixing
Schiopu, R.
2007-05-11
Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by
Kauffman, L.; Saleur, H.
1991-01-01
Various aspects of knot theory are discussed when fermionic degrees of freedom are taken into account in the braid group representations and in the state models. It is discussed how the R matrix for the Alexander polynomial arises from the Fox differential calculus, and how it is related to the quantum group U q gl(1,1). New families of solutions of the Yang Baxter equation obtained from ''linear'' representations of the braid group and exterior algebra are investigated. State models associated with U q sl(n,m), and in the case n=m=1 a state model for the multivariable Alexander polynomial are studied. Invariants of links in solid handlebodies are considered and it is shown how the non trivial topology lifts the boson fermion degeneracy is present in S 3 . (author) 36 refs
Grensing, G.
2002-01-01
The path integral for ghost fermions, which is heuristically made use of in the Batalin-Fradkin-Vilkovisky approach to quantization of constrained systems, is derived from first principles. The derivation turns out to be rather different from that of physical fermions since the definition of Dirac states for ghost fermions is subtle. With these results at hand, it is then shown that the nonminimal extension of the Becchi-Rouet-Stora-Tyutin operator must be chosen differently from the notorious choice made in the literature in order to avoid the boundary terms that have always plagued earlier treatments. Furthermore it is pointed out that the elimination of states with nonzero ghost number requires the introduction of a thermodynamic potential for ghosts; the reason is that Schwarz's Lefschetz formula for the partition function of the time-evolution operator is not capable, despite claims to the contrary, to get rid of nonzero ghost number states on its own. Finally, we comment on the problems of global topological nature that one faces in the attempt to obtain the solutions of the Dirac condition for physical states in a configuration space of nontrivial geometry; such complications give rise to anomalies that do not obey the Wess-Zumino consistency conditions. (orig.)
Interacting composite fermions
nrc762, nrc762
2016-01-01
Numerical studies by Wójs, Yi, and Quinn have suggested that an unconventional fractional quantum Hall effect is plausible at filling factors ν=1/3 and 1/5, provided the interparticle interaction has an unusual form for which the energy of two fermions in the relative angular momentum three channel...... as fractional quantum Hall effect of electrons at ν=4/11, 4/13, 5/13, and 5/17. I investigate in this article the nature of the fractional quantum Hall states at ν=4/5, 5/7, 6/17, and 6/7, which correspond to composite fermions at ν∗=4/3, 5/3, and 6/5, and find that all these fractional quantum Hall states...... are conventional. The underlying reason is that the interaction between composite fermions depends substantially on both the number and the direction of the vortices attached to the electrons. I also study in detail the states with different spin polarizations at 6/17 and 6/7 and predict the critical Zeeman...
Hidden conformal symmetry in Randall–Sundrum 2 model: Universal fermion localization by torsion
G. Alencar
2017-10-01
Full Text Available In this manuscript we describe a hidden conformal symmetry of the second Randall–Sundrum model (RS2. We show how this can be used to localize fermions of both chiralities. The conformal symmetry leaves few free dimensionless constants and constrains the allowed interactions. In this formulation the warping of the extra dimension emerges from a partial breaking of the conformal symmetry in five dimensions. The solution of the system can be described in two alternative gauges: by the metric or by the conformon. By considering this as a fundamental symmetry we construct a conformally invariant action for a vector field which provides a massless photon localized over a Minkowski brane. This is obtained by a conformal non-minimal coupling that breaks the gauge symmetry in five dimensions. We further consider a generalization of the model by including conformally invariant torsion. By coupling torsion non-minimally to fermions we obtain a localized zero mode of both chiralities completing the consistence of the model. The inclusion of torsion introduces a fermion quartic interaction that can be used to probe the existence of large extra dimensions and the validity of the model. This seems to point to the fact that conformal symmetry may be more fundamental than gauge symmetry and that this is the missing ingredient for the full consistence of RS scenarios.
Miao, Jian-Jian; Jin, Hui-Ke; Zhang, Fu-Chun; Zhou, Yi
2018-01-11
We study Kitaev model in one-dimension with open boundary condition by using exact analytic methods for non-interacting system at zero chemical potential as well as in the symmetric case of Δ = t, and by using density-matrix-renormalization-group method for interacting system with nearest neighbor repulsion interaction. We suggest and examine an edge correlation function of Majorana fermions to characterize the long range order in the topological superconducting states and study the phase diagram of the interating Kitaev chain.
Fermion masses from superstrings
Tanaka, K.
1986-01-01
It is assumed that the E 8 gauge group of the E 8 x E 8 heterotic superstring can be broken into SO(10) x SU(4). The mass relations among fermions m/sub u//m/sub d/ = m/sub c//m/sub s/ = m/sub t//m/sub b/ and m/sub ν e//m/sub e/ = m/sub ν mu//m/sub μ/ = m/sub ν tau//m/sub tau/ are discussed. 18 refs
Heavy fermion and actinide materials
1993-01-01
During this period, 1/N expansions have been systematically applied to the calculation of the properties of highly correlated electron systems. These studies include examinations of (a) the class of materials known as heavy fermion semi-conductors, (b) the high energy spectra of heavy fermion systems, and (c) the doped oxide superconductors
Fermion fractionization and index theorem
Hirayama, Minoru; Torii, Tatsuo
1982-01-01
The relation between the fermion fractionization and the Callias-Bott-Seeley index theorem for the Dirac operator in the open space of odd dimension is clarified. Only the case of one spatial dimension is discussed in detail. Sum rules for the expectation values of various quantities in fermion-fractionized configurations are derived. (author)
Phenomenology of colour exotic fermions
Luest, D.
1986-01-01
The authors discuss the phenomenological consequences of a dynamical scenario according to which the electroweak symmetry breaking and generation of fermion masses is due to fermions that transform under high colour representations. Particular emphasis is given to the predictions for rare processes and to the spectrum of high colour boundstates. (Auth.)
Coulomb’s law corrections and fermion field localization in a tachyonic de Sitter thick braneworld
Cartas-Fuentevilla, Roberto; Escalante, Alberto; Germán, Gabriel; Herrera-Aguilar, Alfredo; Mora-Luna, Refugio Rigel
2016-01-01
Following recent studies which show that it is possible to localize gravity as well as scalar and gauge vector fields in a tachyonic de Sitter thick braneworld, we investigate the solution of the gauge hierarchy problem, the localization of fermion fields in this model, the recovering of the Coulomb law on the non-relativistic limit of the Yukawa interaction between bulk fermions and gauge bosons localized in the brane, and confront the predicted 5D corrections to the photon mass with its upper experimental/observational bounds, finding the model physically viable since it passes these tests. In order to achieve the latter aims we first consider the Yukawa interaction term between the fermionic and the tachyonic scalar fields MF(T)ΨΨ-bar in the action and analyze four distinct tachyonic functions F(T) that lead to four different structures of the respective fermionic mass spectra with different physics. In particular, localization of the massless left-chiral fermion zero mode is possible for three of these cases. We further analyze the phenomenology of these Yukawa interactions among fermion fields and gauge bosons localized on the brane and obtain the crucial and necessary information to compute the corrections to Coulomb’s law coming from massive KK vector modes in the non-relativistic limit. These corrections are exponentially suppressed due to the presence of the mass gap in the mass spectrum of the bulk gauge vector field. From our results we conclude that corrections to Coulomb’s law in the thin brane limit have the same form (up to a numerical factor) as far as the left-chiral massless fermion field is localized on the brane. Finally we compute the corrections to the Coulomb’s law for an arbitrarily thick brane scenario which can be interpreted as 5D corrections to the photon mass. By performing consistent estimations with brane phenomenology, we found that the predicted corrections to the photon mass, which are well bounded by the experimentally
Coulomb’s law corrections and fermion field localization in a tachyonic de Sitter thick braneworld
Cartas-Fuentevilla, Roberto; Escalante, Alberto [Instituto de Física, Benemérita Universidad Autónoma de Puebla,Apdo. postal J-48, 72570 Puebla, Pue. (Mexico); Germán, Gabriel [Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México,Apdo. Postal 48-3, 62251 Cuernavaca, Morelos (Mexico); Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road,Oxford, OX1 3NP (United Kingdom); Herrera-Aguilar, Alfredo [Instituto de Física, Benemérita Universidad Autónoma de Puebla,Apdo. postal J-48, 72570 Puebla, Pue. (Mexico); Institutode Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo,Edificio C-3, Ciudad Universitaria, CP 58040, Morelia, Michoacán (Mexico); Mora-Luna, Refugio Rigel [Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México,Apdo. Postal 48-3, 62251 Cuernavaca, Morelos (Mexico)
2016-05-11
Following recent studies which show that it is possible to localize gravity as well as scalar and gauge vector fields in a tachyonic de Sitter thick braneworld, we investigate the solution of the gauge hierarchy problem, the localization of fermion fields in this model, the recovering of the Coulomb law on the non-relativistic limit of the Yukawa interaction between bulk fermions and gauge bosons localized in the brane, and confront the predicted 5D corrections to the photon mass with its upper experimental/observational bounds, finding the model physically viable since it passes these tests. In order to achieve the latter aims we first consider the Yukawa interaction term between the fermionic and the tachyonic scalar fields MF(T)ΨΨ-bar in the action and analyze four distinct tachyonic functions F(T) that lead to four different structures of the respective fermionic mass spectra with different physics. In particular, localization of the massless left-chiral fermion zero mode is possible for three of these cases. We further analyze the phenomenology of these Yukawa interactions among fermion fields and gauge bosons localized on the brane and obtain the crucial and necessary information to compute the corrections to Coulomb’s law coming from massive KK vector modes in the non-relativistic limit. These corrections are exponentially suppressed due to the presence of the mass gap in the mass spectrum of the bulk gauge vector field. From our results we conclude that corrections to Coulomb’s law in the thin brane limit have the same form (up to a numerical factor) as far as the left-chiral massless fermion field is localized on the brane. Finally we compute the corrections to the Coulomb’s law for an arbitrarily thick brane scenario which can be interpreted as 5D corrections to the photon mass. By performing consistent estimations with brane phenomenology, we found that the predicted corrections to the photon mass, which are well bounded by the experimentally
Hulet, R.
1999-01-01
At the quantum level, particles behave very differently depending on whether their spin angular momentum is an integer or a half-integer. Half-integer spin particles are known as fermions, and include all the constituents of atoms: electrons, protons and neutrons. Bosons, on the other hand, are particles with integer spin, such as photons. Atoms are fermions if they are composed of an odd number of particles, like helium-3 or lithium-6. If they have an even number of constituents, like hydrogen, helium-4 or lithium-7, they are known as bosons. Fermions and bosons behave in profoundly different ways under certain conditions, especially at low temperatures. Four years ago, physicists created a Bose condensate, a quantum degenerate gas of bosons. Now the race is on to do the same with fermions. Deborah Jin's group at the US National Institute of Standards and Technology (NIST) and the University of Colorado has cooled a fermion gas to the lowest temperature yet (B DeMarco 1999 Phys. Rev. Lett. 82 4208). And John Thomas and co-workers at Duke University have set a new record for the length of time that fermions can be trapped using lasers (K O'Hara 1999 Phys. Rev. Lett. 82 4204). In this article the author describes the latest advances in the race to create a quantum degenerate gas of fermions. (UK)
Dynamical symmetries for fermions
Guidry, M.
1989-01-01
An introduction is given to the Fermion Dynamical Symmetry Model (FDSM). The analytical symmetry limits of the model are then applied to the calculation of physical quantities such as ground-state masses and B(E 2 ) values in heavy nuclei. These comparisons with data provide strong support for a new principle of collective motion, the Dynamical Pauli Effect, and suggest that dynamical symmetries which properly account for the pauli principle are much more persistent in nuclear structure than the corresponding boson symmetries. Finally, we present an assessment of criticisms which have been voiced concerning the FDSM, and a discussion of new phenomena and ''exotic spectroscopy'' which may be suggested by the model. 14 refs., 8 figs., 4 tabs
Fermions and non-Abelian vortex
Mello, E.R.B. de.
1986-01-01
Some aspectos of the fermion-non-Abelian vortex system are discussed. It is shown that this system presents properties analogous to the fermion-non-Abelian magnetic monopole one. But, differrently from the fermion-monopole case, this system does not present fermion condensate V = 0. (Author) [pt
Low energy fermion number violation
Peccei, R.D.
1989-01-01
After a brief aside on charge quantization in the standard electroweak theory, I concentrate on various aspects of anomaly induced fermion number violation in the standard model. A critical analysis of the role of sphalerons for the universe's baryon asymmetry is presented and the importance of calculating directly fermion number violating Green's functions is stressed. A physical interpretation of the recent observation of Ringwald, that coherent effects in the electroweak theory lead to catastrophic fermion number violation at 100 TeV, is discussed. Possible quantum effects which might spoil this semi-classical picture are examined
Lattice degeneracies of geometric fermions
Raszillier, H.
1983-05-01
We give the minimal numbers of degrees of freedom carried by geometric fermions on all lattices of maximal symmetries in d = 2, 3, and 4 dimensions. These numbers are lattice dependent, but in the (free) continuum limit, part of the degrees of freedom have to escape to infinity by a Wilson mechanism built in, and 2sup(d) survive for any lattice. On self-reciprocal lattices we compare the minimal numbers of degrees of freedom of geometric fermions with the minimal numbers of naive fermions on these lattices and argue that these numbers are equal. (orig.)
Probabilistic simulation of fermion paths
Zhirov, O.V.
1989-01-01
Permutation symmetry of fermion path integral allows (while spin degrees of freedom are ignored) to use in its simulation any probabilistic algorithm, like Metropolis one, heat bath, etc. 6 refs., 2 tabs
Super boson-fermion correspondence
Kac, V.G.; Leur van de, J.W.
1987-01-01
Since the pioneering work of Skyrme, the boson-fermion correspondence has been playing an increasingly important role in 2-dimensional quantum field theory. More recently, it has become an important ingredient in the work of the Kyoto school on the KP hierarchy of soliton equations. In the present paper we establish a super boson-fermion correspondence, having in mind its applications to super KP hierarchies
Fermion-scalar conformal blocks
Iliesiu, Luca [Joseph Henry Laboratories, Princeton University,Washington Road, Princeton, NJ 08544 (United States); Kos, Filip [Department of Physics, Yale University,217 Prospect Street, New Haven, CT 06520 (United States); Poland, David [Department of Physics, Yale University,217 Prospect Street, New Haven, CT 06520 (United States); School of Natural Sciences, Institute for Advanced Study,1 Einstein Dr, Princeton, New Jersey 08540 (United States); Pufu, Silviu S. [Joseph Henry Laboratories, Princeton University,Washington Road, Princeton, NJ 08544 (United States); Simmons-Duffin, David [School of Natural Sciences, Institute for Advanced Study,1 Einstein Dr, Princeton, New Jersey 08540 (United States); Yacoby, Ran [Joseph Henry Laboratories, Princeton University,Washington Road, Princeton, NJ 08544 (United States)
2016-04-13
We compute the conformal blocks associated with scalar-scalar-fermion-fermion 4-point functions in 3D CFTs. Together with the known scalar conformal blocks, our result completes the task of determining the so-called ‘seed blocks’ in three dimensions. Conformal blocks associated with 4-point functions of operators with arbitrary spins can now be determined from these seed blocks by using known differential operators.
Highly imbalanced fermion-fermion mixtures in one dimension
Recher, Christian
2013-01-01
In the framework of exactly solvable quantum many-body systems we study models of interacting spin one-half Fermions in one dimension. The first part deals with systems of spin one-half Fermions which interact via repulsive contact interaction. A reformulation of the Bethe-Ansatz solvable many-body wave function is presented. This simplifies considerably the calculations for the highly imbalanced case, where very few particles of one species (minority Fermions) are present. For the other particle species (majority Fermions) the thermodynamic limit is taken. We assume the majority Fermions to be in the ground state such that their non-interacting momentum distribution is a Fermi-sea. Upon this we consider excitations where the particles of the minority species may occupy an arbitrary state within the Fermi-sea. In the case of only a single minority Fermion, the many-body wave function can be expressed as a determinant. This allows us to derive exact thermodynamic expressions for several expectation values as well as for the density-density correlation function. Moreover it is possible to find closed expressions for the single particle Green's function. All of the above mentioned quantities show a non-trivial dependence on the minority particle's momentum. In particular the Green's function in the Tonks-Girardeau regime of hardcore interaction is shown to undergo a transition from the one of impenetrable Bosons to that of free Fermions as the extra particle's momentum varies from the core to the edge of the Fermi-sea. This transition becomes manifest in an algebraic asymptotic decay of the Green's function. If two minority Fermions are present, the many-body wave function turns out to be more complicated. Nevertheless it is possible to derive exact expressions for the two and the three particle density-density correlation functions. Furthermore we calculate the system's total energy and based on that, identify terms which have a natural
Cut-off parameters in the one-dimensional two-fermion model
Apostol, M.
1982-07-01
It is shown that the usual cut-off procedure (α cut-off parameter) employed in the boson representation of the fermion field opepators of the one-djmensional two-fermion model (TFM) is an incorrect one as the computator of the hermitean-conjugate field operators at the same space-point fails to fulfil a certain relationship which was pointed out long ago by Jordan. The complete form of the boson representation (including the zero-mode) of a single fermion field and the correct values of the cut-off parameter α is reviewed following Jordan and generalized to the TFM. The cut-off parameter α corresponds to a bandwidth cut-off and Jordan's boson representation is exact only in the limit α → 0. The additional zero-mode terms make the exact solution of the backscattering and umklapp scattering problem to be valid only if a supplementary condition is imposed on the coupling constants. Using the present bosonization technique all the inconsistencies of the TFM are removed. The one-particle Green's function and response functions of the Tomonaga-Luttinger model (TLM) are calculated and found to be identical with those obtained by direct diagram summation. The energy gap appearing in the spectrum of the TFM with backscattering and umklapp scattering for certain values of the coupling constants is shown to be proportional to the momentum transfer cut-off γ -1 which has to be kept finite while α goes to zero. Under such conditions the anticommunication relations and Jordan's commutator are invariant under the canonical transformation on the boson operators that diagonalizes the Hamiltonian of the TLM. The charge-density response function of the TFM with backscattering is perturbationally calculated up to the first order. The cut-off α -1 applies in the same way to terms which differ only by their spin indices in the expression of this response function. The charge-density response function is also evaluated at low frequencies for the exactly soluble TFM with
Dual fermion approach to disordered correlated systems
Haase, Patrick
2015-01-01
Disorder is ubiquitous in real materials and influences the physical properties like the conductivity to varying degrees. If electron-electron interactions are strong, theoretical and numerical treatment of these systems becomes challenging. In this thesis a numerical approach is developed to address these systems, treating both interactions and disorder on equal footing. The approach is based on the dual fermion approach for interacting systems developed by Rubtsov et al. Terletska et al. applied the ideas of the dual fermion approach to disordered non-interacting systems. In this approach, the replica trick is used to integrate out the disorder in favor of an effective electron-electron interaction. We extended the approach from Terletska et al. to treat disordered interacting systems. Dual Fermions allow to take into account non-local fluctuations by means of a perturbative expansion around an impurity problem. The impurity reference system is determined self-consistently, analogously to the dynamical mean-field theory. The perturbative expansion is expected to yield good results for small and large values of interaction strength and disorder. A priori, it is not clear what to expect for intermediate values, but experience shows that oftentimes good results are obtained for this region. An advantage of the dual fermion approach is that there is no sign-problem for a single orbital model if quantum Monte Carlo is used to solve the interacting reference system. Additionally, perturbation theory is usually numerically much cheaper than fully solving an interacting lattice or cluster problem. Thus, the dual fermion approach allows to address regions of parameter space that are not accessible to lattice quantum Monte Carlo calculations or cluster extension of dynamical mean-field theory. Cluster extensions of the dynamical mean-field theory are for example the dynamical cluster approximation or the cellular dynamical mean-field theory. The new approach is benchmarked
Fermion bag approach to the sign problem in strongly coupled lattice QED with Wilson fermions
Chandrasekharan, Shailesh; Li, Anyi
2010-01-01
We explore the sign problem in strongly coupled lattice QED with one flavor of Wilson fermions in four dimensions using the fermion bag formulation. We construct rules to compute the weight of a fermion bag and show that even though the fermions are confined into bosons, fermion bags with negative weights do exist. By classifying fermion bags as either simple or complex, we find numerical evidence that complex bags with positive and negative weights come with almost equal probabilities and th...
Smith, J.L.; Fisk, Z.; Ott, H.R.
1987-01-01
The actinide series of elements begins with f-shell electrons forming energy bands, contributing to the bonding, and possessing no magnetic moments. At americium the series switches over to localized f electrons with magnetic moments. In metallic compounds this crossover of behavior can be modified and studied. In this continuum of behavior a few compounds on the very edge of localized f-electron behavior exhibit enormous electronic heat capacities at low temperatures. This is associated with an enhanced thermal mass of the conduction electrons, which is well over a hundred times the free electron mass, and is what led to the label heavy fermion for such compounds. A few of these become superconducting at even lower temperatures. The excitement in this field comes from attempting to understand how this heaviness arises and from the likelihood that the superconductivity is different from that of previously known superconductors. The effects of thorium impurities in UBe 13 were studied as a representative system for studying the nature of the superconductivity
Lippoldt, Stefan
2016-01-21
In this thesis we study a formulation of Dirac fermions in curved spacetime that respects general coordinate invariance as well as invariance under local spin base transformations. We emphasize the advantages of the spin base invariant formalism both from a conceptual as well as from a practical viewpoint. This suggests that local spin base invariance should be added to the list of (effective) properties of (quantum) gravity theories. We find support for this viewpoint by the explicit construction of a global realization of the Clifford algebra on a 2-sphere which is impossible in the spin-base non-invariant vielbein formalism. The natural variables for this formulation are spacetime-dependent Dirac matrices subject to the Clifford-algebra constraint. In particular, a coframe, i.e. vielbein field is not required. We disclose the hidden spin base invariance of the vielbein formalism. Explicit formulas for the spin connection as a function of the Dirac matrices are found. This connection consists of a canonical part that is completely fixed in terms of the Dirac matrices and a free part that can be interpreted as spin torsion. The common Lorentz symmetric gauge for the vielbein is constructed for the Dirac matrices, even for metrics which are not linearly connected. Under certain criteria, it constitutes the simplest possible gauge, demonstrating why this gauge is so useful. Using the spin base formulation for building a field theory of quantized gravity and matter fields, we show that it suffices to quantize the metric and the matter fields. This observation is of particular relevance for field theory approaches to quantum gravity, as it can serve for a purely metric-based quantization scheme for gravity even in the presence of fermions. Hence, in the second part of this thesis we critically examine the gauge, and the field-parametrization dependence of renormalization group flows in the vicinity of non-Gaussian fixed points in quantum gravity. While physical
MSW-resonant fermion mixing during reheating
Kanai, Tsuneto; Tsujikawa, Shinji
2003-10-01
We study the dynamics of reheating in which an inflaton field couples two flavor fermions through Yukawa-couplings. When two fermions have a mixing term with a constant coupling, we show that the Mikheyev-Smirnov-Wolfenstein (MSW)-type resonance emerges due to a time-dependent background in addition to the standard fermion creation via parametric resonance. This MSW resonance not only alters the number densities of fermions generated by a preheating process but also can lead to the larger energy transfer from the inflaton to fermions. Our mechanism can provide additional source terms for the creation of superheavy fermions which may be relevant for the leptogenesis scenario.
MSW-resonant fermion mixing during reheating
Kanai, Tsuneto; Tsujikawa, Shinji
2003-01-01
We study the dynamics of reheating in which an inflaton field couples two flavor fermions through Yukawa-couplings. When two fermions have a mixing term with a constant coupling, we show that the Mikheyev-Smirnov-Wolfenstein (MSW)-type resonance emerges due to a time-dependent background in addition to the standard fermion creation via parametric resonance. This MSW resonance not only alters the number densities of fermions generated by a preheating process but also can lead to the larger energy transfer from the inflaton to fermions. Our mechanism can provide additional source terms for the creation of superheavy fermions which may be relevant for the leptogenesis scenario
How real are composite fermions?
Kang, W.; Stormer, H.L.; Pfeiffer, L.N.; Baldwin, K.W.; West, K.W.
1995-01-01
A new picture of fractional quantum Hall effect (FQHE) in terms of a novel particle called composite fermion has emerged recently. A composite fermion is a composite of two flux quanta which are effectively bound to an electron as a result of electron-electron interaction. A system of electrons at half-filled Landau level can be transformed to an equivalent system of composite fermions at zero effective magnetic field with a distinct Fermi surface. The FQHE is then viewed as the integral quantum Hall effect of composite fermions away from half-filling. In order to test for these new particles, we have studied transport of anti-dot superlattices in a two-dimensional electron gas. At low magnetic fields electron transport exhibits well-known resonances at fields where the classical cyclotron orbit becomes commensurate with the anti-dot lattice. At half-filling we observe the same dimensional resonances. This establishes the ''semi-classical'' behavior of composite fermions. (orig.)
Fermionic Collective Excitations in a Lattice Gas of Rydberg Atoms
Olmos, B.; Gonzalez-Ferez, R.; Lesanovsky, I.
2009-01-01
We investigate the many-body quantum states of a laser-driven gas of Rydberg atoms confined to a large spacing ring lattice. If the laser driving is much stronger than the van der Waals interaction among the Rydberg atoms, these many-body states are collective fermionic excitations. The first excited state is a spin wave that extends over the entire lattice. We demonstrate that our system permits us to study fermions in the presence of disorder although no external atomic motion takes place. We analyze how this disorder influences the excitation properties of the fermionic states. Our work shows a route towards the creation of complex many-particle states with atoms in lattices.
Holographic Fermions in Anisotropic Einstein-Maxwell-Dilaton-Axion Theory
Kuang, Xiao-Mei; Fang, Li-Qing
2015-01-01
We investigate the properties of the holographic Fermionic system dual to an anisotropic charged black brane bulk in Einstein-Maxwell-Dilaton-Axion gravity theory. We consider the minimal coupling between the Dirac field and the gauge field in the bulk gravity theory and mainly explore the dispersion relation exponents of the Green functions of the dual Fermionic operators in the dual field theory. We find that along both the anisotropic and the isotropic directions the Fermi momentum will be effected by the anisotropy of the bulk theory. However, the anisotropy has influence on the dispersion relation which is almost linear for massless Fermions with charge q=2. The universal properties that the mass and the charge of the Fermi possibly correspond to nonlinear dispersion relation are also investigated
Finite boson mappings of fermion systems
Johnson, C.W.; Ginocchio, J.N.
1994-01-01
We discuss a general mapping of fermion pairs to bosons that preserves Hermitian conjugation, with an eye towards producing finite and usable boson Hamiltonians that approximate well the low-energy dynamics of a fermion Hamiltonian
Fermionic One-Way Quantum Computation
Cao Xin; Shang Yun
2014-01-01
Fermions, as another major class of quantum particles, could be taken as carriers for quantum information processing beyond spins or bosons. In this work, we consider the fermionic generalization of the one-way quantum computation model and find that one-way quantum computation can also be simulated with fermions. In detail, using the n → 2n encoding scheme from a spin system to a fermion system, we introduce the fermionic cluster state, then the universal computing power with a fermionic cluster state is demonstrated explicitly. Furthermore, we show that the fermionic cluster state can be created only by measurements on at most four modes with |+〉 f (fermionic Bell state) being free
Null-plane quantization of fermions
Mustaki, D.
1990-01-01
Massive Dirac fermions are canonically quantized on the null plane using the Dirac-Bergmann algorithm. The procedure is carried out in the framework of quantum electrodynamics as an illustration of a rigorous treatment of interacting fermion fields
Three mirror pairs of fermion families
Montvay, I.
1988-01-01
A simple model with three mirror pairs of fermion families is considered which allows for a substantial mixing between the mirror fermion partners without conflicting with known phenomenology. (orig.)
Bosonic behavior of entangled fermions
C. Tichy, Malte; Alexander Bouvrie, Peter; Mølmer, Klaus
2012-01-01
Two bound, entangled fermions form a composite boson, which can be treated as an elementary boson as long as the Pauli principle does not affect the behavior of many such composite bosons. The departure of ideal bosonic behavior is quantified by the normalization ratio of multi-composite-boson st......Two bound, entangled fermions form a composite boson, which can be treated as an elementary boson as long as the Pauli principle does not affect the behavior of many such composite bosons. The departure of ideal bosonic behavior is quantified by the normalization ratio of multi...
On the disordered fermion couplings
Bernaschi, M.; Cabasino, S.; Marinari, E.; Rome-2 Univ.; Sarno, R.; Rome-1 Univ.
1989-01-01
We study the possibility of avoiding the fermion doubling problem by using a random coupling. We use numerical simulations in order to study the theory in the strong disorder region. We find a sharp crossover as a function of the strength of the disorder. For weak quenched disorder we find that the species doubling survives, while for strong quenched disorder only with a particular choice of the random term (antihermitian) it is possible to get a theory that seems to avoid fermion doubling. (orig.)
Fermions as generalized Ising models
C. Wetterich
2017-04-01
Full Text Available We establish a general map between Grassmann functionals for fermions and probability or weight distributions for Ising spins. The equivalence between the two formulations is based on identical transfer matrices and expectation values of products of observables. The map preserves locality properties and can be realized for arbitrary dimensions. We present a simple example where a quantum field theory for free massless Dirac fermions in two-dimensional Minkowski space is represented by an asymmetric Ising model on a euclidean square lattice.
Improved lattice fermion action for heavy quarks
Cho, Yong-Gwi; Hashimoto, Shoji; Jüttner, Andreas; Kaneko, Takashi; Marinkovic, Marina; Noaki, Jun-Ichi; Tsang, Justus Tobias
2015-01-01
We develop an improved lattice action for heavy quarks based on Brillouin-type fermions, that have excellent energy-momentum dispersion relation. The leading discretization errors of O(a) and O(a"2) are eliminated at tree-level. We carry out a scaling study of this improved Brillouin fermion action on quenched lattices by calculating the charmonium energy-momentum dispersion relation and hyperfine splitting. We present a comparison to standard Wilson fermions and domain-wall fermions.
2-fermion and 4-fermion production at LEP2
van Vulpen, Ivo B
2000-01-01
We present the measurements on 2-fermion and 4-fermion production in e + e - collisions at centre-of-mass energies ranging from 192 to 202 Ge V as collected by the 4 LEP experiments in 1999. For processes with 2-fermions in the final state we present both production cross sections and asymmetries for event samples at low and high effective centre-of-mass energies, where the latter process is sensitive to possible contributions from various non-SM physics, like contact interactions or Z' exchange, and can therefore be used to set limits on parameters in those models. We also report on the measured cross sections for a subset of processes leading to 4 fermions in the final state: pair production of heavy vector bosons w+w- (NC03) and ZZ (NC02) followed by single-W production. A measurement of the leptonic branching ratio of the W-boson is used to extract information on IV c• I
Dynamical fermions in lattice quantum chromodynamics
Szabo, Kalman
2007-07-01
The thesis presentS results in Quantum Chromo Dynamics (QCD) with dynamical lattice fermions. The topological susceptibilty in QCD is determined, the calculations are carried out with dynamical overlap fermions. The most important properties of the quark-gluon plasma phase of QCD are studied, for which dynamical staggered fermions are used. (orig.)
Dynamical fermions in lattice quantum chromodynamics
Szabo, Kalman
2007-01-01
The thesis presentS results in Quantum Chromo Dynamics (QCD) with dynamical lattice fermions. The topological susceptibilty in QCD is determined, the calculations are carried out with dynamical overlap fermions. The most important properties of the quark-gluon plasma phase of QCD are studied, for which dynamical staggered fermions are used. (orig.)
Gauge invariance and fermion mass dimensions
Elias, V.
1979-05-01
Renormalization-group equation fermion mass dimensions are shown to be gauge dependent in gauge theories possessing non-vector couplings of gauge bosons to fermions. However, the ratios of running fermion masses are explicitly shown to be gauge invariant in the SU(5) and SU(2) x U(1) examples of such theories. (author)
Theoretical studies of strongly correlated fermions
Logan, D [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)
1997-04-01
Strongly correlated fermions are investigated. An understanding of strongly correlated fermions underpins a diverse range of phenomena such as metal-insulator transitions, high-temperature superconductivity, magnetic impurity problems and the properties of heavy-fermion systems, in all of which local moments play an important role. (author).
Fermions and bosons : a 'spinless' approach
Oliveira, P.M.C. de; Ribeiro, S.C.
1980-07-01
The fundamental difference between fermions and bosons is presented. The treatment used is based only on indistinguishability and its related implications on interference, with no mention to spin. Comparison between indistinguishable (fermions or bosons) and distinguishable identical particles are also made, yielding the enhancement (bosons) or inhibition (fermions) factors which determine the quantum distribution equations. (Author) [pt
Grady, M.
1986-01-01
I describe a fast fermion algorithm which utilizes pseudofermion fields but appears to have little or no systematic error. Test simulations on two-dimensional gauge theories are described. A possible justification for the algorithm being exact is discussed. 8 refs
The fermion stochastic calculus I
Streater, R.F.
1984-01-01
The author describes the stochastic calculus of quantum processes with fermions. After a description of the Clifford algebra as the csup(*)-algebra generated by spinor fields the damped harmonic oscillator with quantum noise is considered as example. Then the Clifford process is described. Finally the Ito-Clifford integral and the Ito-Clifford isometry are presented. (HSI)
Lattices, supersymmetry and Kaehler fermions
Scott, D.M.
1984-01-01
It is shown that a graded extension of the space group of a (generalised) simple cubic lattice exists in any space dimension, D. The fermionic variables which arise admit a Kaehlerian interpretation. Each graded space group is a subgroup of a graded extension of the appropriate Euclidean group, E(D). The relevance of this to the construction of lattice theories is discussed. (author)
Sextet Model with Wilson Fermions
Hansen, Martin; Pica, Claudio
2017-01-01
We present new results from our ongoing study of the SU(3) sextet model with two flavors in the two-index symmetric representation of the gauge group. In the simulations use unimproved Wilson fermions to investigate the infrared properties of the model. We have previously presented results...
Singlets of fermionic gauge symmetries
Bergshoeff, E.A.; Kallosh, R.E.; Rahmanov, M.A.
1989-01-01
We investigate under which conditions singlets of fermionic gauge symmetries which are "square roots of gravity" can exist. Their existence is non-trivial because there are no fields neutral in gravity. We tabulate several examples of singlets of global and local supersymmetry and Îº-symmetry and
Alternative to domain wall fermions
Neuberger, H.
2002-01-01
An alternative to commonly used domain wall fermions is presented. Some rigorous bounds on the condition number of the associated linear problem are derived. On the basis of these bounds and some experimentation it is argued that domain wall fermions will in general be associated with a condition number that is of the same order of magnitude as the product of the condition number of the linear problem in the physical dimensions by the inverse bare quark mass. Thus, the computational cost of implementing true domain wall fermions using a single conjugate gradient algorithm is of the same order of magnitude as that of implementing the overlap Dirac operator directly using two nested conjugate gradient algorithms. At a cost of about a factor of two in operation count it is possible to make the memory usage of direct implementations of the overlap Dirac operator independent of the accuracy of the approximation to the sign function and of the same order as that of standard Wilson fermions
Wilson fermions at finite temperature
Creutz, M.
1996-01-01
The author conjectures on the phase structure expected for lattice gauge theory with two flavors of Wilson fermions, concentrating on large values of the hopping parameter. Numerous phases are expected, including the conventional confinement and deconfinement phases, as well as an Aoki phase with spontaneous breaking of flavor and parity and a large hopping phase corresponding to negative quark masses
UPt3, heavy fermions and superconductivity
Visser, A. de.
1986-01-01
In this thesis an experimental study is presented of one of the heavy-fermion superconductors: UPt 3 (T c =0.5 K). The normal-state properties of this material are governed by pronounced spin-fluctuation effects. The unusual coexistence of spin-fluctuations and superconductivity is strongly suggestive for an unconventional type of superconductivity, mediated by spin-fluctuations instead of phonons, with the condensate formed out of odd-parity electron states. In the first chapter a general introduction is given to the field of the heavy-fermions. In the second chapter a theoretical background for the properties of UPt 3 is presented. Chapter 3 deals with the sample preparation and measuring techniques. In chapter 4 a series of experiments is presented on the normal-phase of UPt 3 , among which are studies of the specific heat, thermal expansion, sound velocity, magnetization, electrical resistivity, magnetoresistivity and magnetostriction. Also the influence of high-magnetic fields (35 T) and high-pressures (5 kbar) has been studied. The superconducting phase of UPt 3 has been discussed in chapter 5. In chapter 6 a series of pseudobinary U(Pt 1-x Pd x ) 3 compounds (x≤0.30) are studied. In the last chapter some final remarks and conclusions are presented. (Auth.)
Azcoiti, V.; Cruz, A.; Di Carlo, G.; Grillo, A.F.; Vladikas, A.
1991-01-01
We attempt to increase the efficiency of simulations of dynamical fermions on the lattice by calculating the fermionic determinant just once for all the values of the theory's gauge coupling and flavor number. Our proposal is based on the determination of an effective fermionic action by the calculation of the fermionic determinant averaged over configurations at fixed gauge energy. The feasibility of our method is justified by the observed volume dependence of the fluctuations of the logarithm of the determinant. The algorithm we have used in order to calculate the fermionic determinant, based on the determination of all the eigenvalues of the fermionic matrix at zero mass, also enables us to obtain results at any fermion mass, with a single fermionic simulation. We test the method by simulating compact lattice QED, finding good agreement with other standard calculations. New results on the phase transition of compact QED with massless fermions on 6 4 and 8 4 lattices are also presented
Searches for Fourth Generation Fermions
Ivanov, A.; /Fermilab
2011-09-01
We present the results from searches for fourth generation fermions performed using data samples collected by the CDF II and D0 Detectors at the Fermilab Tevatron p{bar p} collider. Many of these results represent the most stringent 95% C. L. limits on masses of new fermions to-date. A fourth chiral generation of massive fermions with the same quantum numbers as the known fermions is one of the simplest extensions of the SM with three generations. The fourth generation is predicted in a number of theories, and although historically have been considered disfavored, stands in agreement with electroweak precision data. To avoid Z {yields} {nu}{bar {nu}} constraint from LEP I a fourth generation neutrino {nu}{sub 4} must be heavy: m({nu}{sub 4}) > m{sub Z}/2, where m{sub Z} is the mass of Z boson, and to avoid LEP II bounds a fourth generation charged lepton {ell}{sub 4} must have m({ell}{sub 4}) > 101 GeV/c{sup 2}. At the same time due to sizeable radiative corrections masses of fourth generation fermions cannot be much higher the current lower bounds and masses of new heavy quarks t' and b' should be in the range of a few hundred GeV/c{sup 2}. In the four-generation model the present bounds on the Higgs are relaxed: the Higgs mass could be as large as 1 TeV/c{sup 2}. Furthermore, the CP violation is significantly enhanced to the magnitude that might account for the baryon asymmetry in the Universe. Additional chiral fermion families can also be accommodated in supersymmetric two-Higgs-doublet extensions of the SM with equivalent effect on the precision fit to the Higgs mass. Another possibility is heavy exotic quarks with vector couplings to the W boson Contributions to radiative corrections from such quarks with mass M decouple as 1/M{sup 2} and easily evade all experimental constraints. At the Tevatron p{bar p} collider 4-th generation chiral or vector-like quarks can be either produced strongly in pairs or singly via electroweak production, where the
Chiral fermions on the lattice
Randjbar Daemi, S.; Strathdee, J.
1995-01-01
The overlap approach to chiral gauge theories on arbitrary D-dimensional lattices is studied. The doubling problem and its relation to chiral anomalies for D = 2 and 4 is examined. In each case it is shown that the doublers can be eliminated and the well known perturbative results for chiral anomalies can be recovered. We also consider the multi-flavour case and give the general criteria for the construction of anomaly free chiral gauge theories on arbitrary lattices. We calculate the second order terms in a continuum approximation to the overlap formula in D dimensions and show that they coincide with the bilinear part of the effective action of D-dimensional Weyl fermions coupled to a background gauge field. Finally, using the same formalism we reproduce the correct Lorentz, diffeomorphism and gauge anomalies in the coupling of a Weyl fermion to 2-dimensional gravitation and Maxwell fields. (author). 15 refs
Fermion to boson mappings revisited
Ginocchio, J.N.; Johnson, C.W.
1996-01-01
We briefly review various mappings of fermion pairs to bosons, including those based on mapping operators, such as Belyaev-Zelevinskii, and those on mapping states, such as Marumori; in particular we consider the work of Otsuka-Arima-Iachello, aimed at deriving the Interacting Boson Model. We then give a rigorous and unified description of state-mapping procedures which allows one to systematically go beyond Otsuka-Arima-Iachello and related approaches, along with several exact results. (orig.)
Fermion determinants in lattice QCD
Johnson, Christopher Andrew
2001-01-01
The main topic of this thesis concerns efficient algorithms for the calculation of determinants of the kind of matrix typically encountered in lattice QCD. In particular an efficient method for calculating the fermion determinant is described. Such a calculation is useful to illustrate the effects of light dynamical (virtual) quarks. The methods employed in this thesis are stochastic methods, based on the Lanczos algorithm, which is used for the solution of large, sparse matrix problems via a partial tridiagonalisation of the matrix. Here an implementation is explored which requires less exhaustive treatment of the matrix than previous Lanczos methods. This technique exploits the analogy between the Lanczos tridiagonalisation algorithm and Gaussian quadrature in order to calculate the fermion determinant. A technique for determining a number of the eigenvalues of the matrix is also presented. A demonstration is then given of how one can improve upon this estimate considerably using variance reduction techniques, reducing the variance by a factor of order 100 with a further, equal amount of work. The variance reduction method is a two-stage process, involving a Chebyshev approximation to the quantity in question and then the subtraction of traceless operators. The method is applied to the fermion determinant for non-perturbatively improved Wilson fermions on a 16 3 x 32 lattice. It is also applicable to a wider class of matrix operators. Finally we discuss how dynamical quark effects may be simulated in a Monte Carlo process with an effective partitioning of low and high eigenmodes. This may be done via selective updating of a trial configuration which highlights the physically relevant effects of light quark modes. (author)
Superdeformations and fermion dynamical symmetries
Wu, Cheng-Li
1990-01-01
In this talk, I will present a link between nuclear collective motions and their underlying fermion dynamical symmetries. In particular, I will focus on the microscopic understanding of deformations. It is shown that the SU 3 of the one major shell fermion dynamical symmetry model (FDSM) is responsible for the physics of low and high spins in normal deformation. For the recently observed phenomena of superdeformation, the physics of the problem dictates a generalization to a supershell structure (SFDSM), which also has an SU 3 fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU 3 symmetry. In both cases the dynamical Pauli effect plays a vital role. A particularly noteworthy discovery from this model is that the superdeformed ground band is not the usual unaligned band but the D-pair aligned (DPA) band, which sharply crosses the excited bands. The existence of such DPA band is a key point to understand many properties of superdeformation. Our studies also poses new experimental challenge. This is particularly interesting since there are now plans to build new and exciting γ-ray detecting systems, like the GAMMASPHERE, which could provide answers to some of these challenges. 34 refs., 11 figs., 5 tabs
Light fermions in quantum gravity
Eichhorn, Astrid; Gies, Holger
2011-01-01
We study the impact of quantum gravity, formulated as a quantum field theory of the metric, on chiral symmetry in a fermionic matter sector. Specifically we address the question of whether metric fluctuations can induce chiral symmetry breaking and bound state formation. Our results based on the functional renormalization group indicate that chiral symmetry is left intact even at strong gravitational coupling. In particular, we found that asymptotically safe quantum gravity where the gravitational couplings approach a non-Gaußian fixed point generically admits universes with light fermions. Our results thus further support quantum gravity theories built on fluctuations of the metric field such as the asymptotic-safety scenario. A study of chiral symmetry breaking through gravitational quantum effects may also serve as a significant benchmark test for other quantum gravity scenarios, since a completely broken chiral symmetry at the Planck scale would not be in accordance with the observation of light fermions in our universe. We demonstrate that this elementary observation already imposes constraints on a generic UV completion of gravity. (paper)
Axial anomalies of Lifshitz fermions
Bakas, Ioannis
2011-01-01
We compute the axial anomaly of a Lifshitz fermion theory with anisotropic scaling z=3 which is minimally coupled to geometry in 3+1 space-time dimensions. We find that the result is identical to the relativistic case using path integral methods. An independent verification is provided by showing with spectral methods that the eta-invariant of the Dirac and Lifshitz fermion operators in three dimensions are equal. Thus, by the integrated form of the anomaly, the index of the Dirac operator still accounts for the possible breakdown of chiral symmetry in non-relativistic theories of gravity. We apply this framework to the recently constructed gravitational instanton backgrounds of Horava-Lifshitz theory and find that the index is non-zero provided that the space-time foliation admits leaves with harmonic spinors. Using Hitchin's construction of harmonic spinors on Berger spheres, we obtain explicit results for the index of the fermion operator on all such gravitational instanton backgrounds with SU(2)xU(1) isom...
Symmetry between bosons and fermions
Ohnuki, Y.; Kamefuchi, S.
1986-01-01
By definition Bosons and Fermions behave quite differently as regards statistics. It is equally true, however, that in some other respects they do behave similarly or even symmetrically. In the present paper they would like to show that such similarity or symmetry can be exhibited most fully when the theory is formulated in a specific manner, i.e. in terms of annihilation and creation operators a/sub j/ and a/sub j//sup dagger/ or what they term g-numbers. The difference between Bosons and Fermions can, of course, be traced back to the difference in the signatures (jj) = +,- attached to the brackets in the basic commutation relations: [a/sub j/,a/sub j//sup dagger/]-(jj) = 1, [a/sub j/,a/sub j/]-(jj) = 0. However, the substantial part of the theory can in fact be formulated without specifying the individual signatures (jj). This is why it is possible to treat Bosons and Fermions in a unified manner, and to thereby consider, among the two, super- or more general, g-symmetry transformations. 6 references, 1 table
FLIC-overlap fermions and topology
Kamleh, W.; Kusterer, D.J.; Leinweber, D.B.; Williams, A.G.
2003-01-01
APE smearing the links in the irrelevant operators of clover fermions (Fat-Link Irrelevant Clover (FLIC) fermions) provides significant improvement in the condition number of the Hermitian-Dirac operator and gives rise to a factor of two savings in computing the overlap operator. This report investigates the effects of using a highly-improved definition of the lattice field-strength tensor F μν in the fermion action, made possible through the use of APE-smeared fat links in the construction of the irrelevant operators. Spurious double-zero crossings in the spectral flow of the Hermitian-Wilson Dirac operator associated with lattice artifacts at the scale of the lattice spacing are removed with FLIC fermions composed with an O(α 4 )-improved lattice field strength tensor. Hence, FLIC-Overlap fermions provide an additional benefit to the overlap formalism: a correct realization of topology in the fermion sector on the lattice
Fermions in noncommutative emergent gravity
Klammer, D.
2010-01-01
Noncommutative emergent gravity is a novel framework disclosing how gravity is contained naturally in noncommutative gauge theory formulated as a matrix model. It describes a dynamical space-time which itself is a four-dimensional brane embedded in a higher-dimensional space. In noncommutative emergent gravity, the metric is not a fundamental object of the model; rather it is determined by the Poisson structure and by the induced metric of the embedding. In this work the coupling of fermions to these matrix models is studied from the point of view of noncommutative emergent gravity. The matrix Dirac operator as given by the IKKT matrix model defines an appropriate coupling for fermions to an effective gravitational metric of noncommutative four-dimensional spaces that are embedded into a ten-dimensional ambient space. As it turns out this coupling is non-standard due to a spin connection that vanishes in the preferred but unobservable coordinates defined by the model. The purpose of this work is to study the one-loop effective action of this approach. Standard results of the literature cannot be applied due to this special coupling of the fermions. However, integrating out these fields in a nontrivial geometrical background induces indeed the Einstein-Hilbert action of the effective metric, as well as additional terms which couple the noncommutative structure to the Riemann tensor, and a dilaton-like term. It remains to be understood what the effects of these terms are and whether they can be avoided. In a second step, the existence of a duality between noncommutative gauge theory and gravity which explains the phenomenon of UV/IR mixing as a gravitational effect is discussed. We show how the gravitational coupling of fermions can be interpreted as a coupling of fermions to gauge fields, which suffers then from UV/IR mixing. This explanation does not render the model finite but it reveals why some UV/IR mixing remains even in supersymmetric models, except in the N
Superconductivity in mixed boson-fermion systems
Ioffe, L.; Larkin, A.I.; Ovchinnikov, Yu.N.; Yu, L.
1989-12-01
The superconductivity of mixed boson-fermion systems is studied using a simple boson-fermion transformation model. The critical temperature of the superconducting transition is calculated over a wide range of the narrow boson band position relative to the Fermi level. The BCS scenario and boson condensation picture are recovered in two limiting cases of high and low positions of boson band, respectively, with modifications due to boson-fermion interaction. (author). 11 refs
Lattice quantum chromodynamics with approximately chiral fermions
Hierl, Dieter
2008-05-15
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
Lattice quantum chromodynamics with approximately chiral fermions
Hierl, Dieter
2008-05-01
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the Θ + pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
Fermion systems in discrete space-time
Finster, Felix
2007-01-01
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure
Fermion systems in discrete space-time
Finster, Felix [NWF I - Mathematik, Universitaet Regensburg, 93040 Regensburg (Germany)
2007-05-15
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.
Fermion Systems in Discrete Space-Time
Finster, Felix
2006-01-01
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.
Fermion systems in discrete space-time
Finster, Felix
2007-05-01
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.
Quenched lattice QCD with domain wall fermions and the chiral limit
Blum, T.; Wingate, M.; Chen, P.; Christ, N.; Cristian, C.; Fleming, G.; Kaehler, A.; Liao, X.; Liu, G.; Malureanu, C.; Mawhinney, R.; Siegert, G.; Sui, C.; Wu, L.; Zhestkov, Y.; Dawson, C.; Soni, A.; Ohta, S.; Vranas, P.
2004-01-01
Quenched QCD simulations on three volumes 8 3 x, 12 3 x and 16 3 x32 and three couplings β=5.7, 5.85 and 6.0 using domain wall fermions provide a consistent picture of quenched QCD. We demonstrate that the small induced effects of chiral symmetry breaking inherent in this formulation can be described by a residual mass (m res ) whose size decreases as the separation between the domain walls (L s ) is increased. However, at stronger couplings much larger values of L s are required to achieve a given physical value of m res . For β=6.0 and L s =16, we find m res /m s =0.033(3), while for β=5.7, and L s =48, m res /m s =0.074(5), where m s is the strange quark mass. These values are significantly smaller than those obtained from a more naive determination in our earlier studies. Important effects of topological near zero modes which should afflict an accurate quenched calculation are easily visible in both the chiral condensate and the pion propagator. These effects can be controlled by working at an appropriately large volume. A non-linear behavior of m π 2 in the limit of small quark mass suggests the presence of additional infrared subtlety in the quenched approximation. Good scaling is seen both in masses and in f π over our entire range, with inverse lattice spacing varying between 1 and 2 GeV
Scanning Tunnelling Spectroscopic Studies of Dirac Fermions in Graphene and Topological Insulators
wang K.-L.
2012-03-01
Full Text Available We report novel properties derived from scanning tunnelling spectroscopic (STS studies of Dirac fermions in graphene and the surface state (SS of a strong topological insulator (STI, Bi2Se3. For mono-layer graphene grown on Cu by chemical vapour deposition (CVD, strain-induced scalar and gauge potentials are manifested by the charging effects and the tunnelling conductance peaks at quantized energies, respectively. Additionally, spontaneous time-reversal symmetry breaking is evidenced by the alternating anti-localization and localization spectra associated with the zero-mode of two sublattices while global time-reversal symmetry is preserved under the presence of pseudo-magnetic fields. For Bi2Se3 epitaxial films grown on Si(111 by molecular beam epitaxy (MBE, spatially localized unitary impurity resonances with sensitive dependence on the energy difference between the Fermi level and the Dirac point are observed for samples thicker than 6 quintuple layers (QL. These findings are characteristic of the SS of a STI and are direct manifestation of strong topological protection against impurities. For samples thinner than 6-QL, STS studies reveal the openup of an energy gap in the SS due to overlaps of wave functions between the surface and interface layers. Additionally, spin-preserving quasiparticle interference wave-vectors are observed, which are consistent with the Rashba-like spin-orbit splitting.
More on random-lattice fermions
Kieu, T.D.; Institute for Advanced Study, Princeton, NJ; Markham, J.F.; Paranavitane, C.B.
1995-01-01
The lattice fermion determinants, in a given background gauge field, are evaluated for two different kinds of random lattices and compared to those of naive and wilson fermions in the continuum limit. While the fermion doubling is confirmed on one kind of lattices, there is positive evidence that it may be absent for the other, at least for vector interactions in two dimensions. Combined with previous studies, arbitrary randomness by itself is shown to be not a sufficient condition to remove the fermion doublers. 8 refs., 3 figs
Feynman rules for fermion-number-violating interactions
Denner, A.; Eck, H.; Hahn, O.; Kueblbeck, J.
1992-01-01
We present simple algorithmic Feynman rules for fermion-number-violating interactions. They do not involve explicit charge-conjugation matrices and resemble closely the familiar rules for Dirac fermions. We insist on a fermion flow through the graphs along fermion lines and get the correct relative signs between different interfering Feynman graphs as in the case of Dirac fermions. We only need the familiar Dirac propagator and fewer vertices than in the usual treatment of fermion-number-violating interactions. (orig.)
Fermionic models with superconducting circuits
Las Heras, Urtzi; Garcia-Alvarez, Laura; Mezzacapo, Antonio; Lamata, Lucas [University of the Basque Country UPV/EHU, Department of Physical Chemistry, Bilbao (Spain); Solano, Enrique [University of the Basque Country UPV/EHU, Department of Physical Chemistry, Bilbao (Spain); IKERBASQUE, Basque Foundation for Science, Bilbao (Spain)
2015-12-01
We propose a method for the efficient quantum simulation of fermionic systems with superconducting circuits. It consists in the suitable use of Jordan-Wigner mapping, Trotter decomposition, and multiqubit gates, be with the use of a quantum bus or direct capacitive couplings. We apply our method to the paradigmatic cases of 1D and 2D Fermi-Hubbard models, involving couplings with nearest and next-nearest neighbours. Furthermore, we propose an optimal architecture for this model and discuss the benchmarking of the simulations in realistic circuit quantum electrodynamics setups. (orig.)
Muon studies of heavy fermions
Heffner, R.H.
1991-01-01
Recent muon spin relaxation (μSR) studies have been particularly effective in revealing important properties of the unusual magnetism and superconductivity found in heavy fermion (HF) systems. In this paper μSR experiments elucidating the symmetry of superconducting order parameter in UPt 3 and UBe 13 doped with thorium and reviewed. Also discussed is the correlation between the enhanced superconducting specific heat jump and the reduced Kondo temperature in B-doped UBe 13 , indicating possible direct experimental evidence for a magnetic pairing mechanism in HF superconductors. 23 refs., 3 figs
Probing kink interactions with fermions
Carlitz, R.; Chakrabarti, R.
1985-01-01
A dilute gas of kinks exhibits strong but short-ranged intrinsic interactions. When these intrinsic interactions are supplemented by other ''extrinsic'' interactions, a phase transition can occur in which kinks and antikinks bind to form a gas of bounces. The extrinsic interactions arise from the coupling of kinks to an additional degree of freedom, which we take to be a fermion field. The class of quantum-mechanical models which we study includes examples of supersymmetry. The way in which kinks and antikinks bind depends in detail on aspects of the intrinsic interactions. This structure is probably shared by field-theoretic models
Fermionic quantum mechanics and superfields
Marnelius, R.
1990-01-01
The explicit forms of consistent eigenstate representations for finite dimensional fermionic quantum theories are considered in detail. In particular are the possible Grassmann characters of the eigenstates determined. A straightforward Schrodinger representation is shown to exist if they are even or odd. For an odd number of real eigenvalues, the eigenstates cannot be even or odd. Still a consistent Schrodinger picture is shown to exist provided the basic canonical operators are antilinearly represented. Since the wave functions within the Schrodinger picture are super-fields, the class of superfields which also are first quantized wave functions is determined
S-wave scattering of fermion revisited
Rahaman, Anisur
2011-01-01
A model where a Dirac fermion is coupled to background dilaton field is considered to study s-wave scattering of fermion by a back ground dilaton black hole. It is found that an uncomfortable situation towards information loss scenario arises when one loop correction gets involved during bosonization.
Spectral intensity distribution of trapped fermions
Trapped fermions; local density approximation; spectral intensity distribution function. ... Thus, cold atomic systems allow us to study interesting ... In fermions, synthetic non-Abelian gauge ... energy eigenstates of the isotropic harmonic oscillator [26–28]. ... d i=1. (ni + 1. 2. )ω0. In calculating the SIDF exactly these eigenfunc-.
Coherent states in the fermionic Fock space
Oeckl, Robert
2015-01-01
We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing kernel Hilbert space of continuous holomorphic functions. (paper)
Dynamic origins of fermionic D -terms
Hudson, Jonathan; Schweitzer, Peter
2018-03-01
The D -term is defined through matrix elements of the energy-momentum tensor, similarly to mass and spin, yet this important particle property is experimentally not known any fermion. In this work we show that the D -term of a spin 1/2 fermion is of dynamical origin: it vanishes for a free fermion. This is in pronounced contrast to the bosonic case where already a free spin-0 boson has a non-zero intrinsic D -term. We illustrate in two simple models how interactions generate the D -term of a fermion with an internal structure, the nucleon. All known matter is composed of elementary fermions. This indicates the importance to study this interesting particle property in more detail, which will provide novel insights especially on the structure of the nucleon.
Flavor symmetries and fermion masses
Rasin, A.
1994-04-01
We introduce several ways in which approximate flavor symmetries act on fermions and which are consistent with observed fermion masses and mixings. Flavor changing interactions mediated by new scalars appear as a consequence of approximate flavor symmetries. We discuss the experimental limits on masses of the new scalars, and show that the masses can easily be of the order of weak scale. Some implications for neutrino physics are also discussed. Such flavor changing interactions would easily erase any primordial baryon asymmetry. We show that this situation can be saved by simply adding a new charged particle with its own asymmetry. The neutrality of the Universe, together with sphaleron processes, then ensures a survival of baryon asymmetry. Several topics on flavor structure of the supersymmetric grand unified theories are discussed. First, we show that the successful predictions for the Kobayashi-Maskawa mixing matrix elements, V ub /V cb = √m u /m c and V td /V ts = √m d /m s , are a consequence of a large class of models, rather than specific properties of a few models. Second, we discuss how the recent observation of the decay β → sγ constrains the parameter space when the ratio of the vacuum expectation values of the two Higgs doublets, tanΒ, is large. Finally, we discuss the flavor structure of proton decay. We observe a surprising enhancement of the branching ratio for the muon mode in SO(10) models compared to the same mode in the SU(5) model
Fermion hierarchy from sfermion anarchy
Altmannshofer, Wolfgang; Frugiuele, Claudia; Harnik, Roni
2014-01-01
We present a framework to generate the hierarchical flavor structure of Standard Model quarks and leptons from loops of superpartners. The simplest model consists of the minimal supersymmetric standard model with tree level Yukawa couplings for the third generation only and anarchic squark and slepton mass matrices. Agreement with constraints from low energy flavor observables, in particular Kaon mixing, is obtained for supersymmetric particles with masses at the PeV scale or above. In our framework both the second and the first generation fermion masses are generated at 1-loop. Despite this, a novel mechanism generates a hierarchy among the first and second generations without imposing a symmetry or small parameters. A second-to-first generation mass ratio of order 100 is typical. The minimal supersymmetric standard model thus includes all the necessary ingredients to realize a fermion spectrum that is qualitatively similar to observation, with hierarchical masses and mixing. The minimal framework produces only a few quantitative discrepancies with observation, most notably the muon mass is too low. Furthermore, we discuss simple modifications which resolve this and also investigate the compatibility of our model with gauge and Yukawa coupling Unification
Bosonization of free Weyl fermions
Marino, E. C.
2017-03-01
We generalize the method of bosonization, in its complete form, to a spacetime with 3 + 1 dimensions, and apply it to free Weyl fermion fields, which thereby, can be expressed in terms of a boson field, namely the Kalb-Ramond anti-symmetric tensor gauge field. The result may have interesting consequences both in condensed matter and in particle physics. In the former, the bosonized form of the Weyl chiral currents provides a simple explanation for the angle-dependent magneto-conductance recently observed in materials known as Weyl semimetals. In the latter, conversely, since electrons can be thought of as a combination of left and right Weyl fermions, our result suggests the possibility of a unified description of the elementary particles, which undergo the fundamental interactions, with the mediators of such interactions, namely, the gauge fields. This would fulfill the pioneering attempt of Skyrme, to unify the particles with their interaction mediators (Skyrme 1962 Nucl. Phys. 31 556).
Fermion condensation and gapped domain walls in topological orders
Wan, Yidun [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,Shanghai 200433 (China); Collaborative Innovation Center of Advanced Microstructures, Nanjing University,Nanjing 210093 (China); Perimeter Institute for Theoretical Physics,Waterloo N2L 2Y5, Ontario (Canada); Wang, Chenjie [Perimeter Institute for Theoretical Physics,Waterloo N2L 2Y5, Ontario (Canada)
2017-03-31
We study fermion condensation in bosonic topological orders in two spatial dimensions. Fermion condensation may be realized as gapped domain walls between bosonic and fermionic topological orders, which may be thought of as real-space phase transitions from bosonic to fermionic topological orders. This picture generalizes the previous idea of understanding boson condensation as gapped domain walls between bosonic topological orders. While simple-current fermion condensation was considered before, we systematically study general fermion condensation and show that it obeys a Hierarchy Principle: a general fermion condensation can always be decomposed into a boson condensation followed by a minimal fermion condensation. The latter involves only a single self-fermion that is its own anti-particle and that has unit quantum dimension. We develop the rules of minimal fermion condensation, which together with the known rules of boson condensation, provides a full set of rules for general fermion condensation.
Composite fermions in the quantum Hall effect
Johnson, B.L.; Kirczenow, G.
1997-01-01
The quantum Hall effect and associated quantum transport phenomena in low-dimensional systems have been the focus of much attention for more than a decade. Recent theoretical development of interesting quasiparticles - 'composite fermions' - has led to significant advances in understanding and predicting the behaviour of two-dimensional electron systems under high transverse magnetic fields. Composite fermions may be viewed as fermions carrying attached (fictitious) magnetic flux. Here we review models of the integer and fractional quantum Hall effects, including the development of a unified picture of the integer and fractional effects based upon composite fermions. The composite fermion picture predicts remarkable new physics: the formation of a Fermi surface at high magnetic fields, and anomalous ballistic transport, thermopower, and surface acoustic wave behaviour. The specific theoretical predictions of the model, as well as the body of experimental evidence for these phenomena are reviewed. We also review recent edge-state models for magnetotransport in low-dimensional devices based on the composite fermion picture. These models explain the fractional quantum Hall effect and transport phenomena in nanoscale devices in a unified framework that also includes edge state models of the integer quantum Hall effect. The features of the composite fermion edge-state model are compared and contrasted with those of other recent edge-state models of the fractional quantum Hall effect. (author)
Phase space methods for Majorana fermions
Rushin Joseph, Ria; Rosales-Zárate, Laura E. C.; Drummond, Peter D.
2018-06-01
Fermionic phase space representations are a promising method for studying correlated fermion systems. The fermionic Q-function and P-function have been defined using Gaussian operators of fermion annihilation and creation operators. The resulting phase-space of covariance matrices belongs to the symmetry class D, one of the non-standard symmetry classes. This was originally proposed to study mesoscopic normal-metal-superconducting hybrid structures, which is the type of structure that has led to recent experimental observations of Majorana fermions. Under a unitary transformation, it is possible to express these Gaussian operators using real anti-symmetric matrices and Majorana operators, which are much simpler mathematical objects. We derive differential identities involving Majorana fermion operators and an antisymmetric matrix which are relevant to the derivation of the corresponding Fokker–Planck equations on symmetric space. These enable stochastic simulations either in real or imaginary time. This formalism has direct relevance to the study of fermionic systems in which there are Majorana type excitations, and is an alternative to using expansions involving conventional Fermi operators. The approach is illustrated by showing how a linear coupled Hamiltonian as used to study topological excitations can be transformed to Fokker–Planck and stochastic equation form, including dissipation through particle losses.
Tool kit for staggered fermions
Kilcup, G.W.; Sharpe, S.R.
1986-01-01
The symmetries of staggered fermions are analyzed both discrete and continuous. Tools are presented that allow a simple decomposition of representations of the continuum symmetries into representations of the discrete lattice symmetries, both at zero and non-zero spatial momenta. These tools are used to find the lattice transcriptions of the operators that appear in the weak interaction Hamiltonian. The lattice Ward Identities are derived that follow from the single partially conserved axial symmetry. Using these identities, the lattice equivalents of the continuum PCAC relations are found. Combining all these tools, Ward Identities are obtained, for the matrix elements of the weak interaction Hamiltonian, from which the behavior of the matrix elements as the pion and kaon masses vanish are derived. The same behavior as in the continuum is found
Spinrath, Martin
2014-01-01
We present a series of recent works related to group theoretical factors from GUT symmetry breaking which lead to predictions for the ratios of quark and lepton Yukawa couplings at the unification scale. New predictions for the GUT scale ratios y μ /y s , y τ /y b and y t /y b in particular are shown and compared to experimental data. For this comparison it is important to include possibly large supersymmetric threshold corrections. Due to this reason the structure of the fermion masses at the GUT scale depends on TeV scale physics and makes GUT scale physics testable at the LHC. We also discuss how this new predictions might lead to predictions for mixing angles by discussing the example of the recently measured last missing leptonic mixing angle θ 13 making this new class of GUT models also testable in neutrino experiments
Thermalization of fermionic quantum fields
Berges, Juergen; Borsanyi, Szabolcs; Serreau, Julien
2003-01-01
We solve the nonequilibrium dynamics of a (3+1)-dimensional theory with Dirac fermions coupled to scalars via a chirally invariant Yukawa interaction. The results are obtained from a systematic coupling expansion of the 2PI effective action to lowest nontrivial order, which includes scattering as well as memory and off-shell effects. The dynamics is solved numerically without further approximation, for different far-from-equilibrium initial conditions. The late-time behavior is demonstrated to be insensitive to the details of the initial conditions and to be uniquely determined by the initial energy density. Moreover, we show that at late time the system is very well characterized by a thermal ensemble. In particular, we are able to observe the emergence of Fermi-Dirac and Bose-Einstein distributions from the nonequilibrium dynamics
Multigrid for Staggered Lattice Fermions
Brower, Richard C. [Boston U.; Clark, M. A. [Unlisted, US; Strelchenko, Alexei [Fermilab; Weinberg, Evan [Boston U.
2018-01-23
Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the K\\"ahler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model, however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.
Chiral composite fermions without U(1)'s
Nelson, A.E.
1986-01-01
Some models are discussed which seem likely to produce composite fermions with masses protected only by nonabelian global symmetries. A subgroup of the original global symmetries can be weakly gauged to produce small masses for the fermions. A new feature of these models is that the original global symmetries contain no abelian factors and below the confinement scale there are neither exactly massless fermions nor Goldstone bosons. A candidate is given for a potentially realistic model with up to six families of quarks and leptons. (orig.)
Instantons and Massless Fermions in Two Dimensions
Callan, C. G. Jr.; Dashen, R.; Gross, D. J.
1977-05-01
The role of instantons in the breakdown of chiral U(N) symmetry is studied in a two dimensional model. Chiral U(1) is always destroyed by the axial vector anomaly. For N = 2 chiral SU(N) is also spontaneously broken yielding massive fermions and three (decoupled) Goldstone bosons. For N greater than or equal to 3 the fermions remain massless. Realistic four dimensional theories are believed to behave in a similar way but the critical N above which the fermions cease to be massive is not known in four dimensions.
Ladder physics in the spin fermion model
Tsvelik, A. M.
2017-05-01
A link is established between the spin fermion (SF) model of the cuprates and the approach based on the analogy between the physics of doped Mott insulators in two dimensions and the physics of fermionic ladders. This enables one to use nonperturbative results derived for fermionic ladders to move beyond the large-N approximation in the SF model. It is shown that the paramagnon exchange postulated in the SF model has exactly the right form to facilitate the emergence of the fully gapped d -Mott state in the region of the Brillouin zone at the hot spots of the Fermi surface. Hence, the SF model provides an adequate description of the pseudogap.
Fermionic bound states in distinct kinklike backgrounds
Bazeia, D. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, Paraiba (Brazil); Mohammadi, A. [Universidade Federal de Campina Grande, Departamento de Fisica, Caixa Postal 10071, Campina Grande, Paraiba (Brazil)
2017-04-15
This work deals with fermions in the background of distinct localized structures in the two-dimensional spacetime. Although the structures have a similar topological character, which is responsible for the appearance of fractionally charged excitations, we want to investigate how the geometric deformations that appear in the localized structures contribute to the change in the physical properties of the fermionic bound states. We investigate the two-kink and compact kinklike backgrounds, and we consider two distinct boson-fermion interactions, one motivated by supersymmetry and the other described by the standard Yukawa coupling. (orig.)
Quantum geometry of the Dirac fermions
Korchemskij, G.P.
1989-01-01
The bosonic path integral formalism is developed for Dirac fermions interacting with a nonabelian gauge field in the D-dimensional Euclidean space-time. The representation for the effective action and correlation functions of interacting fermions as sums over all bosonic paths on the complex projective space CP 2d-1 , (2d=2 [ D 2] is derived where all the spinor structure is absorbed by the one-dimensional Wess-Zumino term. It is the Wess-Zumino term that ensures all necessary properties of Dirac fermions under quantization. i.e., quantized values of the spin, Dirac equation, Fermi statistics. 19 refs
Fermionic NNLO contributions to Bhabha scattering
Actis, S.; Riemann, T.; Czakon, M.; Uniwersytet Slaski, Katowice; Gluza, J.
2007-10-01
We derive the two-loop corrections to Bhabha scattering from heavy fermions using dispersion relations. The double-box contributions are expressed by three kernel functions. Convoluting the perturbative kernels with fermionic threshold functions or with hadronic data allows to determine numerical results for small electron mass m e , combined with arbitrary values of the fermion mass m f in the loop, m 2 e 2 f , or with hadronic insertions. We present numerical results for m f =m μ , m τ ,m top at typical small- and large-angle kinematics ranging from 1 GeV to 500 GeV. (orig.)
Grassmann phase space theory for fermions
Dalton, Bryan J. [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria, 3122 (Australia); Jeffers, John [Department of Physics, University of Strathclyde, Glasgow, G4 ONG (United Kingdom); Barnett, Stephen M. [School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ (United Kingdom)
2017-06-15
A phase space theory for fermions has been developed using Grassmann phase space variables which can be used in numerical calculations for cold Fermi gases and for large fermion numbers. Numerical calculations are feasible because Grassmann stochastic variables at later times are related linearly to such variables at earlier times via c-number stochastic quantities. A Grassmann field version has been developed making large fermion number applications possible. Applications are shown for few mode and field theory cases. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Fermionic quantum critical point of spinless fermions on a honeycomb lattice
Wang, Lei; Corboz, Philippe; Troyer, Matthias
2014-01-01
Spinless fermions on a honeycomb lattice provide a minimal realization of lattice Dirac fermions. Repulsive interactions between nearest neighbors drive a quantum phase transition from a Dirac semimetal to a charge-density-wave state through a fermionic quantum critical point, where the coupling of the Ising order parameter to the Dirac fermions at low energy drastically affects the quantum critical behavior. Encouraged by a recent discovery (Huffman and Chandrasekharan 2014 Phys. Rev. B 89 111101) of the absence of the fermion sign problem in this model, we study the fermionic quantum critical point using the continuous-time quantum Monte Carlo method with a worm-sampling technique. We estimate the transition point V/t=1.356(1) with the critical exponents ν=0.80(3) and η=0.302(7). Compatible results for the transition point are also obtained with infinite projected entangled-pair states. (paper)
An SU(2) x SU(2) symmetric Higgs-Fermion model with staggered fermions
Berlin, J.; Heller, U.M.
1991-01-01
We have simulated on SU(2)xSU(2) symmetric Higgs-Fermion model with a four component scalar field coupled with a Yukawa type coupling to two flavours of staggered fermions. The results show two qualitatively different behaviours in the broken phase. One for weak coupling where the fermion masses obey the perturbative tree level relation M F =y , and one for strong coupling where the behaviour agrees with a 1/d expansion. (orig.)
Fermion bag solutions to some sign problems in four-fermion field theories
Li, Anyi
2013-01-01
Lattice four-fermion models containing N flavors of staggered fermions, that are invariant under Z 2 and U(1) chiral symmetries, are known to suffer from sign problems when formulated using the auxiliary field approach. Although these problems have been ignored in previous studies, they can be severe. In this talk, we show that the sign problems disappear when the models are formulated in the fermion bag approach, allowing us to solve them rigorously for the first time.
Fermion bag solutions to some sign problems in four-fermion field theories
Li, Anyi
2013-04-01
Lattice four-fermion models containing N flavors of staggered fermions, that are invariant under Z2 and U(1) chiral symmetries, are known to suffer from sign problems when formulated using the auxiliary field approach. Although these problems have been ignored in previous studies, they can be severe. In this talk, we show that the sign problems disappear when the models are formulated in the fermion bag approach, allowing us to solve them rigorously for the first time.
Fermion number non-conservation and cold neutral fermionic matter in (V-A) gauge theories
Matveev, V.A.; Rubakov, V.A.; Tavkhelidze, A.N.; Tokarev, V.F.
1987-01-01
It is shown that in four-dimensional abelian (V-A) theories, the ground state of cold neutral fermionic matter is an anomalous state containing domains of abnormal phase surrounded by the normal vacuum. Inside these domains, there exists a gauge field condensate which makes real fermions disappear both inside and outside the domains. In non-abelian theories, the abnormal matter is unstable in its turn, and the system rolls back down into the normal state with a small number of fermions above the topologically non-trivial vacuum. Thus, in several non-abelian gauge theories, the fermion number density of cold neutral matter cannot exceed some critical value. (orig.)
Two-dimensional confinement of heavy fermions
Shishido, Hiroaki; Shibauchi, Takasada; Matsuda, Yuji; Terashima, Takahito
2010-01-01
Metallic systems with the strongest electron correlations are realized in certain rare-earth and actinide compounds whose physics are dominated by f-electrons. These materials are known as heavy fermions, so called because the effective mass of the conduction electrons is enhanced via correlation effects up to as much as several hundreds times the free electron mass. To date the electronic structure of all heavy-fermion compounds is essentially three-dimensional. Here we report on the first realization of a two-dimensional heavy-fermion system, where the dimensionality is adjusted in a controllable fashion by fabricating heterostructures using molecular beam epitaxy. The two-dimensional heavy fermion system displays striking deviations from the standard Fermi liquid low-temperature electronic properties. (author)
The principle of the Fermionic projector
Finster, Felix
2006-01-01
The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. This book begins with a brief review of relativity, relativistic quantum mechanics, and classical gauge theories, emphasizing the basic physical concepts and mathematical foundations. The external field problem and Klein's paradox are discussed and then resolved by introducing the fermionic projector, a global object in space-time that generalizes the notion of the Dirac sea. At the mathematical core of the book is a precise definition of the fermionic projector and the use of methods of hyperbolic differential equations for detailed analysis. The fermionic projector makes it possible to formulate a new type of variational principle in space-time. The mathematical tools are developed for the analysis of the corresponding Euler-Lagrange equations. A particular variational principle is proposed that gives rise to an effective...
Pseudoclassical fermionic model and classical solutions
Smailagic, A.
1981-08-01
We study classical limit of fermionic fields seen as Grassmann variables and deduce the proper quantization prescription using Dirac's method for constrained systems and investigate quantum meaning of classical solutions for the Thirring model. (author)
Nonequilibrium fermion production in quantum field theory
Pruschke, Jens
2010-01-01
The creation of matter in the early universe or in relativistic heavy-ion collisions is inevitable connected to nonequilibrium physics. One of the key challenges is the explanation of the corresponding thermalization process following nonequilibrium instabilities. The role of fermionic quantum fields in such scenarios is discussed in the literature by using approximations of field theories which neglect important quantum corrections. This thesis goes beyond such approximations. A quantum field theory where scalar bosons interact with Dirac fermions via a Yukawa coupling is analyzed in the 2PI effective action formalism. The chosen approximation allows for a correct description of the dynamics including nonequilibrium instabilities. In particular, fermion-boson loop corrections allow to study the interaction of fermions with large boson fluctuations. The applied initial conditions generate nonequilibrium instabilities like parametric resonance or spinodal instabilities. The equations of motion for correlation functions are solved numerically and major characteristics of the fermion dynamics are described by analytical solutions. New mechanisms for the production of fermions are found. Simulations in the case of spinodal instability show that unstable boson fluctuations induce exponentially growing fermion modes with approximately the same growth rate. If the unstable regime lasts long enough a thermalization of the infrared part of the fermion occupation number occurs on time scales much shorter than the time scale on which bosonic quantum fields thermalize. Fermions acquire an excess of occupation in the ultraviolet regime compared to a Fermi-Dirac statistic characterized by a power-law with exponent two. The fermion production mechanism via parametric resonance is found to be most efficient after the instability ends. Quantum corrections then provide a very efficient particle creation mechanism which is interpreted as an amplification of decay processes. The ratio
Nonequilibrium fermion production in quantum field theory
Pruschke, Jens
2010-06-16
The creation of matter in the early universe or in relativistic heavy-ion collisions is inevitable connected to nonequilibrium physics. One of the key challenges is the explanation of the corresponding thermalization process following nonequilibrium instabilities. The role of fermionic quantum fields in such scenarios is discussed in the literature by using approximations of field theories which neglect important quantum corrections. This thesis goes beyond such approximations. A quantum field theory where scalar bosons interact with Dirac fermions via a Yukawa coupling is analyzed in the 2PI effective action formalism. The chosen approximation allows for a correct description of the dynamics including nonequilibrium instabilities. In particular, fermion-boson loop corrections allow to study the interaction of fermions with large boson fluctuations. The applied initial conditions generate nonequilibrium instabilities like parametric resonance or spinodal instabilities. The equations of motion for correlation functions are solved numerically and major characteristics of the fermion dynamics are described by analytical solutions. New mechanisms for the production of fermions are found. Simulations in the case of spinodal instability show that unstable boson fluctuations induce exponentially growing fermion modes with approximately the same growth rate. If the unstable regime lasts long enough a thermalization of the infrared part of the fermion occupation number occurs on time scales much shorter than the time scale on which bosonic quantum fields thermalize. Fermions acquire an excess of occupation in the ultraviolet regime compared to a Fermi-Dirac statistic characterized by a power-law with exponent two. The fermion production mechanism via parametric resonance is found to be most efficient after the instability ends. Quantum corrections then provide a very efficient particle creation mechanism which is interpreted as an amplification of decay processes. The ratio
Fermions in Brans-Dicke cosmology
Samojeden, L. L.; Devecchi, F. P.; Kremer, G. M.
2010-01-01
Using the Brans-Dicke theory of gravitation we put under investigation a hypothetical universe filled with a fermionic field (with a self-interaction potential) and a matter constituent ruled by a barotropic equation of state. It is shown that the fermionic field [in combination with the Brans-Dicke scalar field φ(t)] could be responsible for a final accelerated era, after an initial matter dominated period.
Superfluid response in heavy fermion superconductors
Zhong, Yin; Zhang, Lan; Shao, Can; Luo, Hong-Gang
2017-10-01
Motivated by a recent London penetration depth measurement [H. Kim, et al., Phys. Rev. Lett. 114, 027003 (2015)] and novel composite pairing scenario [O. Erten, R. Flint, and P. Coleman, Phys. Rev. Lett. 114, 027002 (2015)] of the Yb-doped heavy fermion superconductor CeCoIn5, we revisit the issue of superfluid response in the microscopic heavy fermion lattice model. However, from the literature, an explicit expression for the superfluid response function in heavy fermion superconductors is rare. In this paper, we investigate the superfluid density response function in the celebrated Kondo-Heisenberg model. To be specific, we derive the corresponding formalism from an effective fermionic large- N mean-field pairing Hamiltonian whose pairing interaction is assumed to originate from the effective local antiferromagnetic exchange interaction. Interestingly, we find that the physically correct, temperature-dependent superfluid density formula can only be obtained if the external electromagnetic field is directly coupled to the heavy fermion quasi-particle rather than the bare conduction electron or local moment. Such a unique feature emphasizes the key role of the Kondo-screening-renormalized heavy quasi-particle for low-temperature/energy thermodynamics and transport behaviors. As an important application, the theoretical result is compared to an experimental measurement in heavy fermion superconductors CeCoIn5 and Yb-doped Ce1- x Yb x CoIn5 with fairly good agreement and the transition of the pairing symmetry in the latter material is explained as a simple doping effect. In addition, the requisite formalism for the commonly encountered nonmagnetic impurity and non-local electrodynamic effect are developed. Inspired by the success in explaining classic 115-series heavy fermion superconductors, we expect the present theory will be applied to understand other heavy fermion superconductors such as CeCu2Si2 and more generic multi-band superconductors.
Fermion mass hierarchies in theories of technicolor
Peskin, M.E.
1981-01-01
Models in which light fermion masses result from dynamical symmetry breaking often produce these masses in a hierarchial pattern. The author exhibits two scenarios for obtaining such hierarchies and illustrates each with a simple model of mass generation. In the first scenario, the light fermion masses are separated by powers of a weak coupling constant; in the second scenario, they are separated by a ratio of large mass scales
Anomalous diffusion of fermions in superlattices
Drozdz, S.; Okolowicz, J.; Srokowski, T.; Ploszajczak, M.
1996-03-01
Diffusion of fermions in the periodic two-dimensional lattice of fermions is studied. It is shown that effects connected with antisymmetrization of the wave function increase chaoticness of motion. Various types of anomalous diffusion, characterized by a power spectral analysis are found. The nonlocality of the Pauli potential destroys cantori in the phase space. Consequently, the diffusion process is dominated by long free paths and the power spectrum is logarithmic at small frequency limit. (author)
The physics and chemistry of heavy Fermions
Fisk, Z.; Sarrao, J.L.
1994-01-01
The heavy Fermions are a subset of the f-element intermetallics straddling the magnetic/non-magnetic boundary. Their low temperature properties are characterized by an electronic energy scale of order 1--10 K. Among the low temperature ground states observed in heavy Fermion compounds are exotic superconductors and magnets, as well as unusual semiconductors. We review here the current experimental and theoretical understanding of these systems
Singlet fermionic dark matter with Veltman conditions
Kim, Yeong Gyun; Lee, Kang Young; Nam, Soo-hyeon
2018-01-01
We reexamine a renormalizable model of a fermionic dark matter with a gauge singlet Dirac fermion and a real singlet scalar which can ameliorate the scalar mass hierarchy problem of the Standard Model (SM). Our model setup is the minimal extension of the SM for which a realistic dark matter (DM) candidate is provided and the cancellation of one-loop quadratic divergence to the scalar masses can be achieved by the Veltman condition (VC) simultaneously. This model extension, although renormaliz...
The Continuum Limit of Causal Fermion Systems
Finster, Felix
2016-01-01
This monograph introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting cases and is therefore a candidate for a unified physical theory. From the mathematical perspective, causal fermion systems provide a general framework for describing and analyzing non-smooth geometries and "quantum geometries." The dynamics is described by...
The effective action for chiral fermions
Alvarez-Gaume, L.
1985-01-01
This paper reports on recent work which given an exact characterization of the imaginary part of the effective action for chiral fermions in 2n dimensions in terms of the spectral asymmetry of a suitable (2n+1)-dimensional operator. In order to keep the discussion as simple as possible, the author concentrates on four dimensional fermions with arbitrary external gauge fields. This approach can be extended without difficulty to higher dimensions and also to include external gravitational fields
Fermionic topological quantum states as tensor networks
Wille, C.; Buerschaper, O.; Eisert, J.
2017-06-01
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.
Fermion-induced quantum critical points.
Li, Zi-Xiang; Jiang, Yi-Fan; Jian, Shao-Kai; Yao, Hong
2017-08-22
A unified theory of quantum critical points beyond the conventional Landau-Ginzburg-Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points. We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a fermion-induced quantum critical points for N = 2, 3, 4, 5 and 6, consistent with the renormalization group analysis. We finally discuss possible experimental realizations of the fermion-induced quantum critical points in graphene and graphene-like materials.Quantum phase transitions are governed by Landau-Ginzburg theory and the exceptions are rare. Here, Li et al. propose a type of Landau-forbidden quantum critical points induced by gapless fermions in two-dimensional Dirac semimetals.
Interacting fermions on a random lattice
Perantonis, S.J.; Wheater, J.F.
1988-01-01
We extend previous work on the properties of the Dirac lagrangian on two-dimensional random lattices to the case where interaction terms are included. Although for free fermions the chiral symmetry of the doubles is spontaneously broken by their interaction with the lattice and tehy decouple from long-distance physics, our results in this paper show that all is undone by quantum corrections in an interacting field theory and taht the end result is very similar to what is found with Wilson fermions. Two field-theoretical models with interacting fermions are studied by perturbation expansion in the field theory coupling constant. These are a model with one fermion and one boson species interacting via a scalar Yukawa coupling and the massive Thirring model. It is shown that on the random lattice ultraviolet finite diagrams and finite parts of ultraviolet divergent diagrams have the correct continuum limit. Ultraviolet divergent parts can be removed by the same renormalisation procedure as in the continuum, but do not exhibit the same dependence on the lagrangian mass. In the case of the massive Thirring model this causes a fermion mass correction of order the cut-off scale, which breaks the chiral symmetry of the remaining light fermion; there is consequently a fine-tuning problem. In the context of the same model we discuss the effect of the Goldstone boson associated with the spontaneous breakdown of the chiral symmetry of the doubles on two-dimensional models with vector couplings. (orig.)
Iterants, Fermions and Majorana Operators
Kauffman, Louis H.
Beginning with an elementary, oscillatory discrete dynamical system associated with the square root of minus one, we study both the foundations of mathematics and physics. Position and momentum do not commute in our discrete physics. Their commutator is related to the diffusion constant for a Brownian process and to the Heisenberg commutator in quantum mechanics. We take John Wheeler's idea of It from Bit as an essential clue and we rework the structure of that bit to a logical particle that is its own anti-particle, a logical Marjorana particle. This is our key example of the amphibian nature of mathematics and the external world. We show how the dynamical system for the square root of minus one is essentially the dynamics of a distinction whose self-reference leads to both the fusion algebra and the operator algebra for the Majorana Fermion. In the course of this, we develop an iterant algebra that supports all of matrix algebra and we end the essay with a discussion of the Dirac equation based on these principles.
Fermionic pentagons and NMHV hexagon
A.V. Belitsky
2015-05-01
Full Text Available We analyze the near-collinear limit of the null polygonal hexagon super Wilson loop in the planar N=4 super-Yang–Mills theory. We focus on its Grassmann components which are dual to next-to-maximal helicity-violating (NMHV scattering amplitudes. The kinematics in question is studied within a framework of the operator product expansion that encodes propagation of excitations on the background of the color flux tube stretched between the sides of Wilson loop contour. While their dispersion relation is known to all orders in 't Hooft coupling from previous studies, we find their form factor couplings to the Wilson loop. This is done making use of a particular tessellation of the loop where pentagon transitions play a fundamental role. Being interested in NMHV amplitudes, the corresponding building blocks carry a nontrivial charge under the SU(4 R-symmetry group. Restricting the current consideration to twist-two accuracy, we analyze two-particle contributions with a fermion as one of the constituents in the pair. We demonstrate that these nonsinglet pentagons obey bootstrap equations that possess consistent solutions for any value of the coupling constant. To confirm the correctness of these predictions, we calculate their contribution to the super Wilson loop demonstrating agreement with recent results to four-loop order in 't Hooft coupling.
Fermion bag solutions to some unsolved sign problems
Li, Anyi; Chandrasekharan, Shailesh
2012-03-01
Some interesting lattice four-fermion models containing N flavors of staggered fermions with Z2 and U(1) chiral symmetries suffer from sign problems in the auxiliary field approach. Earlier calculations have either ignored these sign problems or have circumvented them by adding conjugate fermion fields which changes the model. In this talk we show that the recently proposed fermion bag approach solves these sign problems. The basic idea of the new approach is to collect unpaired fermionic degrees of freedom inside a fermion bag. A resummation of all fermion world lines inside the bag is then sufficient to solve the sign problems. The fermion bag approach provides new opportunities to solve in these ``unsolved'' four-fermion models in the chiral limit efficiently.
Nambu-Goldstone Fermion Mode in Quark-Gluon Plasma and Bose-Fermi Cold Atom System
Satow, D.
2015-01-01
It was suggested that supersymmetry (SUSY) is broken at finite temperature, and as a result of the symmetry breaking, a Nambu-Goldstone fermion (goldstino) related to SUSY breaking appears. Since dispersion relations of quarks and gluons are almost degenerate at extremely high temperature, quasi-zero energy quark excitation was suggested to exist in quark-gluon plasma (QGP), though QCD does not have exact SUSY. On the other hand, in condensed matter system, a setup of cold atom system in which the Hamiltonian has SUSY was proposed, the goldstino was suggested to exist, and the dispersion relation of that mode at zero temperature was obtained recently. In this presentation, we obtain the expressions for the dispersion relation of the goldstino in cold atom system at finite temperature, and compare it with the dispersion of the quasi zero-mode in QGP. Furthermore, we show that the form of the dispersion relation of the goldstino can be understood by using an analogy with a magnon in ferromagnet. We also discuss on how the dispersion relation of the goldstino is reflected in observable quantities in experiment. (author)
Liouville equation of relativistic charged fermion
Wang Renchuan; Zhu Dongpei; Huang Zhuoran; Ko Che-ming
1991-01-01
As a form of density martrix, the Wigner function is the distribution in quantum phase space. It is a 2 X 2 matrix function when one uses it to describe the non-relativistic fermion. While describing the relativistic fermion, it is usually represented by 4 x 4 matrix function. In this paper authors obtain a Wigner function for the relativistic fermion in the form of 2 x 2 matrix, and the Liouville equation satisfied by the Wigner function. this equivalent to the Dirac equation of changed fermion in QED. The equation is also equivalent to the Dirac equation in the Walecka model applied to the intermediate energy nuclear collision while the nucleon is coupled to the vector meson only (or taking mean field approximation for the scalar meson). Authors prove that the 2 x 2 Wigner function completely describes the quantum system just the same as the relativistic fermion wave function. All the information about the observables can be obtained with above Wigner function
The hidden fermions in Z(2) theories
Srednicki, M.
1983-01-01
Low dimensional Z(2) gauge theories have been rewritten in terms of locally coupled fermionic degrees of freedom by means of the Jordan-Wigner transformation. In this paper it is shown that higher dimensional Z(2) gauge theories are also fermionic theories in disguise. The SML solution to the 1+1 dimension Ising model is reviewed. Psi operators are represented pictorially as arrows, psi 1 points to the left, psi 2 to the right, each site of H a multiple of two operators. The 2+1 dimension Ising model is then considered. A fermion plaquette operator is introduced as the generator of a gauge symmetry for the fermionic H. Findings in 1+1 and 2+1 are then applied to 3+1 dimensional Z(2) gauge theory. A construction of this lattice is undertaken. Psi formalism replaces sigma formalism, as it permits extremely simple duality transformations to be made on any Z(2) Hamiltonian. It is shown that the fermionic formalism will lead to new ideas in Z(2) theories
Streuer, T.
2005-07-15
In this thesis QCD on the lattice was simulated with overlap fermions in the valence-quark approximation. We haver studied the spectrum of the light hadrons, spectral properties of the Dirac operator as well as hadronic matrix elements. The dependence of the masses of the light hadrons on the quark mass agrees with the prediction of the chiral perturbation theory. especially the artefacts of the valence-quark approximation at small quark masses are clearly recognizable. The values of the hadron masses determined by us exhibit deviations from the experimental values, which lie in the order of magnitude of ten percent. This we interpret as effect of the valence-quark approximation. The spectral properties of the Dirac operator are far reachingly fixed by the chiral symmetry. In order to study this property on the lattice, it is therefore indispensable to work with a lattice discretization, which respects the chiral symmetry, so that between the topology of the gauge field and the zero modes of the Dirac operator the same connection exists as in the continuum - the Atiyah-Singer index theorem. We have used this connection in order to determine the topological susceptibility, which enters the Witten-Veneziano formula for the mass of the {eta}' particle. The spectral density of the Dirac operator, which we have determined, follows the shape predicted by the chiral perturbation theory; from this we could determine the parameters {sigma} and {delta} of the effective Lagangian density. The distribution of the smallest eigenvalues of the Dirac operator agrees with the prediction of the random matrix theory. The value for the axial charge of the nucleon calculated by us deviates by about ten percent from the experimentally determined value g{sub A}=1.26. The order of magnitude of this deviation is typical for the valence-quark approximation. The matrix element v{sub 2b}, which enters the operator-product expansion of the first moment of the unpolarized nucleon structure
Adding gauge fields to Kaplan's fermions
Blum, T.; Kaerkkaeinen, L.
1994-01-01
We experiment with adding dynamical gauge field to Kaplan (defect) fermions. In the case of U(1) gauge theory we use an inhomogeneous Higgs mechanism to restrict the 3d gauge dynamics to a planar 2d defect. In our simulations the 3d theory produce the correct 2d gauge dynamics. We measure fermion propagators with dynamical gauge fields. They posses the correct chiral structure. The fermions at the boundary of the support of the gauge field (waveguide) are non-chiral, and have a mass two times heavier than the chiral modes. Moreover, these modes cannot be excited by a source at the defect; implying that they are dynamically decoupled. We have also checked that the anomaly relation is fullfilled for the case of a smooth external gauge field. (orig.)
Ladder physics in the spin fermion model
Tsvelik, A. M.
2017-01-01
A link is established between the spin fermion (SF) model of the cuprates and the approach based on the analogy between the physics of doped Mott insulators in two dimensions and the physics of fermionic ladders. This enables one to use nonperturbative results derived for fermionic ladders to move beyond the large-N approximation in the SF model. Here, it is shown that the paramagnon exchange postulated in the SF model has exactly the right form to facilitate the emergence of the fully gapped d-Mott state in the region of the Brillouin zone at the hot spots of the Fermi surface. Hence, the SF model provides an adequate description of the pseudogap.
Entanglement negativity bounds for fermionic Gaussian states
Eisert, Jens; Eisler, Viktor; Zimborás, Zoltán
2018-04-01
The entanglement negativity is a versatile measure of entanglement that has numerous applications in quantum information and in condensed matter theory. It can not only efficiently be computed in the Hilbert space dimension, but for noninteracting bosonic systems, one can compute the negativity efficiently in the number of modes. However, such an efficient computation does not carry over to the fermionic realm, the ultimate reason for this being that the partial transpose of a fermionic Gaussian state is no longer Gaussian. To provide a remedy for this state of affairs, in this work, we introduce efficiently computable and rigorous upper and lower bounds to the negativity, making use of techniques of semidefinite programming, building upon the Lagrangian formulation of fermionic linear optics, and exploiting suitable products of Gaussian operators. We discuss examples in quantum many-body theory and hint at applications in the study of topological properties at finite temperature.
Exotic fermions and electric dipole moments
Joshipura, A.S.
1991-01-01
The contributions of mirror fermions to the electric dipole moments (EDM's) of leptons and neutrons are studied using the available limits on the mixing of the relevant fermions to their mirror partners. These limits imply EDM's several orders of magnitude larger than the current experimental bounds in the case of the electron and the neutron if the relevant CP-violating phases are not unnaturally small. If these phases are large, then the bounds on the EDM's can be used to improve upon the limits on mixing between the ordinary (f) and the mirror (F) fermions. In the specific case of the latter mixing angle being given by (m f /M F ) 1/2 , one can obtain the electron and the neutron EDM's close to experimental bounds
Improved formulation of GNO fermionization theorem
Fre, P.; Gliozzi, F.; Piras, A.
1989-01-01
It is pointed out that in the Kac-Moody algebras fulfilling the fermionization criterion of Goddard, Nahm and Olive and having a non-minimal value of the central charge κ, only a proper subset of the allowed unitary highest weight representations can actually be encoded in a free fermion theory. These truly fermionizable representations are selected by a very specific non-regular embedding of the fermionizable Kac-Moody algebra into the lowest level SO(N F ) Kac-Moody algebra, N F being both the number of fermions and the dimension of the GNO symmetric space. This embedding is a particular case of the embeddings considered by Bais and Bouwknegt and by Schellekens and Warner, for which the Virasoro central charge of the subgroup is equal to that of the group. Furthermore, these fermionizable representations span an orbit of the modular group always leading to a non-trivial modular invariant partition function
Vacuum polarization and chiral lattice fermions
Randjbar Daemi, S.; Strathdee, J.
1995-09-01
The vacuum polarization due to chiral fermions on a 4-dimensional Euclidean lattice is calculated according to the overlap prescription. The fermions are coupled to weak and slowly varying background gauge and Higgs fields, and the polarization tensor is given by second order perturbation theory. In this order the overlap constitutes a gauge invariant regularization of the fermion vacuum amplitude. Its low energy - long wavelength behaviour can be computed explicitly and we verify that it coincides with the Feynman graph result obtainable, for example, by dimensional regularization of continuum gauge theory. In particular, the Standard Model Callan-Symanzik, RG functions are recovered. Moreover, there are no residual lattice artefacts such as a dependence on Wilson-type mass parameters. (author). 16 refs
Thermofield dynamics and Casimir effect for fermions
Queiroz, H.; Silva, J.C. da; Khanna, F.C.; Malbouisson, J.M.C.; Revzen, M.; Santana, A.E.
2005-01-01
A generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermionic counterpart of the formalism introduced earlier for bosons [Phys. Rev. A 66 (2002) 052101], and is based on the thermofield dynamics approach. We analyze the energy-momentum tensor for the Casimir effect of a free massless fermion field in a d-dimensional box at finite temperature. As a particular case the Casimir energy and pressure for the field confined in a three-dimensional parallelepiped box are calculated. It is found that the attractive or repulsive nature of the Casimir pressure on opposite faces changes depending on the relative magnitude of the edges. We also determine the temperature at which the Casimir pressure in a cubic box changes sign and estimate its value when the edge of the cube is of the order of the confining lengths for baryons
Thermal radiation of fermions by an accelerated wall
Horibe, Minoru
1979-01-01
The theory of particle production by an accelerated wall is extended to the massless Dirac particle. It is shown that the mean occupation number of fermions (anti-fermions) is given by the Fermi distribution function. (author)
Four fermion interaction near four dimensions
Zinn-Justin, J.
1991-01-01
It is known that field theories with attractive four-point fermion interactions can produce scalar bound states: Fermion mass generation by spontaneous chiral symmetry breaking associated with such fermion bound states provides an attractive mechanism for building models of composite Higgs bosons. The ratio of fermion and boson masses can then be predicted while it seems to be a free parameter in similar models where a boson field explicitly appears in the action. The main problem is that the corresponding models are renormalizable only in two dimensions, in contrast with models with explicit bosons. Many fermion models with four-point interaction are asymptotically free in two dimensions and then behave also like renormalizable models in higher dimensions, at least within the framework of some 1/N expansion. On the other hand mass ratio predictions also follow in the models with explicit bosons, when they have an IR fixed point, from the additional natural assumption that coupling constants have generic values at the cut-off scale. To the model with a four fermion interaction one can associate an effective model containing an additional scalar field, renormalizable in four dimensions, which has the same large distance, small momentum physics, at least to all orders in some 1/N expansion. Even the leading corrections corresponding to irrelevant or marginal operators are identical. This property is important in four dimensions where the IR fixed point coupling constants vanish: The correction amplitudes can be varied by changing the coupling constants in the renormalizable model and the cut-off function in the perturbatively non-renormalizable model. We shall consider here for definiteness only the Gross-Neveu model but it will be clear that the arguments are more general
Fermion boson metamorphosis in field theory
Ha, Y.K.
1982-01-01
In two-dimensional field theories many features are especially transparent if the Fermi fields are represented by non-local expressions of the Bose fields. Such a procedure is known as boson representation. Bilinear quantities appear in the Lagrangian of a fermion theory transform, however, as simple local expressions of the bosons so that the resulting theory may be written as a theory of bosons. Conversely, a theory of bosons may be transformed into an equivalent theory of fermions. Together they provide a basis for generating many interesting equivalences between theories of different types. In the present work a consistent scheme for constructing a canonical Fermi field in terms of a real scalar field is developed and such a procedure is valid and consistent with the tenets of quantum field theory is verified. A boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. The nature of dynamical generation of mass when the theory undergoes boson transmutation and the preservation of continuous chiral symmetry in the massive case are examined. The dynamics of the system depends to a great extent on the specific number of fermions and different models of the same system can have very different properties. Many unusual symmetries of the fermion theory, such as hidden symmetry, duality and triality symmetries, are only manifest in the boson formulation. The underlying connections between some models with U(N) internal symmetry and another class of fermion models built with Majorana fermions which have O(2N) internal symmetry are uncovered
Fermion-fermion scattering in quantum field theory with superconducting circuits.
García-Álvarez, L; Casanova, J; Mezzacapo, A; Egusquiza, I L; Lamata, L; Romero, G; Solano, E
2015-02-20
We propose an analog-digital quantum simulation of fermion-fermion scattering mediated by a continuum of bosonic modes within a circuit quantum electrodynamics scenario. This quantum technology naturally provides strong coupling of superconducting qubits with a continuum of electromagnetic modes in an open transmission line. In this way, we propose qubits to efficiently simulate fermionic modes via digital techniques, while we consider the continuum complexity of an open transmission line to simulate the continuum complexity of bosonic modes in quantum field theories. Therefore, we believe that the complexity-simulating-complexity concept should become a leading paradigm in any effort towards scalable quantum simulations.
Cosmic expansion from boson and fermion fields
De Souza, Rudinei C; Kremer, Gilberto M
2011-01-01
This paper consists in analyzing an action that describes boson and fermion fields minimally coupled to the gravity and a common matter field. The self-interaction potentials of the fields are not chosen a priori but from the Noether symmetry approach. The Noether forms of the potentials allow the boson field to play the role of dark energy and matter and the fermion field to behave as standard matter. The constant of motion and the cyclic variable associated with the Noether symmetry allow the complete integration of the field equations, whose solution produces a universe with alternated periods of accelerated and decelerated expansion.
Parametrization relating the fermionic mass spectra
Kleppe, A.
1993-01-01
When parametrizing the fermionic mass spectra in terms of the unit matrix and a recursive matrix scrR 0 , which corresponds to an underlying scaling pattern in the mass spectra, each fermionic sector is characterized by three parameters: k, α, and R. Using the set of relations displayed by the parameters of the different sectors, it is possible to formulate a ''family Lagrangian'' which for each sector encompasses all the families. Relations between quark masses are furthermore deduced from these ''family Lagrangians.'' Using the relations between the parameters of the different charge sectors, it is also possible to ''derive'' the quark mass spectra from the (charged) leptonic mass spectrum
A Search for Excited Fermions at HERA
Adloff, C.; Andrieu, B.; Arkadov, V.; Astvatsatourov, A.; Ayyaz, I.; Babaev, A.; Bahr, J.; Baranov, P.; Barrelet, E.; Bartel, W.; Bassler, U.; Bate, P.; Beglarian, A.; Behnke, O.; Beier, C.; Belousov, A.; Benisch, T.; Berger, Christoph; Bernardi, G.; Berndt, T.; Bizot, J.C.; Borras, K.; Boudry, V.; Braunschweig, W.; Brisson, V.; Broker, H.B.; Brown, D.P.; Bruckner, W.; Bruel, P.; Bruncko, D.; Burger, J.; Busser, F.W.; Bunyatyan, A.; Burkhardt, H.; Burrage, A.; Buschhorn, G.; Campbell, A.J.; Cao, Jun; Carli, T.; Caron, S.; Chabert, E.; Clarke, D.; Clerbaux, B.; Collard, C.; Contreras, J.G.; Coughlan, J.A.; Cousinou, M.C.; Cox, B.E.; Cozzika, G.; Cvach, J.; Dainton, J.B.; Dau, W.D.; Daum, K.; Davidsson, M.; Delcourt, B.; Delerue, N.; Demirchyan, R.; De Roeck, A.; De Wolf, E.A.; Diaconu, C.; Dixon, P.; Dodonov, V.; Dowell, J.D.; Droutskoi, A.; Duprel, C.; Eckerlin, Guenter; Eckstein, D.; Efremenko, V.; Egli, S.; Eichler, R.; Eisele, F.; Eisenhandler, E.; Ellerbrock, M.; Elsen, E.; Erdmann, M.; Erdmann, W.; Faulkner, P.J.W.; Favart, L.; Fedotov, A.; Felst, R.; Ferencei, J.; Ferron, S.; Fleischer, M.; Flugge, G.; Fomenko, A.; Foresti, I.; Formanek, J.; Foster, J.M.; Franke, G.; Gabathuler, E.; Gabathuler, K.; Garvey, J.; Gassner, J.; Gayler, Joerg; Gerhards, R.; Ghazaryan, Samvel; Goerlich, L.; Gogitidze, N.; Goldberg, M.; Goodwin, C.; Grab, C.; Grassler, H.; Greenshaw, T.; Grindhammer, Guenter; Hadig, T.; Haidt, D.; Hajduk, L.; Haynes, W.J.; Heinemann, B.; Heinzelmann, G.; Henderson, R.C.W.; Hengstmann, S.; Henschel, H.; Heremans, R.; Herrera, G.; Herynek, I.; Hilgers, M.; Hiller, K.H.; Hladky, J.; Hoting, P.; Hoffmann, D.; Hoprich, W.; Horisberger, R.; Hurling, S.; Ibbotson, M.; Issever, C .; Jacquet, M.; Jaffre, M.; Janauschek, L.; Jansen, D.M.; Janssen, X.; Jemanov, V.; Jonsson, L.; Johnson, D.P.; Jones, M.A.S.; Jung, H.; Kastli, H.K.; Kant, D.; Kapichine, M.; Karlsson, M.; Karschnick, O.; Kaufmann, O.; Kausch, M.; Keil, F.; Keller, N.; Kennedy, J.; Kenyon, I.R.; Kermiche, S.; Kiesling, Christian M.; Klein, M.; Kleinwort, C.; Knies, G.; Koblitz, B.; Kolya, S.D.; Korbel, V.; Kostka, P.; Kotelnikov, S.K.; Krasny, M.W.; Krehbiel, H.; Kroseberg, J.; Kruger, K.; Kupper, A.; Kuhr, T.; Kurca, T.; Kutuev, R.; Lachnit, W.; Lahmann, R.; Lamb, D.; Landon, M.P.J.; Lange, W.; Lastovicka, T.; Lebailly, E.; Lebedev, A.; Leissner, B.; Lemrani, R.; Lendermann, V.; Levonian, S.; Lindstroem, M.; Lobodzinska, E.; Lobodzinski, B.; Loktionova, N.; Lubimov, V.; Luders, S.; Luke, D.; Lytkin, L.; Magnussen, N.; Mahlke-Kruger, H.; Malden, N.; Malinovski, E.; Malinovski, I.; Maracek, R.; Marage, P.; Marks, J.; Marshall, R.; Martyn, H.U.; Martyniak, J.; Maxfield, S.J.; Mehta, A.; Meier, K.; Merkel, P.; Metlica, F.; Meyer, H.; Meyer, J.; Meyer, P.O.; Mikocki, S.; Milstead, D.; Mkrtchyan, T.; Mohr, R.; Mohrdieck, S.; Mondragon, M.N.; Moreau, F.; Morozov, A.; Morris, J.V.; Muller, K.; Murin, P.; Nagovizin, V.; Naroska, B.; Naumann, J.; Naumann, Th.; Negri, I.; Nellen, G.; Newman, Paul R.; Nicholls, T.C.; Niebergall, F.; Niebuhr, C.; Nix, O.; Nowak, G.; Nunnemann, T.; Olsson, J.E.; Ozerov, D.; Panassik, V.; Pascaud, C.; Patel, G.D.; Perez, E.; Phillips, J.P.; Pitzl, D.; Poschl, R.; Potachnikova, I.; Povh, B.; Rabbertz, K.; Radel, G.; Rauschenberger, J.; Reimer, P.; Reisert, B.; Reyna, D.; Riess, S.; Rizvi, E.; Robmann, P.; Roosen, R.; Rostovtsev, A.; Royon, C.; Rusakov, S.; Rybicki, K.; Sankey, D.P.C.; Scheins, J.; Schilling, F.P.; Schleper, P.; Schmidt, D.; Schmitt, S.; Schoeffel, L.; Schoning, A.; Schorner, T.; Schroder, V.; Schultz-Coulon, H.C.; Sedlak, K.; Sefkow, F.; Chekelian, V.; Sheviakov, I.; Shtarkov, L.N.; Siegmon, G.; Sievers, P.; Sirois, Y.; Sloan, T.; Smirnov, P.; Solochenko, V.; Solovev, Y.; Spaskov, V.; Specka, Arnd E.; Spitzer, H.; Stamen, R.; Steinhart, J.; Stella, B.; Stellberger, A.; Stiewe, J.; Straumann, U.; Struczinski, W.; Swart, M.; Tasevsky, M.; Tchernyshov, V.; Tchetchelnitski, S.; Thompson, Graham; Thompson, P.D.; Tobien, N.; Traynor, D.; Truoel, Peter; Tsipolitis, G.; Turnau, J.; Turney, J.E.; Tzamariudaki, E.; Udluft, S.; Usik, A.; Valkar, S.; Valkarova, A.; Vallee, C.; Van Mechelen, P.; Vazdik, Y.; von Dombrowski, S.; Wacker, K.; Wallny, R.; Walter, T.; Waugh, B.; Weber, G.; Weber, M.; Wegener, D.; Wegner, A.; Wengler, T.; Werner, M.; White, G.; Wiesand, S.; Wilksen, T.; Winde, M.; Winter, G.G.; Wissing, C.; Wobisch, M.; Wollatz, H.; Wunsch, E.; Wyatt, A.C.; Zacek, J.; Zalesak, J.; Zhang, Z.; Zhokin, A.; Zomer, F.; Zsembery, J.; zur Nedden, M.
2000-01-01
A search for excited fermions f^* of the first generation in e^+p scattering at the collider HERA is presented using H1 data with an integrated luminosity of 37 pb^(-1). All electroweak decays of excited fermions, f^* -> f gamma, f W, f Z are considered and all possible final states resulting from the Z or W hadronic decays or decays into leptons of the first two generations are taken into account. No evidence for f^* production is found. Mass dependent exclusion limits on cross-sections and on the ratio of coupling constants to the compositeness scale are derived.
On the origin of fermion masses
Shrock, R.E.
1992-01-01
We review some recent work on nonperturbative properties of fermions and connections with chiral gauge theories. In particular, we consider one of the ultimate goals of this program: The understanding of the actual fermion mass spectrum. It is pointed out that if quarks and leptons are composite, their masses may be set by the physics of the preons and their interactions in such a manner as to differ considerably from the Yukawa form m f ∝v (where v is the electroweak symmetry breaking scale) or analogous forms involving v. Some ideas of how this might work are given, and some implications are discussed. (orig.)
Fermionic formula for double Kostka polynomials
Liu, Shiyuan
2016-01-01
The $X=M$ conjecture asserts that the $1D$ sum and the fermionic formula coincide up to some constant power. In the case of type $A,$ both the $1D$ sum and the fermionic formula are closely related to Kostka polynomials. Double Kostka polynomials $K_{\\Bla,\\Bmu}(t),$ indexed by two double partitions $\\Bla,\\Bmu,$ are polynomials in $t$ introduced as a generalization of Kostka polynomials. In the present paper, we consider $K_{\\Bla,\\Bmu}(t)$ in the special case where $\\Bmu=(-,\\mu'').$ We formula...
Fermionic determinant in two and four dimensions
Mignaco, J.A.; Rego Monteiro, M.A. do.
1985-01-01
The fermionic determinant of the two-dimensional Schwinger model and QCD and a four-dimensional model with a pseudo-vectorial coupling are discussed. It is observed that in both cases the Dirac operator can be expressed as a path-ordered product of the gauge field and the fermionic determinant is computed exactly without reference to a particular gauge. The two point Green's function is obtained in all cases as a free particle two point function times a model dependent term. (Author) [pt
Fermion fields in η-ξ spacetime
Gui, Y.
1992-01-01
Fermion fields in η-ζ spacetime are discussed. By the path-integral formulation of quantum field theory, we show that the (zero-temperature) Green's functions for Dirac fields on the Euclidean section in η-ζ spacetime are equal to the imaginary-time thermal Green's functions in Minkowski spacetime, and that the (zero-temperature) Green's functions on the Lorentzian section in η-ζ spacetime correspond to the real-time thermal Green's functions in Minkowski spacetime. The antiperiodicity of fermion fields in η-ζ spacetime originates from Lorentz transformation properties of the fields
Noether symmetry for non-minimally coupled fermion fields
Souza, Rudinei C de; Kremer, Gilberto M
2008-01-01
A cosmological model where a fermion field is non-minimally coupled with the gravitational field is studied. By applying Noether symmetry the possible functions for the potential density of the fermion field and for the coupling are determined. Cosmological solutions are found showing that the non-minimally coupled fermion field behaves as an inflaton describing an inflationary scenario, whereas the minimally coupled fermion field describes a decelerated period, behaving as a standard matter field
The bosonic mother of fermionic D-branes
Chattaraputi, Auttakit; Englert, Francois; Houart, Laurent; Taormina, Anne
2002-01-01
We extend the search for fermionic subspaces of the bosonic string compactified on E8 X SO(16) lattices to include all fermionic D-branes. This extension constraints the truncation procedure previously proposed and relates the fermionic strings, supersymmetric or not, to the global structure of the SO(16) group. The specific properties of all the fermionic D-branes are found to be encoded in its universal covering, whose maximal toroid defines the configuration space torus of their mother bos...
q-deformed charged fermion coherent states and SU(3) charged, Hyper-charged fermion coherent states
Hao Sanru; Li Guanghua; Long Junyan
1994-01-01
By virtue of the algebra of the q-deformed fermion oscillators, the q-deformed charged fermion coherent states and SU(3) charged, hyper-charged fermion coherent states are discussed. The explicit forms of the two kinds of coherent states mentioned above are obtained by making use of the completeness of base vectors in the q-fermion Fock space. By comparing the q-deformed results with the ordinary results, it is found that the q-deformed charged fermion coherent states and SU(3) charged, hyper-charged fermion coherent states are automatically reduced to the ordinary charged fermion coherent states and SU(3) charged hyper-charged fermion coherent states if the deformed parameter q→1
Simulating an arbitrary number of flavors of dynamical overlap fermions
DeGrand, T.; Schaefer, S.
2006-05-01
We present a set of related Hybrid Monte Carlo methods to simulate an arbitrary number of dynamical overlap fermions. Each fermion is represented by a chiral pseudo-fermion field. The new algorithm reduces critical slowing down in the chiral limit and for sectors of nontrivial topology. (Orig.)
Extra Z neutral bosons, families and heavy fermions
Li Tiezhong
1989-08-01
The minimal Grand Unified Theories with three-family should include two extra Z neufral bosons which belong to the different broken scales. Georgi's argument on heavy Dirac fermions has been realized. These fermions should not be bizarre. The extra Z and Dirac fermions are not too heavy. The difficulty of the proton decay may be resolved
Non-perturbative renormalisation of left-left four-fermion operators with Neuberger fermions
Dimopoulos, P.; Giusti, L.; Hernandez, P.; Palombi, F.; Pena, C.; Vladikas, A.; Wennekers, J.; Wittig, H.
2006-01-01
We outline a general strategy for the non-perturbative renormalisation of composite operators in discretisations based on Neuberger fermions, via a matching to results obtained with Wilson-type fermions. As an application, we consider the renormalisation of the four-quark operators entering the ΔS=1 and ΔS=2 effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays
Axial gravity, massless fermions and trace anomalies
Bonora, L. [International School for Advanced Studies (SISSA), Trieste (Italy); KEK, Tsukuba (Japan). KEK Theory Center; INFN, Sezione di Trieste (Italy); Cvitan, M.; Giaccari, S.; Stemberga, T. [Zagreb Univ. (Croatia). Dept. of Physics; Prester, P.D. [Rijeka Univ. (Croatia). Dept. of Physics; Pereira, A.D. [UERJ-Univ. Estadual do Rio de Janeiro (Brazil). Dept. de Fisica Teorica; UFF-Univ. Federal Fluminense, Niteroi (Brazil). Inst. de Fisica
2017-08-15
This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background, the second is the introduction of axial gravity. The motivation for reconsidering the former is to clarify the theoretical background underlying the approach and complete the calculation of the anomaly. The reference is in particular to the difference between Weyl and massless Majorana fermions and to the possible contributions from tadpole and seagull terms in the Feynman diagram approach. A first, basic, result of this paper is that a more thorough treatment, taking account of such additional terms and using dimensional regularization, confirms the earlier result. The introduction of an axial symmetric tensor besides the usual gravitational metric is instrumental to a different derivation of the same result using Dirac fermions, which are coupled not only to the usual metric but also to the additional axial tensor. The action of Majorana and Weyl fermions can be obtained in two different limits of such a general configuration. The results obtained in this way confirm the previously obtained ones. (orig.)
Stable simulations of many fermion systems
Loh, E.Y. Jr.; Gubernatis, J.E.; Scalapino, D.J.; Sugar, R.L.; White, S.R.; Scalettar, R.T.; Los Alamos National Lab., NM; California Univ., Santa Barbara, CA; Illinois Univ., Urbana, IL
1989-01-01
As the inverse temperature β becomes large, the diverse numerical scales present in exp(-βH) plague simulations of many-fermion systems on finite-precision computers. Representation of matrices in factorized form stabilizes these calculations, allowing efficient, low-temperature studies of condensed-matter models
Bragg diffraction of fermions at optical potentials
Deh, Benjamin
2008-01-01
This thesis describes the Bragg diffraction of ultracold fermions at an optical potential. A moving optical lattice was created, by overlaying two slightly detuned lasers. Atoms can be diffracted at this lattice if the detuning fulfills the Bragg condition for resting atoms. This Bragg diffraction is analyzed systematically in this thesis. To this end Rabi oscillations between the diffraction states were driven, as well in the weakly interacting Bragg regime, as in the strongly interacting Kapitza-Dirac regime. Simulations, based on a driven two-, respectively multilevel-system describe the observed effects rather well. Furthermore, the temporal evolution of the diffracted states in the magnetic trapping potential was studied. The anharmonicity of the trap in use and the scattering cross section for p-wave collisions in a 6 Li system was determined from the movement of these states. Moreover the momentum distribution of the fermions was measured with Bragg spectroscopy and first signs of Fermi degeneracy were found. Finally an interferometer with fermions was build, exhibiting a coherence time of more than 100 μs. With this, the possibility for measurement and manipulation of ultracold fermions with Bragg diffraction could bee shown. (orig.)
Compact lattice QED with Wilson fermions
Hoferichter, A.
1994-08-01
We study the phase structure and the chiral limit of 4d compact lattice QED with Wilson fermions (both dynamical and quenched). We use the standard Wilson gauge action and also a modified one suppressing lattice artifacts. Different techniques and observables to locate the chiral limit are discussed. (orig.)
Probabilistic representation of fermionic lattice systems
Beccaria, Matteo; Presilla, Carlo; De Angelis, Gian Fabrizio; Jona-Lasinio, Giovanni
2000-01-01
We describe an exact Feynman-Kac type formula to represent the dynamics of fermionic lattice systems. In this approach the real time or Euclidean time dynamics is expressed in terms of the stochastic evolution of a collection of Poisson processes. From this formula we derive a family of algorithms for Monte Carlo simulations, parametrized by the jump rates of the Poisson processes
Axial gravity, massless fermions and trace anomalies
Bonora, L.; Cvitan, M.; Giaccari, S.; Stemberga, T.; Prester, P.D.; Pereira, A.D.; UFF-Univ. Federal Fluminense, Niteroi
2017-01-01
This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background, the second is the introduction of axial gravity. The motivation for reconsidering the former is to clarify the theoretical background underlying the approach and complete the calculation of the anomaly. The reference is in particular to the difference between Weyl and massless Majorana fermions and to the possible contributions from tadpole and seagull terms in the Feynman diagram approach. A first, basic, result of this paper is that a more thorough treatment, taking account of such additional terms and using dimensional regularization, confirms the earlier result. The introduction of an axial symmetric tensor besides the usual gravitational metric is instrumental to a different derivation of the same result using Dirac fermions, which are coupled not only to the usual metric but also to the additional axial tensor. The action of Majorana and Weyl fermions can be obtained in two different limits of such a general configuration. The results obtained in this way confirm the previously obtained ones. (orig.)
Fermion-boson scattering in ladder approximation
Jafarov, R.G.; Hadjiev, S.A.
1992-10-01
A method of calculation of forward scattering amplitude for fermions and scalar bosons with exchanging of scalar particle is suggested. The Bethe-Salpeter ladder equation for the imaginary part of the amplitude is constructed and a solution in Regge asymptotical form is found and the corrections to the amplitude due to the exit from mass shell are calculated. (author). 8 refs
Singlet fermionic dark matter with Veltman conditions
Kim, Yeong Gyun; Lee, Kang Young; Nam, Soo-hyeon
2018-07-01
We reexamine a renormalizable model of a fermionic dark matter with a gauge singlet Dirac fermion and a real singlet scalar which can ameliorate the scalar mass hierarchy problem of the Standard Model (SM). Our model setup is the minimal extension of the SM for which a realistic dark matter (DM) candidate is provided and the cancellation of one-loop quadratic divergence to the scalar masses can be achieved by the Veltman condition (VC) simultaneously. This model extension, although renormalizable, can be considered as an effective low-energy theory valid up to cut-off energies about 10 TeV. We calculate the one-loop quadratic divergence contributions of the new scalar and fermionic DM singlets, and constrain the model parameters using the VC and the perturbative unitarity conditions. Taking into account the invisible Higgs decay measurement, we show the allowed region of new physics parameters satisfying the recent measurement of relic abundance. With the obtained parameter set, we predict the elastic scattering cross section of the new singlet fermion into target nuclei for a direct detection of the dark matter. We also perform the full analysis with arbitrary set of parameters without the VC as a comparison, and discuss the implication of the constraints by the VC in detail.
Strong correlations in few-fermion systems
Bergschneider, Andrea
2017-07-26
In this thesis, I report on the deterministic preparation and the observation of strongly correlated few-fermion systems in single and double-well potentials. In a first experiment, we studied a system of one impurity interacting with a number of majority atoms which we prepared in a single potential well in the one-dimensional limit. With increasing number of majority particles, we observed a decrease in the quasi-particle residue which is in agreement with expectations from the Anderson orthogonality catastrophe. In a second experiment, we prepared two fermions in a double-well potential which represents the fundamental building block of the Fermi-Hubbard model. By increasing the repulsion between the two fermions, we observed the crossover into the antiferromagnetic Mott-insulator regime. Furthermore, I describe a new imaging technique, which allows spin-resolved single-atom detection both in in-situ and in time-of-flight. We use this technique to investigate the emergence of momentum correlations of two repulsive fermions in the ground state of the double well. With the methods developed in this thesis, we have established a framework for quantum simulation of strongly correlated many-body systems in tunable potentials.
Dual of QCD with One Adjoint Fermion
Mojaza, Matin; Nardecchia, Marco; Pica, Claudio
2011-01-01
We construct the magnetic dual of QCD with one adjoint Weyl fermion. The dual is a consistent solution of the 't Hooft anomaly matching conditions, allows for flavor decoupling and remarkably constitutes the first nonsupersymmetric dual valid for any number of colors. The dual allows to bound...
Fermions Living in a Flat World
Jesus Anguiano-Galicia, Ma. de; Bashir, A.
2006-01-01
In a plane, parity transformation, which changes the sign of only one spatial coordinate, swaps the fermion fields living in two inequivalent representations. A parity invariant Lagrangian thus contains fields corresponding to both the representations. For such a Lagrangian, we show that we can also define a chiral symmetry
Fermionic dimensions and Kaluza-Klein theory
Delbourgo, R.; Zhang, R.B.
1988-01-01
Instead of appending extra bosonic dimensions to spacetime and needing to exorcise the higher modes, it is possible to construct Kaluza-Klein models in which the additional coordinates are fermionic and the higher modes do not arise. We erect a unified gravity/Yang-Mills theory on such a grassmannian framework and then discuss possible generalisations to other internal groups. (orig.)
Mirror fermions in chiral gauge theories
Montvay, I.
1992-06-01
Mirror fermions appear naturally in lattice formulations of the standard model. The phenomenological limits on their existence and discovery limits at future colliders are discussed. After an introduction of lattice actions for chiral Yukawa-models, a recent numerical simulation is presented. In particular, the emerging phase structures and features of the allowed region in renormalized couplings are discussed. (orig.)
Unorthodox lattice fermion derivatives and their shortcomings
Bodwin, G.T.; Kovacs, E.V.
1987-01-01
We discuss the DWY (Lagrangian), Quinn-Weinstein, and Rebbi proposals for incorporating fermions into lattice gauge theory and analyze them in the context of weak coupling perturbation theory. We find that none of these proposals leads to a completely satisfactory lattice transcription of fully-interacting gauge theory
SU(3) sextet model with Wilson fermions
Hansen, Martin; Drach, Vincent; Pica, Claudio
2017-01-01
to be inside or very close to the lower boundary of the conformal window. We use the Wilson discretization for the fermions and map the phase structure of the lattice model. We study several spectral and gradient flow observables both in the bulk and the weak coupling phases. While in the bulk phase we find...
Unconventional superconductivity in heavy-fermion compounds
White, B.D. [Department of Physics, University of California, San Diego, La Jolla, CA 92093 (United States); Center for Advanced Nanoscience, University of California, San Diego, La Jolla, CA 92093 (United States); Thompson, J.D. [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Maple, M.B., E-mail: mbmaple@ucsd.edu [Department of Physics, University of California, San Diego, La Jolla, CA 92093 (United States); Center for Advanced Nanoscience, University of California, San Diego, La Jolla, CA 92093 (United States)
2015-07-15
Highlights: • Quasiparticles in heavy-fermion compounds are much heavier than free electrons. • Superconductivity involves pairing of these massive quasiparticles. • Quasiparticle pairing mediated by magnetic or quadrupolar fluctuations. • We review the properties of superconductivity in heavy-fermion compounds. - Abstract: Over the past 35 years, research on unconventional superconductivity in heavy-fermion systems has evolved from the surprising observations of unprecedented superconducting properties in compounds that convention dictated should not superconduct at all to performing explorations of rich phase spaces in which the delicate interplay between competing ground states appears to support emergent superconducting states. In this article, we review the current understanding of superconductivity in heavy-fermion compounds and identify a set of characteristics that is common to their unconventional superconducting states. These core properties are compared with those of other classes of unconventional superconductors such as the cuprates and iron-based superconductors. We conclude by speculating on the prospects for future research in this field and how new advances might contribute towards resolving the long-standing mystery of how unconventional superconductivity works.
Nonperturbative treatment of reduced model with fermions
Gutierrez, W.R.
1983-01-01
A nonperturbative method is presented to show that the reduced model produces the correct leading large-N contribution to the fermion Green's functions. A new form of the reduced model is introduced, which avoids the quenching procedure. Also the equation for the meson bound states is discussed. The method is illustrated in the case of two-dimensional QCD
Superconducting gap anomaly in heavy fermion systems
of a pseudo-gap due to superconductivity and the signature of a hybridization gap at the. Fermi level. For the choice of the model parameters, the DOS shows that the HFS is a metal and undergoes a transition to the gap-less superconducting state. Keywords. Heavy fermion superconductor; Narrow band system; Valence ...
Superconductivity in Correlated Fermions System | Babalola ...
We have studied the Hubbard model which is a model that is used to describe the physics of strongly correlated Fermions systems. Using the Hubbard model, we worked on some systems in one dimension (1-D) at half fillings. We employed the numerical exact diagonalization technique and found out that there was a ...
Hidden supersymmetry and Fermion number fractionalization
Akhoury, R.
1985-01-01
This paper discusses how a hidden supersymmetry of the underlying field theories can be used to interpret and to calculate fermion number fractionalization in different dimensions. This is made possible by relating it to a corresponding Witten index of the hidden supersymmetry. The closely related anomalies in odd dimensions are also discussed
Hidden symmetry of a free fermion model
Bazhanov, V.V.; Stroganov, Yu.G.
1984-01-01
A well-known eight-vertex free fermion model on a plane lattice is considered. Solving triangle equations and using the symmetry properties of the model, an elliptic parametrization for Boltzmann vertex weights is constructed. In the parametrization the weights are meromorphic functions of three complex variables
Geometry of non-degenerate Susskind fermions
Mitra, P.
1983-01-01
The Dirac-Kaehler equation on the lattice is known to describe the degenerate ''flavours'' appering in Susskind's approach to lattice fermions. We study the modification that has to be made in this equation in order to lift the degeneracy and give the flavours arbitrary different masses. (orig.)
Kaon decay amplitudes using staggered fermions
Sharpe, S.R.
1986-12-01
A status report is given of an attempt, using staggered fermions to calculate the real and imaginary parts of the amplitudes for K → ππ,. Semi-quantitative results are found for the imaginary parts, and these suggest that ε' might be smaller than previously expected in the standard model
Georgios, Anagnostou
2004-01-01
Combined measurements of the 4 LEP collaborations for the fermion pair processes e + e - →f anti f are presented. The results show no significant deviations when compared with the Standard Model predictions and are used to set limits on contact interactions, Z' gauge bosons and low scale gravity models with large extra dimensions. (orig.)
Evaluating the fermionic determinant of dynamical configurations
Hasenfratz, Anna; Alexandru, Andrei
2002-01-01
We propose and study an improved method to calculate the fermionic determinant of dynamical configurations. The evaluation or at least stochastic estimation of the ratios of fermionic determinants is essential for a recently proposed updating method of smeared link dynamical fermions. This update creates a sequence of configurations by changing a subset of the gauge links by a pure gauge heat bath or over-relaxation step. The acceptance of the proposed configuration depends on the ratio of the fermionic determinants on the new and original configurations. We study this ratio as a function of the number of links that are changed in the heat bath update. We find that even when every link of a given direction and parity of a 10 fm 4 configuration is updated, the average of the determinant ratio is still close to one and with the improved stochastic estimator the proposed change is accepted with about 20% probability. This improvement suggests that the new updating technique can be efficient even on large lattices and could provide an updating method for dynamical overlap actions
Asymptotically Safe Standard Model via Vectorlike Fermions
Mann, R. B.; Meffe, J. R.; Sannino, F.; Steele, T. G.; Wang, Z. W.; Zhang, C.
2017-12-01
We construct asymptotically safe extensions of the standard model by adding gauged vectorlike fermions. Using large number-of-flavor techniques we argue that all gauge couplings, including the hypercharge and, under certain conditions, the Higgs coupling, can achieve an interacting ultraviolet fixed point.
Born-Kothari Condensation for Fermions
Arnab Ghosh
2017-09-01
Full Text Available In the spirit of Bose–Einstein condensation, we present a detailed account of the statistical description of the condensation phenomena for a Fermi–Dirac gas following the works of Born and Kothari. For bosons, while the condensed phase below a certain critical temperature, permits macroscopic occupation at the lowest energy single particle state, for fermions, due to Pauli exclusion principle, the condensed phase occurs only in the form of a single occupancy dense modes at the highest energy state. In spite of these rudimentary differences, our recent findings [Ghosh and Ray, 2017] identify the foregoing phenomenon as condensation-like coherence among fermions in an analogous way to Bose–Einstein condensate which is collectively described by a coherent matter wave. To reach the above conclusion, we employ the close relationship between the statistical methods of bosonic and fermionic fields pioneered by Cahill and Glauber. In addition to our previous results, we described in this mini-review that the highest momentum (energy for individual fermions, prerequisite for the condensation process, can be specified in terms of the natural length and energy scales of the problem. The existence of such condensed phases, which are of obvious significance in the context of elementary particles, have also been scrutinized.
Large cutoff effects of dynamical Wilson fermions
Sommer, R.; Hoffmann, R.; Knechtli, F.; Rolf, J.; Wolff, U.; Wetzorke, I.
2003-09-01
We present and discuss results for cutoff effects in the PCAC masses and the mass dependence of r 0 for full QCD and various fermion actions. Our discussion of how one computes mass dependences - here of r 0 - is also relevant for comparisons with chiral perturbation theory. (orig.)
Axial anomaly and index theorem for Dirac-Kaehler fermions
Fonseca Junior, C.A.L. da.
1985-02-01
Some aspects of topological influence on gauge field theory are analysed, considering the geometry and differential topology methods. A review of concepts of differential forms, fibered spaces, connection and curvature, showing an interpretation of gauge theory in this context, is presented. The question of fermions, analysing in details the Dirac-Kaehler which fermionic particle is considered a general differential form, is studied. It is shown how the explicit expressions in function of the Dirac spinor components vary with the Dirac matrix representation. The Dirac-Kahler equation contains 4 times (in 4 dimensions) the Dirac equation, each particle being associated an ideal at left of the algebra of general differential forms. These ideals and the SU(4) symmetry among them are also studied on the point of view of spinors and, the group of reduction to one of the ideals is identified as the Cartan subalgebra of this SU(4). Finally, the axial anomaly is calculated through the functional determinant given by the Dirac-Kaehler operator. The regularization method is the Seeley's coefficients. From that results a comparison of the index theorems for the twisted complexes of signature and spin, which proportionality is given by the number of the algebra ideals contained in the Dirac-Kaehler equation and which also manifests in the respective axial anomaly equations. (L.C.) [pt
Multi-boson block factorization of fermions
Giusti, Leonardo; Cè, Marco; Schaefer, Stefan
2018-03-01
The numerical computations of many quantities of theoretical and phenomenological interest are plagued by statistical errors which increase exponentially with the distance of the sources in the relevant correlators. Notable examples are baryon masses and matrix elements, the hadronic vacuum polarization and the light-by-light scattering contributions to the muon g - 2, and the form factors of semileptonic B decays. Reliable and precise determinations of these quantities are very difficult if not impractical with state-of-the-art standard Monte Carlo integration schemes. I will review a recent proposal for factorizing the fermion determinant in lattice QCD that leads to a local action in the gauge field and in the auxiliary boson fields. Once combined with the corresponding factorization of the quark propagator, it paves the way for multi-level Monte Carlo integration in the presence of fermions opening new perspectives in lattice QCD. Exploratory results on the impact on the above mentioned observables will be presented.
Excitation spectrum of correlated Dirac fermions
Jalali, Z.; Jafari, S. A.
2015-04-01
Motivated by the puzzling optical conductivity measurements in graphene, we speculate on the possible role of strong electronic correlations on the two-dimensional Dirac fermions. In this work we employ the slave-particle method to study the excitations of the Hubbard model on honeycomb lattice, away from half-filling. Since the ratio U/t ≈ 3.3 in graphene is not infinite, double occupancy is not entirely prohibited and hence a finite density of doublonscan be generated. We therefore extend the Ioff-Larkin composition rule to include a finite density of doublons. We then investigate the role played by each of these auxiliary particles in the optical absorption of strongly correlated Dirac fermions.
Perturbative analysis for Kaplan's lattice chiral fermions
Aoki, S.; Hirose, H.
1994-01-01
Perturbation theory for lattice fermions with domain wall mass terms is developed and is applied to investigate the chiral Schwinger model formulated on the lattice by Kaplan's method. We calculate the effective action for gauge fields to one loop, and find that it contains a longitudinal component even for anomaly-free cases. From the effective action we obtain gauge anomalies and Chern-Simons currents without ambiguity. We also show that the current corresponding to the fermion number has a nonzero divergence and it flows off the wall into the extra dimension. Similar results are obtained for a proposal by Shamir, who used a constant mass term with free boundaries instead of domain walls
A nonperturbative fermion-boson vertex
Bashir, A.; Raya, A.
2002-01-01
We calculate the massive fermion propagator at one-loop order in QED3. The Ward-Takahashi identity (WTI) relates the propagator to the vertex. This allows us to split the vertex into its longitudinal and transverse parts. The former is fixed by the WTI. Following the scheme of Ball and Chiu later modified by Kizilersue et. al., we calculate the full vertex at one-loop order. A mere subtraction of the longitudinal part of the vertex gives us the transverse part. The α dependence in the transverse vertex can be eliminated by making use of the perturbative expressions for the wavefunction renormalization function and the mass function of complicated arguments of the incoming and outgoing fermion momenta. This leads us to a vertex which is nonperturbative in nature. We also calculate an effective vertex for which the arguments of the unknown functions have no angular dependence, making it particularly suitable for numerical studies of dynamical symmetry breaking
4d fermionic superstrings with arbitrary twists
Antoniadis, I.; Bachas, C.
1988-01-01
We present the rules for systematically constructing all consistent four-dimensional string theories, using free world-sheet fermions which pick up arbitrary phases when parallel transported around the string. These rules are necessary and sufficient for multi-loop modular invariance. They lead to theories with general Z N (GSO-type) projections, whose merits for model-building we discuss. We classify all boundary conditions yielding massless space-time spinors. We show that, in contrast to the case of only real 2d fermions, all possible realizations of world-sheet supersymmetry are now allowed. This opens the way for the construction of a new class of supersymmetric string models. (orig.)
SU(2) with fundamental fermions and scalars
Hansen, Martin; Janowski, Tadeusz; Pica, Claudio; Toniato, Arianna
2018-03-01
We present preliminary results on the lattice simulation of an SU(2) gauge theory with two fermion flavors and one strongly interacting scalar field, all in the fundamental representation of SU(2). The motivation for this study comes from the recent proposal of "fundamental" partial compositeness models featuring strongly interacting scalar fields in addition to fermions. Here we describe the lattice setup for our study of this class of models and a first exploration of the lattice phase diagram. In particular we then investigate how the presence of a strongly coupled scalar field affects the properties of light meson resonances previously obtained for the SU(2) model. Preprint: CP3-Origins-2017-047 DNRF90
Arbitrary spin fermions on the lattice
Bullinaria, J.A.
1985-01-01
Lattice actions are constructed for free Dirac and Majorana fermions of arbitrary (half-integer) spin various extensions of the spin 1/2 Kogut-Susskind, Kaehler and Wilson formalisms. In each case, the spectrum degeneracy and preservation of gauge invariance is analysed, and the equivalence or non-equivalence to previously constructed actions is determined. The Kogut-Susskind and lattice Kaehler actions are then written explicitly in terms of spinors to demonstrate how the degenerate fermions couple on the lattice and how the original spinorial actions are recovered (or to recovered) in the continuum limit. Both degenerate and non-degenerate mass terms are dealt with and the various U(1) invariances of the lattice actions are pointed out
On charged fermions in two dimensions
Randjbar-Daemi, S.; Salam, A.; Strathdee, J.
1990-09-01
The integer quantum Hall effect and associated magnetic phenomena are reconsidered in a 2-dimensional system with a flat boundary. The electromagnetic properties of this system are governed by an effective Lagrangian which includes an induced Chern-Simons term. The effective lagrangian is relevant for the description of fields which are slowly varying about a uniform magnetic background associated with a fermionic ground state in which a whole number of Landau levels is filled. It is singular for field values that correspond to partially filled levels. The underlying assumption of translation invariance of the fermionic ground state fails in the vicinity of boundaries where the effective field theory is essentially non-local. The width of the boundary layer and the current flowing in it are estimated. (author). 12 refs, 5 figs
Bosonic and fermionic dipoles on a ring
Zöllner, Sascha; Pethick, C. J.; Bruun, Georg Morten
2011-01-01
We show that dipolar bosons and fermions confined in a quasi-one-dimensional ring trap exhibit a rich variety of states because their interaction is inhomogeneous. For purely repulsive interactions, with increasing strength of the dipolar coupling there is a crossover from a gaslike state...... to an inhomogeneous crystal-like one. For small enough angles between the dipoles and the plane of the ring, there are regions with attractive interactions, and clustered states can form....
Semiclassical expansions for confined N fermion systems
Krivine, H.; Martorell, J.; Casas, M.
1989-01-01
A new derivation of the Wigner Kirkwood expansion for N-fermion systems is presented, showing explicitly the connection to the WKB approximation for a single level. This allows to study separately the two ansatz required to obtain the semiclassical expansions: the asymptotic expansions in powers of ℎ and the smoothing of quantal effects. We discuss the one dimensional and three dimensional, with spherical symmetry, cases. Applications for standard potentials used in nuclear physics are described in detail
SU (2) with fundamental fermions and scalars
Hansen, Martin; Janowski, Tadeusz; Pica, Claudio
2018-01-01
We present preliminary results on the lattice simulation of an SU(2) gauge theory with two fermion flavors and one strongly interacting scalar field, all in the fundamental representation of SU(2). The motivation for this study comes from the recent proposal of "fundamental" partial compositeness...... the properties of light meson resonances previously obtained for the SU(2) model. Preprint: CP3-Origins-2017-047 DNRF90...
Extended nonabelian symmetries for free fermionic model
Zaikov, R.P.
1993-08-01
The higher spin symmetry for both Dirac and Majorana massless free fermionic field models are considered. An infinite Lie algebra which is a linear realization of the higher spin extension of the cross products of the Virasoro and affine Kac-Moody algebras is obtained. The corresponding current algebra is closed which is not the case of analogous current algebra in the WZNW model. The gauging procedure for the higher spin symmetry is also given. (author). 12 refs
Numerical properties of staggered overlap fermions
de Forcrand, Philippe; Panero, Marco
2010-01-01
We report the results of a numerical study of staggered overlap fermions, following the construction of Adams which reduces the number of tastes from 4 to 2 without fine-tuning. We study the sensitivity of the operator to the topology of the gauge field, its locality and its robustness to fluctuations of the gauge field. We make a first estimate of the computing cost of a quark propagator calculation, and compare with Neuberger's overlap.
Constraints on fermion mixing with exotics
Nardi, E.; Tommasini, D.
1991-11-01
We analyze the constraints on the mixing angles of the standard fermions with new heavy particles with exotic SU(2) x U(1) quantum number assignments (left-handed singlets or right-handed doublets), that appear in many extensions of the electroweak theory. The updated Charged Current and Neutral Current experimental data, including also the recent Z-peak measurements, are considered. The results of the global analysis of all these data are then presented
Supersymmetric Extension of Technicolor & Fermion Mass Generation
Antola, Matti; Di Chiara, Stefano; Sannino, Francesco
2012-01-01
We provide a complete extension of Minimal Walking Technicolor able to account for the standard model fermion masses. The model is supersymmetric at energies greater or equal to the technicolor compositeness scale. We integrate out, at the supersymmetry breaking scale, the elementary Higgses. We...... tests and experimental bounds on the mass spectrum. We then turn to the composite Higgs phenomenology at the LHC and show that current data are already constraining the parameter space of the model....
Nucleon electromagnetic form factors with Wilson fermions
Goeckeler, M.; Haegler, P.; Horsley, R.
2007-10-01
The nucleon electromagnetic form factors continue to be of major interest for experimentalists and phenomenologists alike. They provide important insights into the structure of nuclear matter. For a range of interesting momenta they can be calculated on the lattice. The limiting factor continues to be the value of the pion mass. We present the latest results of the QCDSF collaboration using gauge configurations with two dynamical, non-perturbatively improved Wilson fermions at pion masses as low as 350 MeV. (orig.)
Nucleon electromagnetic form factors with Wilson fermions
Goeckeler, M. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Haegler, P. [Technische Univ. Muenchen, Garching (Germany). Inst. fuer Theoretische Physik; Horsley, R. [Edinburgh Univ. (GB). School of Physics] (and others)
2007-10-15
The nucleon electromagnetic form factors continue to be of major interest for experimentalists and phenomenologists alike. They provide important insights into the structure of nuclear matter. For a range of interesting momenta they can be calculated on the lattice. The limiting factor continues to be the value of the pion mass. We present the latest results of the QCDSF collaboration using gauge configurations with two dynamical, non-perturbatively improved Wilson fermions at pion masses as low as 350 MeV. (orig.)
Fermion dynamical symmetry and identical bands
Guidry, M.
1994-01-01
Recent general attention has been directed to the phenomenon of identical bands in both normally deformed and superdeformed nuclei. This paper discusses the possibility that such behavior results from a dynamical symmetry of the nuclear many-body system. Phenomenology and the basic principles of Lie algebras are used to place conditions on the acceptable properties of a candidate symmetry. We find that quite general arguments require that such a symmetry have a minimum of 21 generators with a microscopic fermion interpretation
Optical Lattice Gases of Interacting Fermions
2015-12-02
interacting Fermi gases has topological properties similar to the conventional chiral p- wave state. These include a non-zero Chern number and the...interacting cold gases with broad impacts on the interfaces with condensed matter and particle physics . Applications and experiments of some of the physics ...AFRL-AFOSR-VA-TR-2016-0016 Optical Lattice Gases of Interacting Fermions Wensheng Vincent Liu UNIVERSITY OF PITTSBURGH Final Report 12/02/2015
Magnetic properties of heavy-fermion superconductors
Rauchschwalbe, U.
1986-01-01
In the present thesis the magnetic properties of heavy-fermion superconductors are investigated. The magnetoresistance and the critical magnetic fields show a variety of anomalous phenomena. The Kondo lattices CeCu 2 Si and CeAl 3 are analysed by magnetoresistance and the field dependence of the resistivitis of UBe 13 , UPt 3 , URu 2 Si 2 and CeRu 3 Si are measured for temperatures < or approx. 1 K. (BHO)
Chiral Schwinger model and lattice fermionic regularizations
Kieu, T.D.; Sen, D.; Xue, S.
1988-01-01
The chiral Schwinger model is studied on the lattice with use of Wilson fermions. The arbitrary mass term for the gauge boson is shown to originate from the arbitrariness of the Wilson parameter, which is required to avoid the doubling phenomenon on the lattice. The necessity for such a term is thus demonstrated in contrast to the mere admissibility as indicated by previous continuum calculations
Four-fermion interaction near four dimensions
Zinn-Justin, J.
1991-01-01
A large class of models with four-fermion interactions is known to be renormalizable and asymptotically free in two dimensions. It has been noticed very early, in the example of the U(N)-invariant Gross-Neveu model and within the framework of the 1/N expansion, that then these models behave also like renormalizable models in higher dimensions. Some of them are thus natural candidates for composite models of scalar particles like for example the Higgs boson. An important question, however, has to be answered: Are these models more predictive, in four dimensions, than the effective models containing the bosons explicitly? We shall show here that, like for the non-linear σ-model which has been investigated earlier, the answer, at least in some perturbative sense, is negative for a large class of models. The reason can be easily understood: These models are more short-distance sensitive than normal renormalizable models. The new parameters are hidden in the cut-off procedure. In particular in some models the fermions receive masses by spontaneous chiral symmetry breaking. The property that ratio of fermion and boson masses can be predicted is simply a consequence of the IR freedom of both type of models and the natural assumption that coupling constants have generic values at the cut-off scale. We shall consider in this article for definiteness the Gross-Neveu model but it will be clear that the arguments are rather general. (orig.)
Quantum computing with Majorana fermion codes
Litinski, Daniel; von Oppen, Felix
2018-05-01
We establish a unified framework for Majorana-based fault-tolerant quantum computation with Majorana surface codes and Majorana color codes. All logical Clifford gates are implemented with zero-time overhead. This is done by introducing a protocol for Pauli product measurements with tetrons and hexons which only requires local 4-Majorana parity measurements. An analogous protocol is used in the fault-tolerant setting, where tetrons and hexons are replaced by Majorana surface code patches, and parity measurements are replaced by lattice surgery, still only requiring local few-Majorana parity measurements. To this end, we discuss twist defects in Majorana fermion surface codes and adapt the technique of twist-based lattice surgery to fermionic codes. Moreover, we propose a family of codes that we refer to as Majorana color codes, which are obtained by concatenating Majorana surface codes with small Majorana fermion codes. Majorana surface and color codes can be used to decrease the space overhead and stabilizer weight compared to their bosonic counterparts.
The Bethe-Salpeter equation with fermions
Efimov, G.V.
2007-01-01
The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a fermion theory: two fermion fields (constituents) with mass m interacting via an exchange of a scalar field with mass μ. The BS equation can be written in the form of an integral equation in the configuration Euclidean x-space with the symmetric kernel K for which Tr K 2 = ∞ due to the singular character of the fermion propagator. This kernel is represented in the form K = K 0 + K I . The operator K 0 with Tr K 0 2 ∞ is of the 'fall at the center' potential type and describes a continuous spectrum only. Besides the presence of this operator leads to a restriction on the value of the coupling constant. The kernel K I with Tr K I 2 2 c 2 and the variational procedure of calculations of eigenvalues and eigenfunctions can be applied. The quantum pseudoscalar and scalar mesodynamics is considered. The binding energy of the state 1 + (deuteron) as a function of the coupling constant is calculated in the framework of the procedure formulated above. It is shown that this bound state is absent in the pseudoscalar mesodynamics and does exist in the scalar mesodynamics. A comparison with the non-relativistic Schroedinger picture is made. (author)
Symmetries of Ginsparg-Wilson chiral fermions
Mandula, Jeffrey E.
2009-01-01
The group structure of the variant chiral symmetry discovered by Luescher in the Ginsparg-Wilson description of lattice chiral fermions is analyzed. It is shown that the group contains an infinite number of linearly independent symmetry generators, and the Lie algebra is given explicitly. CP is an automorphism of this extended chiral group, and the CP transformation properties of the symmetry generators are found. The group has an infinite-parameter invariant subgroup, and the factor group, whose elements are its cosets, is isomorphic to the continuum chiral symmetry group. Features of the currents associated with these symmetries are discussed, including the fact that some different, noncommuting symmetry generators lead to the same Noether current. These are universal features of lattice chiral fermions based on the Ginsparg-Wilson relation; they occur in the overlap, domain-wall, and perfect-action formulations. In a solvable example, free overlap fermions, these noncanonical elements of lattice chiral symmetry are related to complex energy singularities that violate reflection positivity and impede continuation to Minkowski space.
Effect of quintessence on holographic fermionic spectrum
Kuang, Xiao-Mei [Yangzhou University, Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou (China); Pontificia Universidad Catolica de Valparaiso, Instituto de Fisica, Valparaiso (Chile); Wu, Jian-Pin [Bohai University, Institute of Gravitation and Cosmology, Department of Physics, School of Mathematics and Physics, Jinzhou (China)
2017-10-15
In this letter, we investigate the holographic fermionic spectrum without/with dipole coupling dual to the Reissner-Nordstroem anti-de Sitter (RN-AdS) black brane surrounded by quintessence. We find that the low energy excitation of this fermionic system without dipole coupling behaves as a non-Fermi liquid. In particular, the introduction of quintessence aggravates the degree of deviation from a Fermi liquid. For the system with dipole coupling, the phase transition from (non-)Fermi liquid to Mott phase can be observed. The ratio between the width of gap and the critical temperature, beyond which the gap closes, is also worked out. We find that this ratio is larger than that of the holographic fermionic system dual to the RN-AdS black brane and even the material of V O{sub 2}. It means that our holographic system with quintessence can model new phenomena of the condensed matter system and provide some new insights in their regard. (orig.)
Scaling behavior of heavy fermion metals
Shaginyan, V.R., E-mail: vrshag@thd.pnpi.spb.r [Petersburg Nuclear Physics Institute, RAS, Gatchina, 188300 (Russian Federation); CTSPS, Clark Atlanta University, Atlanta, GA 30314 (United States); Amusia, M.Ya. [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel); Ioffe Physical Technical Institute, RAS, St. Petersburg 194021 (Russian Federation); Msezane, A.Z. [CTSPS, Clark Atlanta University, Atlanta, GA 30314 (United States); Popov, K.G. [Komi Science Center, Ural Division, RAS, 3a, Chernova str. Syktyvkar, 167982 (Russian Federation)
2010-07-15
Strongly correlated Fermi systems are fundamental systems in physics that are best studied experimentally, which until very recently have lacked theoretical explanations. This review discusses the construction of a theory and the analysis of phenomena occurring in strongly correlated Fermi systems such as heavy-fermion (HF) metals and two-dimensional (2D) Fermi systems. It is shown that the basic properties and the scaling behavior of HF metals can be described within the framework of a fermion condensation quantum phase transition (FCQPT) and an extended quasiparticle paradigm that allow us to explain the non-Fermi liquid behavior observed in strongly correlated Fermi systems. In contrast to the Landau paradigm stating that the quasiparticle effective mass is a constant, the effective mass of new quasiparticles strongly depends on temperature, magnetic field, pressure, and other parameters. Having analyzed the collected facts on strongly correlated Fermi systems with quite a different microscopic nature, we find these to exhibit the same non-Fermi liquid behavior at FCQPT. We show both analytically and using arguments based entirely on the experimental grounds that the data collected on very different strongly correlated Fermi systems have a universal scaling behavior, and materials with strongly correlated fermions can unexpectedly be uniform in their diversity. Our analysis of strongly correlated systems such as HF metals and 2D Fermi systems is in the context of salient experimental results. Our calculations of the non-Fermi liquid behavior, the scales and thermodynamic, relaxation and transport properties are in good agreement with experimental facts.
Kinetic theory of fermions in curved spacetime
Fidler, Christian [Catholic University of Louvain, Center for Cosmology, Particle Physics and Phenomenology (CP3), 2, Chemin du Cyclotron, B-1348 Louvain-la-Neuve (Belgium); Pitrou, Cyril, E-mail: christian.fidler@uclouvain.be, E-mail: pitrou@iap.fr [Institut d' Astrophysique de Paris, CNRS-UMR 7095, UPMC—Paris VI, Sorbonne Universités, 98 bis Bd Arago, 75014 Paris (France)
2017-06-01
We build a statistical description of fermions, taking into account the spin degree of freedom in addition to the momentum of particles, and we detail its use in the context of the kinetic theory of gases of fermions particles. We show that the one-particle distribution function needed to write a Liouville equation is a spinor valued operator. The degrees of freedom of this function are covariantly described by an intensity function and by a polarisation vector which are parallel transported by free streaming. Collisions are described on the microscopic level and lead to a Boltzmann equation for this operator. We apply our formalism to the case of weak interactions, which at low energies can be considered as a contact interaction between fermions, allowing us to discuss the structure of the collision term for a few typical weak-interaction mediated reactions. In particular we find for massive particles that a dipolar distribution of velocities in the interacting species is necessary to generate linear polarisation, as opposed to the case of photons for which linear polarisation is generated from the quadrupolar distribution of velocities.
Mode entanglement of Gaussian fermionic states
Spee, C.; Schwaiger, K.; Giedke, G.; Kraus, B.
2018-04-01
We investigate the entanglement of n -mode n -partite Gaussian fermionic states (GFS). First, we identify a reasonable definition of separability for GFS and derive a standard form for mixed states, to which any state can be mapped via Gaussian local unitaries (GLU). As the standard form is unique, two GFS are equivalent under GLU if and only if their standard forms coincide. Then, we investigate the important class of local operations assisted by classical communication (LOCC). These are central in entanglement theory as they allow one to partially order the entanglement contained in states. We show, however, that there are no nontrivial Gaussian LOCC (GLOCC) among pure n -partite (fully entangled) states. That is, any such GLOCC transformation can also be accomplished via GLU. To obtain further insight into the entanglement properties of such GFS, we investigate the richer class of Gaussian stochastic local operations assisted by classical communication (SLOCC). We characterize Gaussian SLOCC classes of pure n -mode n -partite states and derive them explicitly for few-mode states. Furthermore, we consider certain fermionic LOCC and show how to identify the maximally entangled set of pure n -mode n -partite GFS, i.e., the minimal set of states having the property that any other state can be obtained from one state inside this set via fermionic LOCC. We generalize these findings also to the pure m -mode n -partite (for m >n ) case.
Fidelity Witnesses for Fermionic Quantum Simulations
Gluza, M.; Kliesch, M.; Eisert, J.; Aolita, L.
2018-05-01
The experimental interest and developments in quantum spin-1 /2 chains has increased uninterruptedly over the past decade. In many instances, the target quantum simulation belongs to the broader class of noninteracting fermionic models, constituting an important benchmark. In spite of this class being analytically efficiently tractable, no direct certification tool has yet been reported for it. In fact, in experiments, certification has almost exclusively relied on notions of quantum state tomography scaling very unfavorably with the system size. Here, we develop experimentally friendly fidelity witnesses for all pure fermionic Gaussian target states. Their expectation value yields a tight lower bound to the fidelity and can be measured efficiently. We derive witnesses in full generality in the Majorana-fermion representation and apply them to experimentally relevant spin-1 /2 chains. Among others, we show how to efficiently certify strongly out-of-equilibrium dynamics in critical Ising chains. At the heart of the measurement scheme is a variant of importance sampling specially tailored to overlaps between covariance matrices. The method is shown to be robust against finite experimental-state infidelities.
Strong CP, flavor, and twisted split fermions
Harnik, Roni; Perez, Gilad; Schwartz, Matthew D.; Shirman, Yuri
2005-01-01
We present a natural solution to the strong CP problem in the context of split fermions. By assuming CP is spontaneously broken in the bulk, a weak CKM phase is created in the standard model due to a twisting in flavor space of the bulk fermion wavefunctions. But the strong CP phase remains zero, being essentially protected by parity in the bulk and CP on the branes. As always in models of spontaneous CP breaking, radiative corrections to theta bar from the standard model are tiny, but even higher dimension operators are not that dangerous. The twisting phenomenon was recently shown to be generic, and not to interfere with the way that split fermions naturally weaves small numbers into the standard model. It follows that out approach to strong CP is compatible with flavor, and we sketch a comprehensive model. We also look at deconstructed version of this setup which provides a viable 4D model of spontaneous CP breaking which is not in the Nelson-Barr class. (author)
Dirac Fermions in an Antiferromagnetic Semimetal
Tang, Peizhe; Zhou, Quan; Xu, Gang; Zhang, Shou-Cheng; Shou-Cheng Zhang's Group Team, Prof.
Analogues of the elementary particles have been extensively searched for in condensed matter systems for both scientific interest and technological applications. Recently, massless Dirac fermions were found to emerge as low energy excitations in materials now known as Dirac semimetals. All the currently known Dirac semimetals are nonmagnetic with both time-reversal symmetry and inversion symmetry "". Here we show that Dirac fermions can exist in one type of antiferromagnetic systems, where both and "" are broken but their combination "" is respected. We propose orthorhombic antiferromagnet CuMnAs as a candidate, analyze the robustness of the Dirac points under symmetry protections, and demonstrate its distinctive bulk dispersions as well as the corresponding surface states by ab initio calculations. Our results provide a possible platform to study the interplay of Dirac fermion physics and magnetism. We acknowledge the DOE, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract DE-AC02-76SF00515, NSF under Grant No.DMR-1305677 and FAME, one of six centers of STARnet.
Virtual hadronic and heavy-fermion O({alpha}{sup 2}) corrections to Bhabha scattering
Actis, Stefano [Inst. fuer Theoretische Physik E, RWTH Aachen (Germany); Czakon, Michal [Wuerzburg Univ. (Germany). Inst. fuer Theoretische Physik und Astrophysik]|[Uniwersytet Slaski, Katowice (Poland). Inst. of Physics and Chemistry of Metals; Gluza, Janusz [Uniwersytet Slaski, Katowice (Poland). Inst. of Physics and Chemistry of Metals; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2008-07-15
Effects of vacuum polarization by hadronic and heavy-fermion insertions were the last unknown two-loop QED corrections to high-energy Bhabha scattering. Here we describe the corrections in detail and explore their numerical influence. The hadronic contributions to the virtual O({alpha}{sup 2}) QED corrections to the Bhabha-scattering cross-section are evaluated using dispersion relations and computing the convolution of hadronic data with perturbatively calculated kernel functions. The technique of dispersion integrals is also employed to derive the virtual O({alpha}{sup 2}) corrections generated by muon-, tau- and top-quark loops in the small electron-mass limit for arbitrary values of the internal-fermion masses. At a meson factory with 1 GeV center-of-mass energy the complete effect of hadronic and heavy-fermion corrections amounts to less than 0.5 per mille and reaches, at 10 GeV, up to about 2 per mille. At the Z resonance it amounts to 2.3 per mille at 3 degrees; overall, hadronic corrections are less than 4 per mille. For ILC energies (500 GeV or above), the combined effect of hadrons and heavy fermions becomes 6 per mille at 3 degrees; hadrons contribute less than 20 per mille in the whole angular region. (orig.)
Goldstone fermions in supersymmetric theories at finite temperature
Aoyama, H.; Boyanovsky, D.
1984-01-01
The behavior of supersymmetric theories at finite temperature is examined. It is shown that supersymmetry is broken for any T> or =0 because of the different statistics obeyed by bosons and fermions. This breaking is always associated with a Goldstone mode(s). This phenomenon is shown to take place even in a free massive theory, where the Goldstone modes are created by composite fermion-boson bilinear operators. In the interacting theory with chiral symmetry, the same bilinear operators create the chiral doublet of Goldstone fermions, which is shown to saturate the Ward-Takahashi identities up to one loop. Because of this spontaneous supersymmetry breaking, the fermions and the bosons acquire different effective masses. In theories without chiral symmetry, at the tree level the fermion-boson bilinear operators create Goldstone modes, but at higher orders these modes become massive and the elementary fermion becomes the Goldstone field because of the mixing with these bilinear operators
arXiv Charged Fermions Below 100 GeV
Egana-Ugrinovic, Daniel; Ruderman, Joshua T.
2018-05-03
How light can a fermion be if it has unit electric charge? We revisit the lore that LEP robustly excludes charged fermions lighter than about 100 GeV. We review LEP chargino searches, and find them to exclude charged fermions lighter than 90 GeV, assuming a higgsino-like cross section. However, if the charged fermion couples to a new scalar, destructive interference among production channels can lower the LEP cross section by a factor of 3. In this case, we find that charged fermions as light as 75 GeV can evade LEP bounds, while remaining consistent with constraints from the LHC. As the LHC collects more data, charged fermions in the 75–100 GeV mass range serve as a target for future monojet and disappearing track searches.
FCNC Effects in a Minimal Theory of Fermion Masses
Buras, Andrzej J; Pokorski, Stefan; Ziegler, Robert
2011-01-01
As a minimal theory of fermion masses we extend the SM by heavy vectorlike fermions, with flavor-anarchical Yukawa couplings, that mix with chiral fermions such that small SM Yukawa couplings arise from small mixing angles. This model can be regarded as an effective description of the fermionic sector of a large class of existing flavor models and thus might serve as a useful reference frame for a further understanding of flavor hierarchies in the SM. Already such a minimal framework gives rise to FCNC effects through exchange of massive SM bosons whose couplings to the light fermions get modified by the mixing. We derive general formulae for these corrections and discuss the bounds on the heavy fermion masses. Particularly stringent bounds, in a few TeV range, come from the corrections to the Z couplings.
An exact fermion-pair to boson mapping
Johnson, C.W.
1993-01-01
I derive in a novel fashion exact formulas for the calculation of general matrix elements, including the overlap (norm) matrix, between states constructed from fermion pairs. Mapping the fermion pairs to bosons, I show how to construct finite and exact (in the sense of preserving matrix elements) boson representations of the norm operator and one- and two-fermion operators. This may lead to a microscopic basis for the Interacting Boson Model, as well as new truncation schemes for the nuclear shell model
Gauge-invariant dressed fermion propagator in massless QED3
Mitra, Indrajit; Ratabole, Raghunath; Sharatchandra, H.S.
2006-01-01
The infrared behaviour of the gauge-invariant dressed fermion propagator in massless QED 3 is discussed for three choices of dressing. It is found that only the propagator with the isotropic (in three Euclidean dimensions) choice of dressing is acceptable as the physical fermion propagator. It is explained that the negative anomalous dimension of this physical fermion does not contradict any field-theoretical requirement
Pole mass, width, and propagators of unstable fermions
Kniehl, B.A.; Sirlin, A.
2008-01-01
The concepts of pole mass and width are extended to unstable fermions in the general framework of parity-nonconserving gauge theories, such as the Standard Model. In contrast with the conventional on-shell definitions, these concepts are gauge independent and avoid severe unphysical singularities, properties of great importance since most fundamental fermions in nature are unstable particles. General expressions for the unrenormalized and renormalized dressed propagators of unstable fermions and their field-renormalization constants are presented. (orig.)
Continuum-limit scaling of overlap fermions as valence quarks
Cichy, Krzysztof; Herdoiza, Gregorio; Jansen, Karl
2009-10-01
We present the results of a mixed action approach, employing dynamical twisted mass fermions in the sea sector and overlap valence fermions, with the aim of testing the continuum limit scaling behaviour of physical quantities, taking the pion decay constant as an example. To render the computations practical, we impose for this purpose a fixed finite volume with lattice size L∼1.3 fm. We also briefly review the techniques we have used to deal with overlap fermions. (orig.)
Fermionic covariant prolongation structure theory for supernonlinear evolution equation
Cheng Jipeng; Wang Shikun; Wu Ke; Zhao Weizhong
2010-01-01
We investigate the superprincipal bundle and its associated superbundle. The super(nonlinear)connection on the superfiber bundle is constructed. Then by means of the connection theory, we establish the fermionic covariant prolongation structure theory of the supernonlinear evolution equation. In this geometry theory, the fermionic covariant fundamental equations determining the prolongation structure are presented. As an example, the supernonlinear Schroedinger equation is analyzed in the framework of this fermionic covariant prolongation structure theory. We obtain its Lax pairs and Baecklund transformation.
Squeezed fermions and back-to-back correlations
Panda, P.K.; Krein, G.; Padula, S.S.; Csoergoe, T.; Hama, Y.
2001-01-01
Back-to-back correlations of asymptotic fermion pairs appear if in-medium interactions lead to mass modifications of fermion states in a thermalized medium. The back-to-back correlations of protons and anti-protons will be experimentally observable in ultrarelativistic heavy ion collisions. The strength of back-to-back correlations of fermions can be unlimitedly large, diverging as the momentum of the pair increases and the net baryon density decreases. (author)
Squeezed fermions and back-to-back correlations
Panda, P.K.; Krein, G.; Padula, S.S. [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Csoergoe, T. [Hungarian Academy of Sciences, Budapest (Hungary). Research Institute for Particle and Nuclear Physics (RMKI, KFKI); Hama, Y. [Sao Paulo Univ., SP (Brazil). Inst. de Fisica
2001-07-01
Back-to-back correlations of asymptotic fermion pairs appear if in-medium interactions lead to mass modifications of fermion states in a thermalized medium. The back-to-back correlations of protons and anti-protons will be experimentally observable in ultrarelativistic heavy ion collisions. The strength of back-to-back correlations of fermions can be unlimitedly large, diverging as the momentum of the pair increases and the net baryon density decreases. (author)
Spin-excited oscillations in two-component fermion condensates
Maruyama, Tomoyuki; Bertsch, George F.
2006-01-01
We investigate collective spin excitations in two-component fermion condensates with special consideration of unequal populations of the two components. The frequencies of monopole and dipole modes are calculated using Thomas-Fermi theory and the scaling approximation. As the fermion-fermion coupling is varied, the system shows various phases of the spin configuration. We demonstrate that spin oscillations have more sensitivity to the spin phase structures than the density oscillations
Quantum Hall effect of massless Dirac fermions and free fermions in Hofstadter's butterfly
Yoshioka, Nobuyuki; Matsuura, Hiroyasu; Ogata, Masao
2016-01-01
We propose a new physical interpretation of the Diophantine equation of σ xy for the Hofstadter problem. First, we divide the energy spectrum, or Hofstadter's butterfly, into smaller self-similar areas called 'subcells', which were first introduced by Hofstadter to describe the recursive structure. We find that in the energy gaps between subcells, there are two ways to account for the quantization rule of σ xy , that are consistent with the Diophantine equation: Landau quantization of (1) massless Dirac fermions or (2) free fermions in Hofstadter's butterfly. (author)
On the trace anomaly of a Weyl fermion
Bastianelli, Fiorenzo; Martelli, Riccardo [Dipartimento di Fisica e Astronomia, Università di Bologna,via Irnerio 46, I-40126 Bologna (Italy); INFN - Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy)
2016-11-29
We calculate the trace anomaly of a Weyl fermion coupled to gravity by using Fujikawa’s method supplemented by a consistent regulator. The latter is constructed out of Pauli-Villars regulating fields. The motivation for presenting such a calculation stems from recent studies that suggest that the trace anomaly of chiral fermions in four dimensions might contain an imaginary part proportional to the Pontryagin density. We find that the trace anomaly of a Weyl fermion is given by half the trace anomaly of a Dirac fermion, so that no imaginary part proportional to the Pontryagin density is seen to arise.
Fermions in nonrelativistic AdS/CFT correspondence
Akhavan, Amin; Alishahiha, Mohsen; Davody, Ali; Vahedi, Ali
2009-01-01
We extend the nonrelativistic AdS/CFT correspondence to the fermionic fields. In particular, we study the two point function of a fermionic operator in nonrelativistic CFTs by making use of a massive fermion propagating in geometries with Schroedinger group isometry. Although the boundary of the geometries with Schroedinger group isometry differ from that in AdS geometries where the dictionary of AdS/CFT is established, using the general procedure of AdS/CFT correspondence, we see that the resultant two point function has the expected form for fermionic operators in nonrelativistic CFTs, though a nontrivial regularization may be needed.
Functional approach without path integrals to finite temperature free fermions
Souza, S.M. de; Santos, O. Rojas; Thomaz, M.T.
1999-01-01
Charret et al applied the properties of Grassmann generators to develop a new method to calculate the coefficients of the high temperature expansion of the grand canonical partition function of self-interacting fermionic models on d-dimensions (d ≥1). The methodology explores the anti-commuting nature of fermionic fields and avoids the calculation of the fermionic path integral. we apply this new method to the relativistic free Dirac fermions and recover the known results in the literature without the β-independent and μindependent infinities that plague the continuum path integral formulation. (author)
Wilson Fermions and Axion Electrodynamics in Optical Lattices
Bermudez, A.; Martin-Delgado, M. A.; Mazza, L.; Rizzi, M.; Goldman, N.; Lewenstein, M.
2010-01-01
We show that ultracold Fermi gases in optical superlattices can be used as quantum simulators of relativistic lattice fermions in 3+1 dimensions. By exploiting laser-assisted tunneling, we find an analogue of the so-called naive Dirac fermions, and thus provide a realization of the fermion doubling problem. Moreover, we show how to implement Wilson fermions, and discuss how their mass can be inverted by tuning the laser intensities. In this regime, our atomic gas corresponds to a phase of matter where Maxwell electrodynamics is replaced by axion electrodynamics: a 3D topological insulator.
Phases of renormalized lattice gauge theories with fermions
Caracciolo, S.; Menotti, P.; and INFN Sezione di Pisa, Italy)
1979-01-01
Starting from the formulation of gauge theories on a lattice we derive renormalization group transformation of the Migdal-Kadanoff type in the presence of fermions. We consider the effect of the fermion vacuum polarization on the gauge Lagrangian but we neglect fermion mass renormalization. We work out the weak coupling and strong coupling expansion in the same framework. Asymptotic freedom is recovered for the non-Abelian case provided the number of fermion multiplets is lower than a critical number. Fixed points are determined both for the U (1) and SU (2) case. We determine the renormalized trajectories and the phases of the theory
Bosonization of fermions coupled to topologically massive gravity
Fradkin, Eduardo; Moreno, Enrique F.; Schaposnik, Fidel A.
2014-03-01
We establish a duality between massive fermions coupled to topologically massive gravity (TMG) in d=3 space-time dimensions and a purely gravity theory which also will turn out to be a TMG theory but with different parameters: the original graviton mass in the TMG theory coupled to fermions picks up a contribution from fermion bosonization. We obtain explicit bosonization rules for the fermionic currents and for the energy-momentum tensor showing that the identifications do not depend explicitly on the parameters of the theory. These results are the gravitational analog of the results for 2+1 Abelian and non-Abelian bosonization in flat space-time.
Bosonization of fermions coupled to topologically massive gravity
Fradkin, Eduardo; Moreno, Enrique F.; Schaposnik, Fidel A.
2014-01-01
We establish a duality between massive fermions coupled to topologically massive gravity (TMG) in d=3 space–time dimensions and a purely gravity theory which also will turn out to be a TMG theory but with different parameters: the original graviton mass in the TMG theory coupled to fermions picks up a contribution from fermion bosonization. We obtain explicit bosonization rules for the fermionic currents and for the energy–momentum tensor showing that the identifications do not depend explicitly on the parameters of the theory. These results are the gravitational analog of the results for 2+1 Abelian and non-Abelian bosonization in flat space–time.
Bosonization of fermions coupled to topologically massive gravity
Fradkin, Eduardo [Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801-3080 (United States); Moreno, Enrique F. [Department of Physics, Northeastern University, Boston, MA 02115 (United States); Schaposnik, Fidel A. [Departamento de Física, Universidad Nacional de La Plata, Instituto de Física La Plata, C.C. 67, 1900 La Plata (Argentina)
2014-03-07
We establish a duality between massive fermions coupled to topologically massive gravity (TMG) in d=3 space–time dimensions and a purely gravity theory which also will turn out to be a TMG theory but with different parameters: the original graviton mass in the TMG theory coupled to fermions picks up a contribution from fermion bosonization. We obtain explicit bosonization rules for the fermionic currents and for the energy–momentum tensor showing that the identifications do not depend explicitly on the parameters of the theory. These results are the gravitational analog of the results for 2+1 Abelian and non-Abelian bosonization in flat space–time.
Calculation of CWKB envelope in boson and fermion productions
Biswas, S.; Chowdhury, I.
2007-01-01
We present the calculation of envelope of boson and of both low-and high-mass fermion production at the end of inflation when the coherently oscillating inflations decay into bosons and fermions. We consider three different models of inflation and use CWKB technique to calculate the envelope to understand the structure of resonance band formation. We observe that though low-mass fermion production is not effective in preheating because of Pauli blocking, it is quite probable for high-mass fermion to take part in pre heating. (author)
Fermion frontiers in vector lattice gauge theories: Proceedings. Volume 8
1998-01-01
The inclusion of fermions into simulations of lattice gauge theories is very difficult both theoretically and numerically. With the presence of Teraflops-scale computers for lattice gauge theory, the authors wanted a forum to discuss new approaches to lattice fermions. The workshop concentrated on approaches which are ripe for study on such large machines. Although lattice chiral fermions are vitally important to understand, there is not technique at hand which is viable on these Teraflops-scale machines for real-world problems. The discussion was therefore focused on recent developments and future prospects for QCD-like theories. For the well-known fermion formulations, the Aoki phase in Wilson fermions, novelties of U A (1) symmetry and the η' for staggered fermions and new approaches for simulating the determinant for Wilson fermions were discussed. The newer domain-wall fermion formulation was reviewed, with numerical results given by many speakers. The fermion proposal of Friedberg, Lee and Pang was introduced. They also were able to compare and contrast the dependence of QCD and QCD-like SUSY theories on the number of quark flavors. These proceedings consist of several transparencies and a summary page from each speaker. This should serve to outline the major points made in each talk
On the regularized fermionic projector of the vacuum
Finster, Felix
2008-03-01
We construct families of fermionic projectors with spherically symmetric regularization, which satisfy the condition of a distributional MP-product. The method is to analyze regularization tails with a power law or logarithmic scaling in composite expressions in the fermionic projector. The resulting regularizations break the Lorentz symmetry and give rise to a multilayer structure of the fermionic projector near the light cone. Furthermore, we construct regularizations which go beyond the distributional MP-product in that they yield additional distributional contributions supported at the origin. The remaining freedom for the regularization parameters and the consequences for the normalization of the fermionic states are discussed.
On the regularized fermionic projector of the vacuum
Finster, Felix
2008-01-01
We construct families of fermionic projectors with spherically symmetric regularization, which satisfy the condition of a distributional MP-product. The method is to analyze regularization tails with a power law or logarithmic scaling in composite expressions in the fermionic projector. The resulting regularizations break the Lorentz symmetry and give rise to a multilayer structure of the fermionic projector near the light cone. Furthermore, we construct regularizations which go beyond the distributional MP-product in that they yield additional distributional contributions supported at the origin. The remaining freedom for the regularization parameters and the consequences for the normalization of the fermionic states are discussed
Ziino, G.
1989-01-01
We assume a strictly invariant definition of the Dirac parity operator under fermion ↔ antifermion exchange. We see that the opposite-intrinsic-parity condition then requires two opposite-mass Dirac equations for the fermion and the antifermion. This leads us to introduce an asymptotically left-handed (fermion) and right-handed (antifermion) chiral field, as just an alternative basis in the internal space spanned by the new pair of charge-conjugate Dirac fields. Hence a dual intrinsic model of a spin - 1/2 massive fermion is drawn: it predicts the coexistence of two anticommuting general varieties of conserved charges, namely a scalar variety, responsible for parity-invariant phenomenology, plus a pseudoscalar one, responsible for chiral phenomenology. In this light, CP-symmetry is seen to be nothing but P-symmetry; and a spontaneous CP-violation mechanism is also derived, that should work in any single process occurring via both scalar-and pseudoscalar-charge interactions. We show, at last, that our scheme automatically yields Weyl's one for a merely left-handed neutrino and a merely right-handed antineutrino, further assigning them the special meaning of pure pseudoscalar-charge objects. Some general consequences as regards magnetic monopoles are briefly discussed too
Clifford Algebra Implying Three Fermion Generations Revisited
Krolikowski, W.
2002-01-01
The author's idea of algebraic compositeness of fundamental particles, allowing to understand the existence in Nature of three fermion generations, is revisited. It is based on two postulates. Primo, for all fundamental particles of matter the Dirac square-root procedure √p 2 → Γ (N) ·p works, leading to a sequence N=1, 2, 3, ... of Dirac-type equations, where four Dirac-type matrices Γ (N) μ are embedded into a Clifford algebra via a Jacobi definition introducing four ''centre-of-mass'' and (N - 1) x four ''relative'' Dirac-type matrices. These define one ''centre-of-mass'' and N - 1 ''relative'' Dirac bispinor indices. Secundo, the ''centre-of-mass'' Dirac bispinor index is coupled to the Standard Model gauge fields, while N - 1 ''relative'' Dirac bispinor indices are all free indistinguishable physical objects obeying Fermi statistics along with the Pauli principle which requires the full antisymmetry with respect to ''relative'' Dirac indices. This allows only for three Dirac-type equations with N = 1, 3, 5 in the case of N odd, and two with N = 2, 4 in the case of N even. The first of these results implies unavoidably the existence of three and only three generations of fundamental fermions, namely leptons and quarks, as labelled by the Standard Model signature. At the end, a comment is added on the possible shape of Dirac 3 x 3 mass matrices for four sorts of spin-1/2 fundamental fermions appearing in three generations. For charged leptons a prediction is m τ = 1776.80 MeV, when the input of experimental m e and m μ is used. (author)
The quantum HMF model: I. Fermions
Chavanis, Pierre-Henri
2011-01-01
We study the thermodynamics of quantum particles with long-range interactions at T = 0. Specifically, we generalize the Hamiltonian mean-field (HMF) model to the case of fermions. We consider the Thomas–Fermi approximation that becomes exact in a proper thermodynamic limit N→+∞ with a coupling constant k ∼ N. The equilibrium configurations, described by the mean-field Fermi (or waterbag) distribution, are equivalent to polytropes of index n = 1/2. We show that the homogeneous phase, which is unstable in the classical regime, becomes stable in the quantum regime. The homogeneous phase is stabilized by the Pauli exclusion principle. This takes place through a first-order phase transition where the control parameter is the normalized Planck constant. The homogeneous phase is unstable for ℎ c ≡2/√(π), metastable for ℎ c t ≡1.16 and stable for ℎ>ℎ t . The inhomogeneous phase is stable for ℎ t , metastable for ℎ t * ≡1.18 and disappears for ℎ>ℎ * (for ℎ c * , there exists an unstable inhomogeneous phase with magnetization 0 * ≡ 0.37). We point out analogies between the fermionic HMF model and the concept of fermion stars in astrophysics. Finally, as a by-product of our analysis, we obtain new results concerning the Vlasov dynamical stability of the waterbag distribution which is the ground state of the Lynden-Bell distribution in the theory of violent relaxation of the classical HMF model. We show that spatially homogeneous waterbag distributions are Vlasov-stable iff ε ≥ ε c = 1/3 and spatially inhomogeneous waterbag distributions are Vlasov-stable iff ε ≤ ε * = 0.379 and b ≥ b * = 0.37, where ε and b are the normalized energy and magnetization. The magnetization curve displays a first-order phase transition at ε t = 0.352 and the domain of metastability ranges from ε c to ε *
Clifford Algebra Implying Three Fermion Generations Revisited
Krolikowski, Wojciech
2002-09-01
The author's idea of algebraic compositeness of fundamental particles, allowing to understand the existence in Nature of three fermion generations, is revisited. It is based on two postulates. Primo, for all fundamental particles of matter the Dirac square-root procedure √ {p2} → {Γ }(N)p works, leading to a sequence N = 1,2,3, ... of Dirac-type equations, where four Dirac-type matrices {Γ }(N)μ are embedded into a Clifford algebra via a Jacobi definition introducing four ``centre-of-mass'' and (N-1)× four ``relative'' Dirac-type matrices. These define one ``centre-of-mass'' and (N-1) ``relative'' Dirac bispinor indices. Secundo, the ``centre-of-mass'' Dirac bispinor index is coupled to the Standard Model gauge fields, while (N-1) ``relative'' Dirac bispinor indices are all free indistinguishable physical objects obeying Fermi statistics along with the Pauli principle which requires the full antisymmetry with respect to ``relative'' Dirac indices. This allows only for three Dirac-type equations with N = 1,3,5 in the case of N odd, and two with N = 2,4 in the case of N even. The first of these results implies unavoidably the existence of three and only three generations of fundamental fermions, namely leptons and quarks, as labelled by the Standard Model signature. At the end, a comment is added on the possible shape of Dirac 3x3 mass matrices for four sorts of spin-1/2 fundamental fermions appearing in three generations. For charged leptons a prediction is mτ = 1776.80 MeV, when the input of experimental me and mμ is used.
Many-body formalism for fermions: The partition function
Watson, D. K.
2017-09-01
The partition function, a fundamental tenet in statistical thermodynamics, contains in principle all thermodynamic information about a system. It encapsulates both microscopic information through the quantum energy levels and statistical information from the partitioning of the particles among the available energy levels. For identical particles, this statistical accounting is complicated by the symmetry requirements of the allowed quantum states. In particular, for Fermi systems, the enforcement of the Pauli principle is typically a numerically demanding task, responsible for much of the cost of the calculations. The interplay of these three elements—the structure of the many-body spectrum, the statistical partitioning of the N particles among the available levels, and the enforcement of the Pauli principle—drives the behavior of mesoscopic and macroscopic Fermi systems. In this paper, we develop an approach for the determination of the partition function, a numerically difficult task, for systems of strongly interacting identical fermions and apply it to a model system of harmonically confined, harmonically interacting fermions. This approach uses a recently introduced many-body method that is an extension of the symmetry-invariant perturbation method (SPT) originally developed for bosons. It uses group theory and graphical techniques to avoid the heavy computational demands of conventional many-body methods which typically scale exponentially with the number of particles. The SPT application of the Pauli principle is trivial to implement since it is done "on paper" by imposing restrictions on the normal-mode quantum numbers at first order in the perturbation. The method is applied through first order and represents an extension of the SPT method to excited states. Our method of determining the partition function and various thermodynamic quantities is accurate and efficient and has the potential to yield interesting insight into the role played by the Pauli
Magnetic fluctuations in heavy-fermion metals
Mason, T.E.; Petersen, T.; Aeppli, G.
1995-01-01
Elastic and inelastic neutron scattering have been used to study the antiferromagnetic ordering and magnetic excitations of the U heavy-fermion superconductors UPd2Al3 and URu2Si2 above and below T-N. While both materials exhibit the coexistence of superconductivity and antiferromagnetic order......, the nature of the antiferromagnetic order and magnetic fluctuations is qualitatively quite different. UPd2Al3 resembles a rare earth magnetic system with coupling of the 4f electrons to the conduction electrons manifested in a broadening of otherwise conventional spin wave excitations. This is in marked...
Einstein equations and Fermion degrees of freedom
Luetz, E.F.; Vasconcellos, C.A.Z.
2001-01-01
When Dirac derived the special relativistic quantum equation which brings his name, it became evident that the spin is a consequence of the space-time geometry. However, taking gravity into account (as for, instance, in the study of neutron stars), most authors do not take into account the relation between hyperbolic geometry and spin and derive an Einstein equation which implicitly takes into account only boson degrees of freedom. In this work we introduce a consistent quantum general relativistic formalism which allows us to study the effects of the existence of fermion degrees of freedom. (author)
Einstein equations and Fermion degrees of freedom
Luetz, E.F.; Vasconcellos, C.A.Z. [Rio Grande do Sul Univ., Porto Alegre, RS (Brazil). Inst. de Fisica
2001-07-01
When Dirac derived the special relativistic quantum equation which brings his name, it became evident that the spin is a consequence of the space-time geometry. However, taking gravity into account (as for, instance, in the study of neutron stars), most authors do not take into account the relation between hyperbolic geometry and spin and derive an Einstein equation which implicitly takes into account only boson degrees of freedom. In this work we introduce a consistent quantum general relativistic formalism which allows us to study the effects of the existence of fermion degrees of freedom. (author)
Fermions, Skyrmions and the 3-sphere
Goatham, Stephen W; Krusch, Steffen
2010-01-01
This paper investigates a background charge one Skyrme field chirally coupled to light fermions on the 3-sphere. The Dirac equation for the system commutes with a generalized angular momentum or grand spin. It can be solved explicitly for a Skyrme configuration given by the hedgehog form. The energy spectrum and degeneracies are derived for all values of the grand spin. Solutions for non-zero grand spin are each characterized by a set of four polynomials. The paper also discusses the energy of the Dirac sea using zeta-function regularization.
Fermion dynamical symmetry and identical bands
Guidry, M.
1995-01-01
Recent general attention has been directed to the phenomenon of identical bands in both normally deformed and superdeformed nuclei. This paper discusses the possibility that such behavior results from a dynamical symmetry of the nuclear many-body system. Phenomenology and the basis principles of Lie algebras are used to place conditions on the acceptable properties of a candidate symmetry. We find that quite general arguments require that such a symmetry have a minimum of 21 generators with a microscopic fermion interpretation. (author). 9 refs., 11 figs., 1 tab
An ambiguity in fermionic string perturbation theory
Atick, J.J.; Rabin, J.M.
1988-01-01
Recent investigation by Verlinde and Verlinde has shown that the fermionic string loop amplitudes change by a total derivative term in the moduli space under a change of basis of the supermoduli. This ambiguity is addressed in the context of the heterotic string theory, and shown to be a consequence of an inherent ambiguity in defining integration over the variables of a Grassmann algebra - in this case the Grassmann-valued coordinates of the supermoduli space. A resolution of this ambiguity in genus-two within this formalism is also presented. (orig.)
A possible model of heavy fermion superconductivity
Zhang Liyuan.
1986-08-01
We have used the periodic Anderson Hamiltonian to study the behaviour of heavy fermion systems. It has been argued that the properly large mixing between f and the conduction electrons, the strong Coulomb correlation between f electrons and the related renormalization effect are the main causes of the large effective mass of the quasiparticle. Further, we have introduced phenomenologically the BCS attractive interaction between the heavy quasiparticles and explained that the value of ΔC/γT c and T c may be quite different from that of the BCS theory as a result of the interaction between two branches of the quasiparticles. (author)
Magnetic fluctuations in heavy fermion systems
Broholm, C.L.
1989-06-01
Magnetic order and fluctuations in the heavy Fermion systems UPt 3 , U 2 Zn 17 and URu 2 Si 2 have been studied by neutron scattering. Single crystalline samples and triple-axis neutron-scattering techniques with energy transfers between 0 and 40 meV and energy resolutions between 0.1 meV and 4 meV have been employed. UPt 3 develops an antiferromagnetically ordered moment of (0.02±0.005) μ B below T N = 5 K which doubles the unit cell in the basal plane and coexists with superconductivity below T c = 0.5 K. The magnetic fluctuations are relaxational, and enhanced at the antiferromagnetic zone center in a low-energy regime. The characteristic zone-center relaxation energy is 0.3 meV. The temperature- and field-dependence of the antiferromagnetic order in the superconducting phase suggest a close relation between these two properties in UPt 3 . U 2 Zn 17 has a broad spectrum of magnetic fluctuations, even below T N = 9.7 K, of which the transverse part below 10 meV is strongly enhanced at the antiferromagnetic zone center. The system has an anomalously extended critical region and the antiferromagnetic phase transition seems to be driven by the temperature-dependence of an effective RKKY interaction, as anticipated theoretically. URu 2 Si 2 , a strongly anisotropic heavy Fermion system, has a high-energy regime of antiferromagnetically-correlated overdamped magnetic fluctuations. Below T N = 17.5 K weak antiferromagnetic order, μ = (0.04±0.01)μ B , with finite correlations along the tetragonal c axis, develops along with a low-energy regime of strongly dispersive singlet-singlet excitations. Below T c = 1 K antiferromagnetism coexists with superconductivity. A phenomenological model describing the exchange-enhanced overdamped magnetic fluctuations of heavy Fermion systems is proposed. Our experimental results are compared to the anomalous bulk properties of heavy Fermion systems, and to magnetic fluctuations in other metallic magnets. (orig.)
Higher level WZW sectors from free fermions
Boeckenhauer, J.
1996-02-01
We introduce a gauge group of internal symmetries of an ambient algebra as a new tool for investigating the superselection structure of WZW theories and the representation theory of the corresponding affine Lie algebras. The relevant ambient algebra arises from the description of these conformal field theories in terms of free fermions. As an illustration we analyze in detail the so(N) WZW theories at level two. In this case there is actually a homorphism from the representation ring of the gauge group to the WZW fusion ring, even though the level-two observable algebra is smaller than the gauge invariant subalgebra of the field algebra. (orig.)
Heavy-fermion quasiparticles in UPt3
Taillefer, L.; Lonzarich, G.G.
1988-01-01
The quasiparticle band structure of the heavy-fermion superconductor UPt 3 has been investigated by means of angle-resolved measurements of the de Haas--van Alphen effect. Most of the results are consistent with a model of five quasiparticle bands at the Fermi level corresponding to Fermi surfaces similar to those calculated by band theory. However, as inferred from the extremely high cyclotron masses, the quasiparticle bands are much flatter than the calculated ones. The nature of the observed quasiparticles and their relationship to thermodynamic properties are briefly considered
Krein Spectral Triples and the Fermionic Action
Dungen, Koen van den
2016-01-01
Motivated by the space of spinors on a Lorentzian manifold, we define Krein spectral triples, which generalise spectral triples from Hilbert spaces to Krein spaces. This Krein space approach allows for an improved formulation of the fermionic action for almost-commutative manifolds. We show by explicit calculation that this action functional recovers the correct Lagrangians for the cases of electrodynamics, the electro-weak theory, and the Standard Model. The description of these examples does not require a real structure, unless one includes Majorana masses, in which case the internal spaces also exhibit a Krein space structure.
Fermions in interaction with time dependent fields
Falkensteiner, P.; Grosse, H.
1988-01-01
We solve a two dimensional model describing the interaction of fermions with time dependent external fields. We work out the second quantized formulation and obtain conditions for equivalence of representations at different times. This implies the existence of sectors which describe charged states. We obtain the time dependence of charges and observe that charge differences become integer for unitary equivalent states. For scattering we require the equivalence of in- and out-representations; nevertheless charged sectors may be reached by suitable interactions and ionization is possible. 20 refs. (Author)
Some Improved Nonperturbative Bounds for Fermionic Expansions
Lohmann, Martin, E-mail: marlohmann@gmail.com [Universita di Roma Tre, Dipartimento di Matematica (Italy)
2016-06-15
We reconsider the Gram-Hadamard bound as it is used in constructive quantum field theory and many body physics to prove convergence of Fermionic perturbative expansions. Our approach uses a recursion for the amplitudes of the expansion, discovered in a model problem by Djokic (2013). It explains the standard way to bound the expansion from a new point of view, and for some of the amplitudes provides new bounds, which avoid the use of Fourier transform, and are therefore superior to the standard bounds for models like the cold interacting Fermi gas.
Zero-point energy of confined fermions
Milton, K.A.
1980-01-01
A closed form for the reduced Green's function of massless fermions in the interior of a spherical bag is obtained. In terms of this Green's function, the corresponding zero-point or Casimir energy is computed. It is proposed that a resulting quadratic divergence can be absorbed by renormalizing a suitable parameter in the bag model (that is, absorbed by a contact term). The residual Casimir stress is attractive, but smaller than the repulsive Casimir stress of gluons in the model. The result for the total zero-point energy is in substantial disagreement with bag model phenomenological values
Role of four-fermion interaction and impurity in the states of two-dimensional semi-Dirac materials.
Wang, Jing
2018-03-28
We study the effects of four-fermion interaction and impurity on the low-energy states of 2D semi-Dirac materials by virtue of the unbiased renormalization group approach. The coupled flow equations that govern the energy-dependent evolutions of all correlated interaction parameters are derived after taking into account one-loop corrections from the interplay between four-fermion interaction and impurity. Whether and how four-fermion interaction and impurity influence the low-energy properties of 2D semi-Dirac materials are discreetly explored and addressed attentively. After carrying out the standard renormalization group analysis, we find that both trivial insulating and nontrivial semimetal states are qualitatively stable against all four kinds of four-fermion interactions. However, while switching on both four-fermion interaction and impurity, certain insulator-semimetal phase transitions and the distance of Dirac nodal points can be respectively induced and modified due to their strong interplay and intimate competition. Moreover, several non-Fermi liquid behaviors that deviate from the conventional Fermi liquids are exhibited at the lowest-energy limit.
Parameters of the lowest order chiral Lagrangian from fermion eigenvalues
DeGrand, T.; Schaefer, S.
2007-08-01
Recent advances in Random Matrix Theory enable one to determine the pseudoscalar decay constant from the response of eigenmodes of quenched fermions to an imaginary isospin chemical potential. We perform a pilot test of this idea, from simulations with two flavors of dynamical overlap fermions. (orig.)
Composite fermions a unified view of the quantum Hall regime
1998-01-01
One of the most exciting recent developments to have emerged from the quantum Hall effect is the subject of composite fermions. This important volume gives a self-contained, comprehensive description of the subject, including fundamentals, more advanced theoretical work, and results from experimental observations of composite fermions.
Fermionic construction of vertex operators for twisted affine algebras
Frappat, L.; Sorba, P.; Sciarrino, A.
1988-03-01
We construct vertex operator representations of the twisted affine algebras in terms of fermionic (or parafermionic in some cases) elementary fields. The folding method applied to the extended Dynkin diagrams of the affine algebras allows us to determine explicitly these fermionic fields as vertex operators
Nambu-Jona-Lasinio model with Wilson fermions
Rantaharju, Jarno; Drach, Vincent; Pica, Claudio
2017-01-01
We present a lattice study of a Nambu-Jona-Lasinio (NJL) model using Wilson fermions. Four-fermion interactions are a natural part of several extensions of the Standard Model, appearing as a low-energy description of a more fundamental theory. In models of dynamical electroweak symmetry breaking...
Tuning up an oldtimer: hybrid Monte Carlo with Wilson fermions
Schilling, K.; Hannemann, V.; Lippert, T.; Noeckel, B.
1995-01-01
We show that BiCGStab inversion algorithm helps to speed up by 50% the computation of the fermionic force inside the Hybrid Monte Carlo (HMC) simulation of full QCD with Wilson fermions, in the chiral regime of small quark masses. ((orig.))
Calculation of CWKB envelope in boson and fermion productions
Abstract. We present the calculation of envelope of boson and of both low- and high- mass fermion production at the end of inflation when the coherently oscillating inflatons decay into bosons and fermions. We consider three different models of inflation and use. CWKB technique to calculate the envelope to understand the ...
The Chiral Index of the Fermionic Signature Operator
Finster, Felix
2014-01-01
We define an index of the fermionic signature operator on even-dimensional globally hyperbolic spin manifolds of finite lifetime. The invariance of the index under homotopies is studied. The definition is generalized to causal fermion systems with a chiral grading. We give examples of space-times and Dirac operators thereon for which our index is non-trivial.
Fermionic constructions of exceptional Kac-Moody algebras
Schwimmer, A.
1985-01-01
The author discusses the fermionic representations of SO(2n) Kac Moody algebras. He describes construction of the E/sub 8/ algebra in terms of free fermionic operators, and generalises procedures for the basic representations of the Kac-Moody algebras appearing in Freudenthal's magic square
Worldline path integrals for fermions with general couplings
D'Hoker, E.; Gagne, D.G.
1996-01-01
We derive a worldline path integral representation for the effective action of a multiplet of Dirac fermions coupled to the most general set of matrix-valued scalar, pseudoscalar, vector, axial vector and antisymmetric tensor background fields. By representing internal degrees of freedom in terms of worldline fermions as well, we obtain a formulation which manifestly exhibits chiral gauge invariance. (orig.)
Landau levels of Majorana fermions in a spin liquid
Rachel, Stephan; Fritz, Lars; Vojta, Matthias
2016-01-01
Majorana fermions were originally proposed as elementary particles acting as their own antiparticles. In recent years, it has become clear that Majorana fermions can instead be realized in condensed-matter systems as emergent quasiparticles, a situation often accompanied by topological order. Here
Fermion field as inflaton, dark energy and dark matter
Grams, Guilherme; Souza, Rudinei C de; Kremer, Gilberto M
2014-01-01
The search for constituents that can explain the periods of accelerating expansion of the Universe is a fundamental topic in cosmology. In this context, we investigate how fermionic fields minimally and non-minimally coupled with the gravitational field may be responsible for accelerated regimes during the evolution of the Universe. The forms of the potential and coupling of the model are determined through the technique of the Noether symmetry for two cases. The first case comprises a Universe filled only with the fermion field. Cosmological solutions are straightforwardly obtained for this case and an exponential inflation mediated by the fermion field is possible with a non-minimal coupling. The second case takes account of the contributions of radiation and baryonic matter in the presence of the fermion field. In this case the fermion field plays the role of dark energy and dark matter, and when a non-minimal coupling is allowed, it mediates a power-law inflation. (paper)
Fermion tunneling from higher-dimensional black holes
Lin Kai; Yang Shuzheng
2009-01-01
Via the semiclassical approximation method, we study the 1/2-spin fermion tunneling from a higher-dimensional black hole. In our work, the Dirac equations are transformed into a simple form, and then we simplify the fermion tunneling research to the study of the Hamilton-Jacobi equation in curved space-time. Finally, we get the fermion tunneling rates and the Hawking temperatures at the event horizon of higher-dimensional black holes. We study fermion tunneling of a higher-dimensional Schwarzschild black hole and a higher-dimensional spherically symmetric quintessence black hole. In fact, this method is also applicable to the study of fermion tunneling from four-dimensional or lower-dimensional black holes, and we will take the rainbow-Finsler black hole as an example in order to make the fact explicit.
Anomalous fermion number nonconservation: Paradoxes in the level crossing picture
Burnier, Y.
2006-01-01
In theories with anomalous fermion number nonconservation, the level-crossing picture is considered a faithful representation of the fermionic quantum number variation. It represents each created fermion by an energy level that crosses the zero-energy line from below. If several fermions of various masses are created, the level-crossing picture contains several levels that cross the zero-energy line and cross each other. However, we know from quantum mechanics that the corresponding levels cannot cross if the different fermions are mixed via some interaction potential. The simultaneous application of these two requirements on the level behavior leads to paradoxes. For instance, a naive interpretation of the resulting level-crossing picture gives rise to charge nonconservation. In this paper, we resolve this paradox by a precise calculation of the transition probability, and discuss what are the implications for the electroweak theory. In particular, the nonperturbative transition probability is higher if top quarks are present in the initial state
Perturbative improvement of staggered fermions using fat links
Lee, Weonjong
2002-01-01
We study the possibility of improving staggered fermions using various fat links in order to reduce perturbative corrections to the gauge-invariant staggered fermion operators. We prove five theorems on SU(3) projection, triviality in renormalization, multiple SU(3) projections, uniqueness, and equivalence. As a result of these theorems, we show that, at the one-loop level, the renormalization of staggered fermion operators is identical between SU(3) projected Fat7 links and hypercubic links, as long as the action and operators are constructed by imposing the same perturbative improvement condition. In addition, we propose a new view of SU(3) projection as a tool of tadpole improvement for the staggered fermion doublers. As a conclusion, we present alternative choices of constructing fat links to improve the staggered fermion action and operators, which deserve further investigation
Hybrid Monte Carlo algorithm with fat link fermion actions
Kamleh, Waseem; Leinweber, Derek B.; Williams, Anthony G.
2004-01-01
The use of APE smearing or other blocking techniques in lattice fermion actions can provide many advantages. There are many variants of these fat link actions in lattice QCD currently, such as flat link irrelevant clover (FLIC) fermions. The FLIC fermion formalism makes use of the APE blocking technique in combination with a projection of the blocked links back into the special unitary group. This reunitarization is often performed using an iterative maximization of a gauge invariant measure. This technique is not differentiable with respect to the gauge field and thus prevents the use of standard Hybrid Monte Carlo simulation algorithms. The use of an alternative projection technique circumvents this difficulty and allows the simulation of dynamical fat link fermions with standard HMC and its variants. The necessary equations of motion for FLIC fermions are derived, and some initial simulation results are presented. The technique is more general however, and is straightforwardly applicable to other smearing techniques or fat link actions
Field theories with multiple fermionic excitations
Crawford, J.P.
1978-01-01
The reason for the existence of the muon has been an enigma since its discovery. Since that time there has been a continuing proliferation of elementary particles. It is proposed that this proliferation of leptons and quarks is comprehensible if there are only four fundamental particles, the leptons ν/sub e/ and e - , and the quarks u and d. All other leptons and quarks are imagined to be excited states of these four fundamental entities. Attention is restricted to the charged leptons and the electromagnetic interactions only. A detailed study of a field theory in which there is only one fundamental charged fermionic field having two (or more) excitations is made. When the electromagnetic interactions are introduced and the theory is second quantized, under certain conditions this theory reproduces the S matrix obtained from usual OED. In this case no electromagnetic transitions are allowed. A leptonic charge operator is defined and a superselection rule for this leptonic charge is found. Unfortunately, the mass spectrum cannot be obtained. This theory has many renormalizable generalizations including non-abelian gauge theories, Yukawa-type theories, and Fermi-type theories. Under certain circumstances the Yukawa- and Fermi-type theories are finite in perturbation theory. It is concluded that there are no fundamental objections to having fermionic fields with more than one excitation
Quantum chaos in a fermion system
Pal, Santanu
1992-01-01
With the growing realisation that the dynamics of a system with a few degrees of freedom is chaotic more as a rule than an exception, the relevance of quantum chaos in nuclear single-particle motion is now receiving closer scrutinisation. This on one hand is helping to gain a deeper understanding of dissipative processes in nuclear dynamics as well as revealing certain interesting features of a fermion system on the other. In the present talk, we would discuss the chaotic features of the single-particle motion in a di nucleus with a view to study the signatures of an effective underlying classical dynamics in the system. As the present day understanding of quantum chaos relies quite heavily on the existence of classical trajectories, it is rather interesting to study how far such considerations can be pushed for systems which do not have a obvious classical analogue such as the spin-orbit interaction in our system. This question has been further investigated for a relativistic fermion system, similar to the Bogoliubov bag. This model is particularly suited as spin, without a classical analogue, has its natural place in the Dirac equation. The results of this study have been presented in the talk. (author). 25 refs., 14 figs
Free Fermions and the Classical Compact Groups
Cunden, Fabio Deelan; Mezzadri, Francesco; O'Connell, Neil
2018-06-01
There is a close connection between the ground state of non-interacting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated determinantal point processes can be extended in two natural directions: (i) we consider the full family of admissible quantum boundary conditions (i.e., self-adjoint extensions) for the Laplacian on a bounded interval, and the corresponding projection correlation kernels; (ii) we construct the grand canonical extensions at finite temperature of the projection kernels, interpolating from Poisson to random matrix eigenvalue statistics. The scaling limits in the bulk and at the edges are studied in a unified framework, and the question of universality is addressed. Whether the finite temperature determinantal processes correspond to the eigenvalue statistics of some matrix models is, a priori, not obvious. We complete the picture by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of free fermions with classical boundary conditions.
The interacting boson-fermion model
Iachello, F.; Van Isacker, P.
1990-01-01
The interacting boson-fermion model has become in recent years the standard model for the description of atomic nuclei with an odd number of protons and/or neutrons. This book describes the mathematical framework on which the interacting boson-fermion model is built and presents applications to a variety of situations encountered in nuclei. The book addresses both the analytical and the numerical aspects of the problem. The analytical aspect requires the introduction of rather complex group theoretic methods, including the use of graded (or super) Lie algebras. The first (and so far only) example of supersymmetry occurring in nature is also discussed. The book is the first comprehensive treatment of the subject and will appeal to both theoretical and experimental physicists. The large number of explicit formulas for level energies, electromagnetic transition rates and intensities of transfer reactions presented in the book provide a simple but detailed way to analyze experimental data. This book can also be used as a textbook for advanced graduate students
Free Fermions and the Classical Compact Groups
Cunden, Fabio Deelan; Mezzadri, Francesco; O'Connell, Neil
2018-04-01
There is a close connection between the ground state of non-interacting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated determinantal point processes can be extended in two natural directions: (i) we consider the full family of admissible quantum boundary conditions (i.e., self-adjoint extensions) for the Laplacian on a bounded interval, and the corresponding projection correlation kernels; (ii) we construct the grand canonical extensions at finite temperature of the projection kernels, interpolating from Poisson to random matrix eigenvalue statistics. The scaling limits in the bulk and at the edges are studied in a unified framework, and the question of universality is addressed. Whether the finite temperature determinantal processes correspond to the eigenvalue statistics of some matrix models is, a priori, not obvious. We complete the picture by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of free fermions with classical boundary conditions.
Monotop signature from a fermionic top partner
Gonçalves, Dorival; Kong, Kyoungchul; Sakurai, Kazuki; Takeuchi, Michihisa
2018-01-01
We investigate monotop signatures arising from phenomenological models of fermionic top partners, which are degenerate in mass and decay into a bosonic dark matter candidate, either spin 0 or spin 1. Such a model provides a monotop signature as a smoking gun, while conventional searches with t t ¯ + missing transverse momentum are limited. Two such scenarios, (i) a phenomenological third generation extradimensional model with excited top and electroweak sectors, and (ii) a model where only a top partner and a dark matter particle are added to the standard model, are studied in the degenerate mass regime. We find that in the case of extra dimension a number of different processes give rise to effectively the same monotop final state, and a great gain can be obtained in the sensitivity for this channel. We show that the monotop search can explore top-partner masses up to 630 and 300 GeV for the third generation extradimensional model and the minimal fermionic top-partner model, respectively, at the high luminosity LHC.
Search for Majorana fermions in topological superconductors.
Pan, Wei [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Shi, Xiaoyan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Hawkins, Samuel D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Klem, John Frederick [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2014-10-01
The goal of this project is to search for Majorana fermions (a new quantum particle) in a topological superconductor (a new quantum matter achieved in a topological insulator proximitized by an s-wave superconductor). Majorana fermions (MFs) are electron-like particles that are their own anti-particles. MFs are shown to obey non-Abelian statistics and, thus, can be harnessed to make a fault-resistant topological quantum computer. With the arrival of topological insulators, novel schemes to create MFs have been proposed in hybrid systems by combining a topological insulator with a conventional superconductor. In this LDRD project, we will follow the theoretical proposals to search for MFs in one-dimensional (1D) topological superconductors. 1D topological superconductor will be created inside of a quantum point contact (with the metal pinch-off gates made of conventional s-wave superconductors such as niobium) in a two-dimensional topological insulator (such as inverted type-II InAs/GaSb heterostructure).
Quantum phases of AB2 fermionic chains
Murcia-Correa, L S; Franco, R; Silva-Valencia, J
2016-01-01
A fermionic chain is a one-dimensional system with fermions that interact locally and can jump between sites in the lattice, in particular an AB n chain type, where A and B are sites that exhibit a difference in energy level of Δ and site B is repeated n-times, such that the unit cell has n +1 sites. A limit case of this model, called the ionic Hubbard model (n = 1), has been widely studied due to its interesting physics and applications. In this paper, we study the ground state of an AB 2 chain, which describes the material R 4 [Pt 2 (P 2 O 5 H 2 ) 4 X] · nH 2 O. Specifically, we consider a filling with two electrons per unit cell, and using the density matrix renormalization group method we found that the system exhibits the band insulator and Mott correlated insulator phases, as well as an intermediate phase between them. For couplings of Δ = 2,10 and 20, we estimate the critical points that separate these phases through the structure factor and the energy gap in the sector of charge and spin, finding that the position of the critical point rises as a function of Δ. (paper)
Path integral for gauge theories with fermions
Fujikawa, K.
1980-01-01
The Atiyah-Singer index theorem indicates that a naive unitary transformation of basis vectors for fermions interacting with gauge fields is not allowed in general. On the basis of this observation, it was previously shown that the path-integral measure of a gauge-invariant fermion theory is transformed nontrivially under the chiral transformation, and thus leads to a simple derivation of ''anomalous'' chiral Ward-Takahashi identities. We here clarify some of the technical aspects associated with the discussion. It is shown that the Jacobian factor in the path-integral measure, which corresponds to the Adler-Bell-Jackiw anomaly, is independent of any smooth regularization procedure of large eigenvalues of D in Euclidean theory; this property holds in any even-dimensional space-time and also for the gravitational anomaly. The appearance of the anomaly and its connection with the index theorem are thus related to the fact that the primary importance is attached to the Lorentz-covariant ''energy'' operator D and that D and γ 5 do not commute. The abnormal behavior of the path-integral measure at the zero-frequency sector in the presence of instantons and its connection with spontaneous symmetry breaking is also clarified. We comment on several other problems associated with the anomaly and on the Pauli-Villars regularization method
Fermion families and vacuum in the two measures theory
Guendelman, E.; Kaganovich, A.
2005-01-01
We present an alternative gravity and matter fields theory where the consistency condition of equations of motion yields strong correlation between states of 'primordial' fermion fields and local value of the scalar fields (dilaton and Higgs) energy density. The same 'primordial' fermion field at different densities can be either in states of regular fermionic matter or in states presumably corresponding to the dark fermionic matter. In regime of the fermion densities typical for normal particle physics, each of the primordial fermions splits into three generations identified with regular fermions. When restricting ourselves to the first two fermion generations, the theory reproduces general relativity and regular particle theory. As fermion energy density is comparable with vacuum energy density, the theory allows new type of states. Such Cosmo-Low Energy Physics (CLEP) state is studied in the framework of the model where 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. Some of the features of the CLEP state in the late time universe: neutrino mass increases as α 3/2 (α = α(t) is the scale factor); its energy density scales as a sort of dark energy and approaches constant as α→∞; this cold dark matter possesses negative pressure and its equation of state approaches that of the cosmological constant as α→∞; the total energy density of such universe is less than it would be in the universe free of fermionic matter at all. The latter means that nonrelativistic neutrinos are able to produce expanding bubbles of the CLEP state playing the role of a true 'cosmological vacuum' surrounded by a 'regular' vacuum. (authors)
Renormalization group analysis of order parameter fluctuations in fermionic superfluids
Obert, Benjamin
2014-01-01
In this work fluctuation effects in two interacting fermion systems exhibiting fermionic s-wave superfluidity are analyzed with a modern renormalization group method. A description in terms of a fermion-boson theory allows an investigation of order parameter fluctuations already on the one-loop level. In the first project a quantum phase transition between a semimetal and a s-wave superfluid in a Dirac cone model is studied. The interplay between fermions and quantum critical fluctuations close to and at the quantum critical point at zero and finite temperatures are studied within a coupled fermion-boson theory. At the quantum critical point non-Fermi liquid and non-Gaussian behaviour emerge. Close to criticality several quantities as the susceptibility show a power law behaviour with critical exponents. We find an infinite correlation length in the entire semimetallic ground state also away from the quantum critical point. In the second project, the ground state of an s-wave fermionic superfluid is investigated. Here, the mutual interplay between fermions and order parameter fluctuations is studied, especially the impact of massless Goldstone fluctuations, which occur due to spontaneous breaking of the continuous U(1)-symmetry. Fermionic gap and bosonic order parameter are distinguished. Furthermore, the bosonic order parameter is decomposed in transverse and longitudinal fluctuations. The mixing between transverse and longitudinal fluctuations is included in our description. Within a simple truncation of the fermion-boson RG flow, we describe the fermion-boson theory for the first time in a consistent manner. Several singularities appear due the Goldstone fluctuations, which partially cancel due to symmetry. Our RG flow captures the correct infrared asymptotics of the system, where the collective excitations act as an interacting Bose gas. Lowest order Ward identities and the massless Goldstone mode are fulfilled in our truncation.
Level Density In Interacting Boson-Fermion-Fermion Model (IBFFM) Of The Odd-Odd Nucleus 196Au
Kabashi, Skender; Bekteshi, Sadik
2007-01-01
The level density of the odd-odd nucleus 196Au is investigated in the interacting boson-fermion-fermion model (IBFFM) which accounts for collectivity and complex interaction between quasiparticle and collective modes.The IBFFM total level density is fitted by Gaussian and its tail is also fitted by Bethe formula and constant temperature Fermi gas model
Kitaev honeycomb model. Majorana fermion representation and disorder
Zschocke, Fabian
2016-01-01
Many interesting phenomena in quantum physics arise through the quantum mechanical interaction of a large number of particles. In most cases describing the relevant physical properties is extremely difficult, because the complexity of the system increases exponentially with the number of interacting particles and solving the underlying Schroedinger equation becomes impossible. Nevertheless, our understanding of complex phenomena has progressed through some groundbreaking discoveries in the history of condensed matter physics. Examples include the development of Landau's theory of Fermi liquids, the BCS theory of superconductivity, the theory of superfluidity and the theory of the fractional quantum Hall effect. In all these cases a theoretical understanding was achieved with so-called quasi-particles. Instead of explaining a phenomenon through the behavior of fundamental particles, such as electrons, the corresponding properties can be described by the simple behavior of quasi-particles, which are themselves a result of the complex collective interaction. One of the rare examples, where a strongly correlated quantum mechanical problem can be solved analytical, is the Kitaev model. It describes interacting spins on a honeycomb lattice and exhibits a spin liquid ground state. Here the solution was achieved by means of certain quasi-particles, called Majorana fermions. However, it has not been possible to clearly identify such a spin liquid experimentally, because its defining feature is the absence of any conventional order, in particular magnetic order. In contrast, the observation of quasiparticle excitations may hint at the nature of the ground state. But also a definite detection of Majorana fermions in any kind of system remains one of the outstanding issues in modern condensed matter physics. Therefore this thesis is devoted to the question how such quasiparticles may be found experimentally. For this reason we study the influence of disorder on the states
Model space dimensionalities for multiparticle fermion systems
Draayer, J.P.; Valdes, H.T.
1985-01-01
A menu driven program for determining the dimensionalities of fixed-(J) [or (J,T)] model spaces built by distributing identical fermions (electrons, neutrons, protons) or two distinguihable fermion types (neutron-proton and isospin formalisms) among any mixture of positive and negative parity spherical orbitals is presented. The algorithm, built around the elementary difference formula d(J)=d(M=J)-d(M=J+1), takes full advantage of M->-M and particle-hole symmetries. A 96 K version of the program suffices for as compilated a case as d[(+1/2, +3/2, + 5/2, + 7/2-11/2)sup(n-26)J=2 + ,T=7]=210,442,716,722 found in the 0hω valence space of 56 126 Ba 70 . The program calculates the total fixed-(Jsup(π)) or fixed-(Jsup(π),T) dimensionality of a model space generated by distributing a specified number of fermions among a set of input positive and negative parity (π) spherical (j) orbitals. The user is queried at each step to select among various options: 1. formalism - identical particle, neutron-proton, isospin; 2. orbits -bumber, +/-2*J of all orbits; 3. limits -minimum/maximum number of particles of each parity; 4. specifics - number of particles, +/-2*J (total), 2*T; 5. continue - same orbit structure, new case quit. Though designed for nuclear applications (jj-coupling), the program can be used in the atomic case (LS-coupling) so long as half integer spin values (j=l+-1/2) are input for the valnce orbitals. Mutiple occurrences of a given j value are properly taken into account. A minor extension provides labelling information for a generalized seniority classification scheme. The program logic is an adaption of methods used in statistical spectroscopy to evaluate configuration averages. Indeed, the need for fixed symmetry leve densities in spectral distribution theory motivated this work. The methods extend to other group structures where there are M-like additive quantum labels. (orig.)
Physics of heavy fermions heavy fermions and strongly correlated electrons systems
Onuki, Yoshichika
2018-01-01
A large variety of materials prove to be fascinating in solid state and condensed matter physics. New materials create new physics, which is spearheaded by the international experimental expert, Prof Yoshichika Onuki. Among them, the f electrons of rare earth and actinide compounds typically exhibit a variety of characteristic properties, including spin and charge orderings, spin and valence fluctuations, heavy fermions, and anisotropic superconductivity. These are mainly manifestations of better competitive phenomena between the RKKY interaction and the Kondo effect. The present text is written so as to understand these phenomena and the research they prompt. For example, superconductivity was once regarded as one of the more well-understood many-body problems. However, it is, in fact, still an exciting phenomenon in new materials. Additionally, magnetism and superconductivity interplay strongly in heavy fermion superconductors. The understanding of anisotropic superconductivity and magnetism is a challengin...
Fermion-number violation in regularizations that preserve fermion-number symmetry
Golterman, Maarten; Shamir, Yigal
2003-01-01
There exist both continuum and lattice regularizations of gauge theories with fermions which preserve chiral U(1) invariance (“fermion number”). Such regularizations necessarily break gauge invariance but, in a covariant gauge, one recovers gauge invariance to all orders in perturbation theory by including suitable counterterms. At the nonperturbative level, an apparent conflict then arises between the chiral U(1) symmetry of the regularized theory and the existence of ’t Hooft vertices in the renormalized theory. The only possible resolution of the paradox is that the chiral U(1) symmetry is broken spontaneously in the enlarged Hilbert space of the covariantly gauge-fixed theory. The corresponding Goldstone pole is unphysical. The theory must therefore be defined by introducing a small fermion-mass term that breaks explicitly the chiral U(1) invariance and is sent to zero after the infinite-volume limit has been taken. Using this careful definition (and a lattice regularization) for the calculation of correlation functions in the one-instanton sector, we show that the ’t Hooft vertices are recovered as expected.
Interacting fermions in one spatial dimensions
Wolf, D.
1982-01-01
This thesis contains in its first part a critical survey about the method of the bosonization of fermi fields in one spatial dimension and its application to the Luttinger and the massive Thirring model. The first chapter served for the explanation of the term of the unitary inequivalence. Thereby two generally valid facts could be demonstrated very illustratively by the example of a fermion algebra and its representations, namely first that infinite, direct product space are not separable, and second that weak equivalence of the vacua is equivalent to the unitary equivalence of the corresponding representations of the field algebra. In the second part the statement first studied by Luther (1976) and since then often cited, that the continuum limit of the Heisenberg model is the massive Thirring model. It is concluded that it can up to today not be considered as proved although indications for its validity can be found. (orig./HSI) [de
Standard model fermions and N=8 supergravity
Nicolai, Hermann [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Muehlenberg 1, Potsdam-Golm (Germany)
2016-07-01
In a scheme originally proposed by Gell-Mann, and subsequently shown to be realized at the SU(3) x U(1) stationary point of maximal gauged SO(8) supergravity, the 48 spin-1/2 fermions of the theory remaining after the removal of eight Goldstinos can be identified with the 48 quarks and leptons (including right-chiral neutrinos) of the Standard model, provided one identifies the residual SU(3) with the diagonal subgroup of the color group SU(3){sub c} and a family symmetry SU(3){sub f}. However, there remained a systematic mismatch in the electric charges by a spurion charge of ± 1/6. We here identify the ''missing'' U(1) that rectifies this mismatch, and that takes a surprisingly simple, though unexpected form, and show how it is related to the conjectured R symmetry K(E10) of M Theory.
Reasonable fermionic quantum information theories require relativity
Friis, Nicolai
2016-01-01
We show that any quantum information theory based on anticommuting operators must be supplemented by a superselection rule deeply rooted in relativity to establish a reasonable notion of entanglement. While quantum information may be encoded in the fermionic Fock space, the unrestricted theory has a peculiar feature: the marginals of bipartite pure states need not have identical entropies, which leads to an ambiguous definition of entanglement. We solve this problem, by proving that it is removed by relativity, i.e., by the parity superselection rule that arises from Lorentz invariance via the spin-statistics connection. Our results hence unveil a fundamental conceptual inseparability of quantum information and the causal structure of relativistic field theory. (paper)
Fermionic functional integrals and the renormalization group
Feldman, Joel; Trubowitz, Eugene
2002-01-01
This book, written by well-known experts in the field, offers a concise summary of one of the latest and most significant developments in the theoretical analysis of quantum field theory. The renormalization group is the name given to a technique for analyzing the qualitative behavior of a class of physical systems by iterating a map on the vector space of interactions for the class. In a typical nonrigorous application of this technique, one assumes, based on one's physical intuition, that only a certain finite dimensional subspace (usually of dimension three or less) is important. The material in this book concerns a technique for justifying this approximation in a broad class of fermionic models used in condensed matter and high energy physics. This volume is based on the Aisenstadt Lectures given by Joel Feldman at the Centre de Recherches Mathematiques (Montreal, Canada). It is suitable for graduate students and research mathematicians interested in mathematical physics. Included are many problems and so...
Fermionic Casimir effect with helix boundary condition
Zhai, Xiang-hua; Li, Xin-zhou; Feng, Chao-Jun
2011-01-01
In this paper, we consider the fermionic Casimir effect under a new type of space-time topology using the concept of quotient topology. The relation between the new topology and that in Feng and Li (Phys. Lett. B 691:167, 2010), Zhai et al. (Mod. Phys. Lett. A 26:669, 2011) is something like that between a Moebius strip and a cylindric. We obtain the exact results of the Casimir energy and force for the massless and massive Dirac fields in the (D+1)-dimensional space-time. For both massless and massive cases, there is a Z 2 symmetry for the Casimir energy. To see the effect of the mass, we compare the result with that of the massless one and we found that the Casimir force approaches the result of the force in the massless case when the mass tends to zero and vanishes when the mass tends to infinity. (orig.)
Electron spectroscopy studies in heavy fermions
Arko, A.J.
1986-02-01
Photoemission experiments (whereby an electron absorbs a packet of light energy and is able to escape from the host material due to its increased energy) can measure directly the energy distribution of electrons in various materials. Our measurements on a recently-discovered class of metallic materials called ''heavy fermions'' show that the electrons that actually carry the electric current in these metals exist only within an extremely narrow range of energies. This range, which we will call the bandwidth, is narrower than that found in ordinary metals like copper by at least a factor of 10. Indeed it is surprising that they can carry electric current at all since such narrow energy ranges (or band widths) are characteristic of electrons confined to their host atoms, as in a non-metal, rather than of electrons that are free to wander through a metal. 8 refs
Machine Learning Phases of Strongly Correlated Fermions
Kelvin Ch’ng
2017-08-01
Full Text Available Machine learning offers an unprecedented perspective for the problem of classifying phases in condensed matter physics. We employ neural-network machine learning techniques to distinguish finite-temperature phases of the strongly correlated fermions on cubic lattices. We show that a three-dimensional convolutional network trained on auxiliary field configurations produced by quantum Monte Carlo simulations of the Hubbard model can correctly predict the magnetic phase diagram of the model at the average density of one (half filling. We then use the network, trained at half filling, to explore the trend in the transition temperature as the system is doped away from half filling. This transfer learning approach predicts that the instability to the magnetic phase extends to at least 5% doping in this region. Our results pave the way for other machine learning applications in correlated quantum many-body systems.
Heavy-light fermion mixtures at unitarity
Gezerlis, Alexandros [Los Alamos National Laboratory; Carlson, Joseph [Los Alamos National Laboratory; Gandol, S [UNIV. ILL; Schmidt, E [ITALY
2009-01-01
We investigate fermion pairing in the unitary regime for a mass ratio corresponding to a {sup 6}Li-{sup 40}K mixture using quantum Monte Carlo methods. The ground-state energy and the average light- and heavy-particle excitation spectrum for the unpolarized superfluid state are nearly independent of the mass ratio. In the majority light system, the polarized superfluid is close to the energy of a phase separated mixture of nearly fully polarized normal and unpolarized superfluid. For a majority of heavy particles, we find an energy minimum for a normal state with a ratio of {approx}3:1 heavy to light particles. A slight increase in attraction to k{sub F}a{approx}2.5 yields a ground state energy of nearly zero for this ratio. A cold unpolarized system in a harmonic trap at unitarity should phase separate into three regions, with a shell of unpolarized superfluid in the middle.
Multiplicities of states od equivalent fermion shells
Savukinas, A.Yu.; Glembotskij, I.I.
1980-01-01
Classification of states of three or four equivalent fermions has been studied, i.e. possible terms and their multiplicities have been determined. For this purpose either the group theory or evident expressions for the fractional-parentage coefficients have been used. In the first approach the formulas obtained by other authors for the multiplicities of terms through the characters of the transformation matrices of bond moments have been used. This approach happens to be more general as compared with the second one, as expressions for the fractional-parentage coefficients in many cases are not known. The multiplicities of separate terms have been determined. It has been shown that the number of terms of any multiplicity becomes constant when l or j is increased [ru
Ambiguities of functional integrals for fermionic systems
Cordero, P.
1981-01-01
We study the path integral quantization of a purely fermionic system in the semiclassical approximation. It is crucial that the analogue of the usual method of stationary phase works for integrals over Grassmann variables. Our analysis is based on a quite trivial example (the exact solution is known), and therefore we can check when the results make sense. It is shown that just as in the boson case the path integral method depends on the discretization (we use the Faddeev discretization) and some attempts to do the same derivations directly in the continuous time limit are shown to yield either ill-defined objects or simply wrong results. It seems correct to conclude that the key point is the discretization
Domain decomposition and multilevel integration for fermions
Ce, Marco; Giusti, Leonardo; Schaefer, Stefan
2016-01-01
The numerical computation of many hadronic correlation functions is exceedingly difficult due to the exponentially decreasing signal-to-noise ratio with the distance between source and sink. Multilevel integration methods, using independent updates of separate regions in space-time, are known to be able to solve such problems but have so far been available only for pure gauge theory. We present first steps into the direction of making such integration schemes amenable to theories with fermions, by factorizing a given observable via an approximated domain decomposition of the quark propagator. This allows for multilevel integration of the (large) factorized contribution to the observable, while its (small) correction can be computed in the standard way.
Actinides: from heavy fermions to plutonium metallurgy
Smith, J.L.; Fisk, Z.; Hecker, S.S.
1984-01-01
The actinide elements mark the emergence of 5f electrons. The f electrons possess sufficiently unusual characteristics that their participation in atomic binding often result in dramatic changes in properties. This provides an excellent opportunity to study the question of localization of electrons; a question that is paramount in predicting the physical and chemical properties of d and f electron transition metals. The transition region between localized (magnetic) and itinerant (often superconducting) behavior provides for many interesting phenomena such as structural instabilities (polymorphism), spin fluctuations, mixed valences, charge density waves, exceptional catalytic activity and hydrogen storage. This region offers most interesting behavior such as that exhibited by the actinide compounds UBe 13 and UPt 3 . Both compounds are heavy-fermion superconductors in which both magnetic and superconducting behavior exist in the same electrons. The consequences of f-electron bonding (which appears greatest at Plutonium) show dramatic effects on phase stability, alloying behavior, phase transformations and mechanical behavior
Two-dimensional thermofield bosonization II: Massive fermions
Amaral, R.L.P.G.; Belvedere, L.V.; Rothe, K.D.
2008-01-01
We consider the perturbative computation of the N-point function of chiral densities of massive free fermions at finite temperature within the thermofield dynamics approach. The infinite series in the mass parameter for the N-point functions are computed in the fermionic formulation and compared with the corresponding perturbative series in the interaction parameter in the bosonized thermofield formulation. Thereby we establish in thermofield dynamics the formal equivalence of the massive free fermion theory with the sine-Gordon thermofield model for a particular value of the sine-Gordon parameter. We extend the thermofield bosonization to include the massive Thirring model
Boundary effects and gapped dispersion in rotating fermionic matter
Shu Ebihara
2017-01-01
Full Text Available We discuss the importance of boundary effects on fermionic matter in a rotating frame. By explicit calculations at zero temperature we show that the scalar condensate of fermion and anti-fermion cannot be modified by the rotation once the boundary condition is properly implemented. The situation is qualitatively changed at finite temperature and/or in the presence of a sufficiently strong magnetic field that supersedes the boundary effects. Therefore, to establish an interpretation of the rotation as an effective chemical potential, it is crucial to consider further environmental effects such as the finite temperature and magnetic field.
Lattice fermions at non-zero temperature and chemical potential
Bender, I.
1993-01-01
We study the free fermion gas at finite temperature and chemical potential in the lattice regularized version proposed by Hasenfratz and Karsch. Special emphasis is placed on the identification of the particle and antiparticle contributions to the partition function. In the case of naive fermions we show that the partition function no longer separates into particle-antiparticle contributions in the way familiar from the continuum formulation. The use of Wilson fermions, on the other hand, eliminates this unpleasant feature, and leads, after subtracting the vacuum contributions, to the familiar expressions for the average energy and charge densities. (orig.)
Collective Interference of Composite Two-Fermion Bosons
Tichy, Malte; Bouvrie, Peter Alexander; Mølmer, Klaus
2012-01-01
The composite character of two-fermion bosons manifests itself in the interference of many composites as a deviation from the ideal bosonic behavior. A state of many composite bosons can be represented as a superposition of different numbers of perfect bosons and fermions, which allows us...... to provide the full Hong–Ou–Mandel-like counting statistics of interfering composites. Our theory quantitatively relates the deviation from the ideal bosonic interference pattern to the entanglement of the fermions within a single composite boson....
Massless fermions and Kaluza--Klein theory with torsion
Wu, Y.; Zee, A.
1984-01-01
A pure Kaluza--Klein theory contains no massless fermion in four-dimensional theory. We investigate the effect of introducing torsion on the internal manifold and find that there are massless fermions. The hope is that given an isometry group the representation to which these fermions belong is fixed, in contrast to the situation in Yang--Mills theory. We show that this is indeed the case, but the representations do not appear to be the ones favored by current theoretical prejudice. The cases with parallelizable torsions on a group manifold as the internal manifold are analyzed in detail
Chiral anomaly, fermionic determinant and two dimensional models
Rego Monteiro, M.A. do.
1985-01-01
The chiral anomaly in random pair dimension is analysed. This anomaly is perturbatively calculated by dimensional regularization method. A new method for non-perturbative Jacobian calculation of a general chiral transformation, 1.e., finite and non-Abelian, is developed. This method is used for non-perturbative chiral anomaly calculation, as an alternative to bosonization of two-dimensional theories for massless fermions and to study the phenomenum of fermion number fractionalization. The fermionic determinant from two-dimensional quantum chromodynamics is also studied, and calculated, exactly, as in decoupling gauge as with out reference to a particular gauge. (M.C.K.) [pt
Trapped Fermions with Density Imbalance in the Bose-Einstein Condensate Limit
Pieri, P.; Strinati, G.C.
2006-01-01
We analyze the effects of imbalancing the populations of two-component trapped fermions, in the Bose-Einstein condensate limit of the attractive interaction between different fermions. Starting from the gap equation with two fermionic chemical potentials, we derive a set of coupled equations that describe composite bosons and excess fermions. We include in these equations the processes leading to the correct dimer-dimer and dimer-fermion scattering lengths. The coupled equations are then solved in the Thomas-Fermi approximation to obtain the density profiles for composite bosons and excess fermions, which are relevant to the recent experiments with trapped fermionic atoms
Propagator of the lattice domain wall fermion and the staggered fermion
Furui, S.
2009-01-01
We calculate the propagator of the domain wall fermion (DWF) of the RBC/UKQCD collaboration with 2 + 1 dynamical flavors of 16 3 x 32 x 16 lattice in Coulomb gauge, by applying the conjugate gradient method. We find that the fluctuation of the propagator is small when the momenta are taken along the diagonal of the 4-dimensional lattice. Restricting momenta in this momentum region, which is called the cylinder cut, we compare the mass function and the running coupling of the quark-gluon coupling a s,g1 (q) with those of the staggered fermion of the MILC collaboration in Landau gauge. In the case of DWF, the ambiguity of the phase of the wave function is adjusted such that the overlap of the solution of the conjugate gradient method and the plane wave at the source becomes real. The quark-gluon coupling a s,g1 (q) of the DWF in the region q > 1.3 GeV agrees with ghost-gluon coupling a s (q) that we measured by using the configuration of the MILC collaboration, i.e., enhancement by a factor (1 + c/q 2 ) with c ∼ 2.8 GeV 2 on the pQCD result. In the case of staggered fermion, in contrast to the ghost-gluon coupling a s (q) in Landau gauge which showed infrared suppression, the quark-gluon coupling a s,g1 (q) in the infrared region increases monotonically as q → 0. Above 2 GeV, the quark-gluon coupling a s,g1 (q) of staggered fermion calculated by naive crossing becomes smaller than that of DWF, probably due to the complex phase of the propagator which is not connected with the low energy physics of the fermion taste. An erratum to this article can be found at http://dx.doi.org/10.1007/s00601-009-0053-4. (author)
Holographic fermions at strong translational symmetry breaking: a Bianchi-VII case study
Bagrov, A. [Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, Nijmegen 6525 AJ (Netherlands); Kaplis, N.; Krikun, A.; Schalm, K.; Zaanen, J. [Institute Lorentz ITP, Leiden University, PO Box 9506, Leiden 2300 RA (Netherlands)
2016-11-09
It is presently unknown how strong lattice potentials influence the fermion spectral function of the holographic strange metals predicted by the AdS/CFT correspondence. This embodies a crucial test for the application of holography to condensed matter experiments. We show that for one particular momentum direction this spectrum can be computed for arbitrary strength of the effective translational symmetry breaking potential of the so-called Bianchi-VII geometry employing ordinary differential equations. Deep in the strange metal regime we find rather small changes to the single-fermion response computed by the emergent quantum critical IR, even when the potential becomes relevant in the infra-red. However, in the regime where holographic quasi-particles occur, defining a Fermi surface in the continuum, they acquire a finite lifetime at any finite potential strength. At the transition from irrelevancy to relevancy of the Bianchi potential in the deep infra-red the quasi-particle remnants disappear completely and the fermion spectrum exhibits a purely relaxational behaviour.
A group property for the coherent state representation of fermionic squeezing operators
Fan, Hong-yi; Li, Chao
2004-06-01
For the two-mode fermionic squeezing operators we find that their coherent state projection operator representation make up a loyal representation, which is homomorphic to an SO(4) group, though the fermionic coherent states are not mutual orthogonal. Thus the result of successively operating with many fermionic squeezing operators on a state can be equivalent to a single operation. The fermionic squeezing operators are mappings of orthogonal transformations in Grassmann number pseudo-classical space in the fermionic coherent state representation.
A group property for the coherent state representation of fermionic squeezing operators
Fan Hongyi; Li Chao
2004-01-01
For the two-mode fermionic squeezing operators we find that their coherent state projection operator representation make up a loyal representation, which is homomorphic to an SO(4) group, though the fermionic coherent states are not mutual orthogonal. Thus the result of successively operating with many fermionic squeezing operators on a state can be equivalent to a single operation. The fermionic squeezing operators are mappings of orthogonal transformations in Grassmann number pseudo-classical space in the fermionic coherent state representation
Diffusion in higher dimensional SYK model with complex fermions
Cai, Wenhe; Ge, Xian-Hui; Yang, Guo-Hong
2018-01-01
We construct a new higher dimensional SYK model with complex fermions on bipartite lattices. As an extension of the original zero-dimensional SYK model, we focus on the one-dimension case, and similar Hamiltonian can be obtained in higher dimensions. This model has a conserved U(1) fermion number Q and a conjugate chemical potential μ. We evaluate the thermal and charge diffusion constants via large q expansion at low temperature limit. The results show that the diffusivity depends on the ratio of free Majorana fermions to Majorana fermions with SYK interactions. The transport properties and the butterfly velocity are accordingly calculated at low temperature. The specific heat and the thermal conductivity are proportional to the temperature. The electrical resistivity also has a linear temperature dependence term.
Wigner functions for fermions in strong magnetic fields
Sheng, Xin-li; Rischke, Dirk H.; Vasak, David; Wang, Qun
2018-02-01
We compute the covariant Wigner function for spin-(1/2) fermions in an arbitrarily strong magnetic field by exactly solving the Dirac equation at non-zero fermion-number and chiral-charge densities. The Landau energy levels as well as a set of orthonormal eigenfunctions are found as solutions of the Dirac equation. With these orthonormal eigenfunctions we construct the fermion field operators and the corresponding Wigner-function operator. The Wigner function is obtained by taking the ensemble average of the Wigner-function operator in global thermodynamical equilibrium, i.e., at constant temperature T and non-zero fermion-number and chiral-charge chemical potentials μ and μ_5, respectively. Extracting the vector and axial-vector components of the Wigner function, we reproduce the currents of the chiral magnetic and separation effect in an arbitrarily strong magnetic field.
Strongly-interacting mirror fermions at the LHC
Triantaphyllou George
2017-01-01
Full Text Available The introduction of mirror fermions corresponding to an interchange of leftwith right-handed fermion quantum numbers of the Standard Model can lead to a model according to which the BEH mechanism is just an effective manifestation of a more fundamental theory while the recently-discovered Higgs-like particle is composite. This is achieved by a non-abelian gauge symmetry encompassing three mirror-fermion families strongly coupled at energies near 1 TeV. The corresponding non-perturbative dynamics lead to dynamical mirror-fermion masses between 0.14 - 1.2 TeV. Furthermore, one expects the formation of composite states, i.e. “mirror mesons”, with masses between 0.1 and 3 TeV. The number and properties of the resulting new degrees of freedom lead to a rich and interesting phenomenology, part of which is analyzed in the present work.
Projective flatness in the quantisation of bosons and fermions
Wu, Siye
2015-07-01
We compare the quantisation of linear systems of bosons and fermions. We recall the appearance of projectively flat connection and results on parallel transport in the quantisation of bosons. We then discuss pre-quantisation and quantisation of fermions using the calculus of fermionic variables. We define a natural connection on the bundle of Hilbert spaces and show that it is projectively flat. This identifies, up to a phase, equivalent spinor representations constructed by various polarisations. We introduce the concept of metaplectic correction for fermions and show that the bundle of corrected Hilbert spaces is naturally flat. We then show that the parallel transport in the bundle of Hilbert spaces along a geodesic is a rescaled projection provided that the geodesic lies within the complement of a cut locus. Finally, we study the bundle of Hilbert spaces when there is a symmetry.
Ambiguities and symmetry relations associated with fermionic tensor densities
Dallabona, G.; Battistel, O. A.
2004-01-01
We consider the consistent evaluation of perturbative (divergent) Green functions associated with fermionic tensor densities and the derivation of symmetry relations for them. We show that, in spite of current algebra methods being not applicable, it is possible to derive symmetry properties analogous to the Ward identities of vector and axial-vector densities. The proposed method, which is applicable to any previously chosen order of perturbative calculation, gives the same results as those of current algebra when such a tool is applicable. By using a very general calculational strategy, concerning the manipulations and calculations involving divergent Feynman integrals, we evaluate the purely fermionic two-point functions containing tensor vertices and derive their symmetry properties. The present investigation is the first step in the study and characterization of possible anomalies involving fermionic tensor densities, particularly in purely fermionic three-point functions
Mixed fermion-photon condensate in strongly coupled quantum electrodynamics
Gusynin, V.P.; Kushnir, V.A.
1989-01-01
The existence of a new mixed fermion-photon condensate breaking chiral symmetry in strongly coupled phase of quantum electrodynamics is shown. An analytical expression for the renormalized condensate is obtained. 20 refs.; 2 figs
Quasi-relativistic fermions and dynamical flavour oscillations
Alexandre, Jean; Mavromatos, Nick E.
2014-01-01
We introduce new Lorentz-symmetry violating kinematics for a four-fermion interaction model, where dynamical mass generation is allowed, irrespectively of the strength of the coupling. In addition, these kinematics lead to a quasi-relativistic dispersion relation, in the sense that it is relativistic in both the infrared and the ultraviolet, but not in an intermediate regime, characterized by the mass $M$. For two fermions, we show that a flavour-mixing mass matrix is generated dynamically, and the Lorentz symmetric limit $M\\to\\infty$ leads to two free relativistic fermions, with flavour oscillations. This model, valid for either Dirac or Majorana fermions, can describe any set of phenomenological values for the eigen masses and the mixing angle.
Quarks and leptons as quasi Nambu-Goldstone fermions
Buchmueller, W.; Peccei, R.D.; Yanagida, T.
1983-01-01
We discuss a new idea for constructing composite quarks and leptons which have (approximately) vanishing mass. They are associated with fermionic partners of Goldstone bosons arising from the spontaneous breakdown of an internal symmetry Gsub(f) in a supersymmetric preon theory. For Gsub(f)=SU(5) being broken to SU(3) x U(1)sub(em) there arise as quasi Goldstone fermions, naturally and unequivocally, precisely the quarks and leptons of one family. The dynamics of these quasi Goldstone fermions is explored by constructing a general supersymmetric nonlinear effective lagrangian. By means of a reduced model, we show that the first nontrivial interactions of the quasi Goldstone fermions can give rise, in an effective way, to the weak interactions. Issues connected with the incorporation of families in the scheme and the generation of masses, as well as the possible structure of the underlying preon theory are briefly discussed. (orig.)
Iterative methods for overlap and twisted mass fermions
Chiarappa, T.; Jansen, K.; Shindler, A.; Wetzorke, I.; Scorzato, L.; Urbach, C.; Wenger, U.
2006-09-01
We present a comparison of a number of iterative solvers of linear systems of equations for obtaining the fermion propagator in lattice QCD. In particular, we consider chirally invariant overlap and chirally improved Wilson (maximally) twisted mass fermions. The comparison of both formulations of lattice QCD is performed at four fixed values of the pion mass between 230 MeV and 720 MeV. For overlap fermions we address adaptive precision and low mode preconditioning while for twisted mass fermions we discuss even/odd preconditioning. Taking the best available algorithms in each case we find that calculations with the overlap operator are by a factor of 30-120 more expensive than with the twisted mass operator. (orig.)
Iterative methods for overlap and twisted mass fermions
Chiarappa, T. [Univ. di Milano Bicocca (Italy); Jansen, K.; Shindler, A.; Wetzorke, I. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Nagai, K.I. [Wuppertal Univ. (Gesamthochschule) (Germany). Fachbereich Physik; Papinutto, M. [INFN Sezione di Roma Tre, Rome (Italy); Scorzato, L. [European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT), Villazzano (Italy); Urbach, C. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences; Wenger, U. [ETH Zuerich (Switzerland). Inst. fuer Theoretische Physik
2006-09-15
We present a comparison of a number of iterative solvers of linear systems of equations for obtaining the fermion propagator in lattice QCD. In particular, we consider chirally invariant overlap and chirally improved Wilson (maximally) twisted mass fermions. The comparison of both formulations of lattice QCD is performed at four fixed values of the pion mass between 230 MeV and 720 MeV. For overlap fermions we address adaptive precision and low mode preconditioning while for twisted mass fermions we discuss even/odd preconditioning. Taking the best available algorithms in each case we find that calculations with the overlap operator are by a factor of 30-120 more expensive than with the twisted mass operator. (orig.)
The GL(1 vertical stroke 1)-symplectic fermion correspondence
Creutzig, Thomas; Roenne, Peter B.
2008-12-01
In this note we prove a correspondence between the Wess-Zumino-Novikov-Witten model of the Lie supergroup GL(1 vertical stroke 1) and a free model consisting of two scalars and a pair of symplectic fermions. This model was discussed earlier by LeClair. Vertex operators for the symplectic fermions include twist fields, and correlation functions of GL(1 vertical stroke 1) agree with the known results for the scalars and symplectic fermions. We perform a detailed study of boundary states for symplectic fermions and apply them to branes in GL(1 vertical stroke 1). This allows us to compute new amplitudes of strings stretching between branes of different types and confirming Cardy's condition. (orig.)
The GL(1 vertical stroke 1)-symplectic fermion correspondence
Creutzig, Thomas; Roenne, Peter B.
2008-12-15
In this note we prove a correspondence between the Wess-Zumino-Novikov-Witten model of the Lie supergroup GL(1 vertical stroke 1) and a free model consisting of two scalars and a pair of symplectic fermions. This model was discussed earlier by LeClair. Vertex operators for the symplectic fermions include twist fields, and correlation functions of GL(1 vertical stroke 1) agree with the known results for the scalars and symplectic fermions. We perform a detailed study of boundary states for symplectic fermions and apply them to branes in GL(1 vertical stroke 1). This allows us to compute new amplitudes of strings stretching between branes of different types and confirming Cardy's condition. (orig.)
B-Parameters of 4-Fermion Operators from Lattice QCD
Gupta, Rajan
1997-07-01
This talk summarizes the status of the calculations of B K , B 7 , B 8 , and B s , done in collaboration with T. Bhattacharya, C. Kilcup, and S. Sharpe. Results for staggered, Wilson, and Clover fermions are presented
Exotic fermions in the left-right symmetric model
Choi, J.; Volkas, R.R.
1992-01-01
A systematic study is made of non-standard fermion multiplets in left-right symmetric models with gauge group SU(3) x SU(2) L x SU(2) R x U(1) BL . Constraints from gauge anomaly cancellation and invariance of Yukawa coupling terms are used to define interesting classes of exotic fermions. The standard quark lepton spectrum of left-right symmetric models was identified as the simplest member of an infinite class. Phenomenological implications of the next simplest member of this class are then studied. Classes of exotic fermions which may couple to the standard fermions through doublet Higgs bosons were also considered, then shown that some of these exotics may be used to induce a generalised universal see-saw mechanism. 12 refs., 1 tab
Production and decay of exotic fermions in high energy collisions
Queiroz Filho, Pedro Pacheco de
1995-05-01
In this work, we investigate the production and decay of exotic fermions predicted by some extensions of the standard model. We select for our study the more popular models: vector singlet, vector doublet and Fermion Mirror-Fermion. We want to establish the differences between these models and also in relation to the Standard Model. We make investigations by Monte Carlo simulations, to study the phenomenology of the particles expected in these models, particularly the exotic fermions. These studies were done for electron-proton collisions at DESY HERA energies. We considered the investigation of exotic quark production, electron-positron collisions in LEP II and NLC energies in order to study the production of exotic leptons, and virtual exotic lepton contribution in the specific process e + e - → ιν-bar ι W + . (author)
Confinement in (1+1) dimensions and fermions
Boya, L.J.; Gomez, C.
1979-01-01
The sign ambiguity in fermions in (1+1) dimensions leads to half-integer gauge transformations and to non-zero vacuum expectation values of the physical fermi field which strongly suggest confinement. (Auth.)
Grassmann phase space methods for fermions. II. Field theory
Dalton, B.J., E-mail: bdalton@swin.edu.au [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122 (Australia); Jeffers, J. [Department of Physics, University of Strathclyde, Glasgow G4ONG (United Kingdom); Barnett, S.M. [School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ (United Kingdom)
2017-02-15
In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.
End States, Ladder Compounds, and Domain-Wall Fermions
Creutz, M.
1999-01-01
A magnetic field applied to a cross-linked ladder compound can generate isolated electronic states bound to the ends of the chain. After exploring the interference phenomena responsible, I discuss a connection to the domain-wall approach to chiral fermions in lattice gauge theory. The robust nature of the states under small variations of the bond strengths is tied to chiral symmetry and the multiplicative renormalization of fermion masses. copyright 1999 The American Physical Society
A gauge field theory of fermionic continuous-spin particles
Bekaert, X., E-mail: xavier.bekaert@lmpt.univ-tours.fr [Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 7350 du CNRS, Fédération de Recherche 2964 Denis Poisson, Université François Rabelais, Parc de Grandmont, 37200 Tours (France); B.W. Lee Center for Fields, Gravity and Strings, Institute for Basic Science, Daejeon (Korea, Republic of); Najafizadeh, M., E-mail: mnajafizadeh@gmail.com [Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 7350 du CNRS, Fédération de Recherche 2964 Denis Poisson, Université François Rabelais, Parc de Grandmont, 37200 Tours (France); Department of Physics, Faculty of Sciences, University of Kurdistan, 66177-15177 Sanandaj (Iran, Islamic Republic of); Setare, M.R., E-mail: rezakord@ipm.ir [Department of Physics, Faculty of Sciences, University of Kurdistan, 66177-15177 Sanandaj (Iran, Islamic Republic of)
2016-09-10
In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang–Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.
A gauge field theory of fermionic continuous-spin particles
Bekaert, X.; Najafizadeh, M.; Setare, M.R.
2016-01-01
In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang–Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.
The derivative expansion of the fermion number current
D'Hoker, E.; Goldstone, J.
1985-01-01
The fermion number current is evaluated to leading order in the derivative expansion for chiral fermions in the background of arbitrary Higgs and chiral gauge fields. This current is given by the gauged topological current plus a total divergence term. The total divergence term is absent in Weinberg-Salam theory with one scalar Higgs doublet, even for an arbitrary mass matrix, but appears when several Higgs doublets are present. (orig.)
Hierarchy in fermion masses and the phantom axion
Nanopoulos, D.V.
1981-01-01
An SU(5) model is presented with hierarchical fermion masses without strong CP violation and with an almost unobservable axion. The key point is to ''tie'' the highly desirable U(1)sub(P-Q) symmetry to the symmetry needed for the fermion mass hierarchy. Since the symmetry is broken at super-high energies (10 15 GeV), the axion becomes super-difficult to detect. This is the Phantom Axion. (author)
Dirac and Weyl fermion dynamics on two-dimensional surface
Kavalov, A.R.; Sedrakyan, A.G.; Kostov, I.K.
1986-01-01
Fermions on 2-dimensional surface, embedded into a 3-dimensional space are investigated. The determinant of induced Dirac operator for the Dirac and Weyl fermions is calculated. The reparametrization-invariant effective action is determined by conformal anomaly (giving Liouville action) and also by Lorentz anomaly leading to Wess-Zumino term, the structure of which at d=3 is determined by the Hopf topological invariant of the S 3 → S 2 map
Itinerant quantum multicriticality of two-dimensional Dirac fermions
Roy, Bitan; Goswami, Pallab; Juričić, Vladimir
2018-05-01
We analyze emergent quantum multicriticality for strongly interacting, massless Dirac fermions in two spatial dimensions (d =2 ) within the framework of Gross-Neveu-Yukawa models, by considering the competing order parameters that give rise to fully gapped (insulating or superconducting) ground states. We focus only on those competing orders which can be rotated into each other by generators of an exact or emergent chiral symmetry of massless Dirac fermions, and break O(S1) and O(S2) symmetries in the ordered phase. Performing a renormalization-group analysis by using the ɛ =(3 -d ) expansion scheme, we show that all the coupling constants in the critical hyperplane flow toward a new attractive fixed point, supporting an enlarged O(S1+S2) chiral symmetry. Such a fixed point acts as an exotic quantum multicritical point (MCP), governing the continuous semimetal-insulator as well as insulator-insulator (for example, antiferromagnet to valence bond solid) quantum phase transitions. In comparison with the lower symmetric semimetal-insulator quantum critical points, possessing either O(S1) or O(S2) chiral symmetry, the MCP displays enhanced correlation length exponents, and anomalous scaling dimensions for both fermionic and bosonic fields. We discuss the scaling properties of the ratio of bosonic and fermionic masses, and the increased dc resistivity at the MCP. By computing the scaling dimensions of different local fermion bilinears in the particle-hole channel, we establish that most of the four fermion operators or generalized density-density correlation functions display faster power-law decays at the MCP compared to the free fermion and lower symmetric itinerant quantum critical points. Possible generalization of this scenario to higher-dimensional Dirac fermions is also outlined.
Fermion Bag Approach to Lattice Hamiltonian Field Theories
Huffman, Emilie
2018-03-01
Using a model in the Gross-Neveu Ising universality class, we show how the fermion bag idea can be applied to develop algorithms to Hamiltonian lattice field theories. We argue that fermion world lines suggest an alternative method to the traditional techniques for calculating ratios of determinants in a stable manner. We show the power behind these ideas by extracting the physics of the model on large lattices.
Grassmann phase space methods for fermions. II. Field theory
Dalton, B.J.; Jeffers, J.; Barnett, S.M.
2017-01-01
In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.
A study of block algorithms for fermion matrix inversion
Henty, D.
1990-01-01
We compare the convergence properties of Lanczos and Conjugate Gradient algorithms applied to the calculation of columns of the inverse fermion matrix for Kogut-Susskind and Wilson fermions in lattice QCD. When several columns of the inverse are required simultaneously, a block version of the Lanczos algorithm is most efficient at small mass, being over 5 times faster than the single algorithms. The block algorithm is also less susceptible to critical slowing down. (orig.)
The Dirac-Kaehler equation and fermions on the lattice
Becher, P.
1982-05-01
The geometrical description of spinor fields by E. Kaehler is used to formulate a consistent lattice approximation of fermions. The relation to free simple Dirac fields as well as to Susskind's description of lattice fermions is clarified. The first steps towards a quantized interacting theory are given. The correspondence between the calculus of differential forms and concepts of algebraic topology is shown to be a useful method for a completely analogous treatment of the problems in the continuum and on the lattice. (orig.)
Fermion interactions with a Kaluza-Klein dyon
Xi, Z.M.
1986-04-01
The fermion dynamics in the background of a five-dimensional Kaluza-Klein dyon is studied. It is found that the hamiltonian is self-adjoint despite the singular nature of the origin, and the fermion scattering on the dyon in the lowest angular momentum j = 0 channel is a helicity flip process. The possibility for charge-exchange process in the non-Abelian Kaluza-Klein theories is discussed
Standard model fermion hierarchies with multiple Higgs doublets
Solaguren-Beascoa Negre, Ana
2016-01-01
The hierarchies between the Standard Model (SM) fermion masses and mixing angles and the origin of neutrino masses are two of the biggest mysteries in particle physics. We extend the SM with new Higgs doublets to solve these issues. The lightest fermion masses and the mixing angles are generated through radiative effects, correctly reproducing the hierarchy pattern. Neutrino masses are generated in the see-saw mechanism.
SO(10) - Grand unification and fermion masses
Oezer, A.D.
2005-01-01
In this work, we study SO(10) grand unification in its full extent by using different explicit matrix representations which exhibit the structure of SO(10) in a very transparent way. Our approach consists mainly of two stages: We derive the explicit expressions of the mass-eigenvalues and mass-eigenstates of the physical gauge bosons from a mass squared-matrix that contains all the information about the mixing parameters among the gauge fields and the phases which are sources for CP violation. In the light of this analysis, we derive the explicit expressions for the interaction Lagrangians of the charged currents, the neutral currents and the charged and colored currents in SO(10). We present explicit expressions of the vector and axial-vector couplings of the two neutral currents in SO(10). We show how the baryon, lepton and baryon minus lepton number violating processes and their explicit CP violating phases are accommodated in the SO(10) theory. The Higgs potential that we use to implement in the Higgs mechanism is constructed in a most general fashion through a careful study of the Higgs fields of SO(10), where we give special emphasis on illustrating the explicit matrix representation of these Higgs fields. The potential part of the Higgs Lagrangian will give us the properties of the minimum of the vacuum, and the kinetic part will give us the mass-squared matrix of the gauge bosons via spontaneous symmetry breakdown. The same Higgs multiplets will be coupled to fermions through a democratic Yukawa matrix. Thereby, we derive explicit expressions for the fermion masses of the third family including Majorana and Dirac masses for neutrinos. We introduce a flavor-eigenbasis for neutrinos and find the mass-eigenstates and mass-eigenvalues of the neutrinos. Explicit expressions for CP violation in the neutrino sector are obtained. In the second stage of our work, we evaluate all the above mentioned quantities. In addition, we present the values of the physical
Transport through interacting quantum dots with Majorana fermions or phonons
Huetzen, Roland
2013-01-01
Recent advances in the search for Majorana fermions within condensed matter systems inspired the first part of the thesis. These hypothetical particles which are their own antiparticles are predicted to arise in the form of quasi-particle excitations called Majorana bound states at the surface of engineered condensed matter systems. An experimental detection is challenging since their defining property also implies that they possess no charge, no energy and no spin. This significantly reduces the possibilities to interact with them and get a proof of their existence from a measurement. The most promising experimental results are based on transport measurements where current-voltage-characteristics play the role of a spectroscopy signal. In this thesis, we investigate a single electron transistor setup which hosts a spatially separated pair of Majorana fermions with respect to their influence on its transport characteristics. We focus on a master equation approach including sequential and cotunneling contributions. After deducing all relevant rates we solve the system numerically over a broad parameter regime. For some limits, we also elaborate analytical solutions. In comparison with collaboratively worked out other methods we provide a broad understanding of the setup and make a proposal how our results could be used as a detection scheme for Majorana fermions. The second part of the thesis investigates the spinless Anderson-Holstein model which is the minimal model for molecular transport. It models a molecule with electronic and vibronic degrees of freedom which is placed between metallic leads at different chemical potentials to investigate again its transport properties. Also here we intended to gain access to a broad parameter regime and successfully extended the numerical ''iterative summation of path-integrals'' scheme to this model. It is based on a real-time path-integral approach in combination with the nonequilibrium Keldysh
Transport through interacting quantum dots with Majorana fermions or phonons
Huetzen, Roland
2013-07-04
Recent advances in the search for Majorana fermions within condensed matter systems inspired the first part of the thesis. These hypothetical particles which are their own antiparticles are predicted to arise in the form of quasi-particle excitations called Majorana bound states at the surface of engineered condensed matter systems. An experimental detection is challenging since their defining property also implies that they possess no charge, no energy and no spin. This significantly reduces the possibilities to interact with them and get a proof of their existence from a measurement. The most promising experimental results are based on transport measurements where current-voltage-characteristics play the role of a spectroscopy signal. In this thesis, we investigate a single electron transistor setup which hosts a spatially separated pair of Majorana fermions with respect to their influence on its transport characteristics. We focus on a master equation approach including sequential and cotunneling contributions. After deducing all relevant rates we solve the system numerically over a broad parameter regime. For some limits, we also elaborate analytical solutions. In comparison with collaboratively worked out other methods we provide a broad understanding of the setup and make a proposal how our results could be used as a detection scheme for Majorana fermions. The second part of the thesis investigates the spinless Anderson-Holstein model which is the minimal model for molecular transport. It models a molecule with electronic and vibronic degrees of freedom which is placed between metallic leads at different chemical potentials to investigate again its transport properties. Also here we intended to gain access to a broad parameter regime and successfully extended the numerical ''iterative summation of path-integrals'' scheme to this model. It is based on a real-time path-integral approach in combination with the nonequilibrium Keldysh
Improved continuum limit lattice action for QCD with Wilson fermions
Sheikholeslami, B.; Wohlert, R.
1985-03-01
Two possible ways of extending Symanzik's improvement programme to lattice fermions namely improvement to first and second order in the lattice spacing 'a' are discussed. The corresponding lattice actions for fermions are constructed and tree level improvement conditions are derived by considering classical improvement. The concept of on shell improvement is generalized to the lattice fermions studied here and the free parameters are determined for O(a) and O(a 2 ) on shell improved actions to all orders of perturbation theory. No evidence is found that the complicated structure of the O(a 2 ) on shell improved action especially the arising fermion contact terms can be removed beyond tree level. The effect of terms in the action that explicitly break chiral symmetry and therefore remove the phenomenon of species doubling are investigated by considering the energy momentum relations of the arising tree level improved actions. Our main result is that the O(a) improved action is a slightly modified Wilson fermion action which can still be written with only nearest neighbour fermion interactions. (orig.)
Zero Modes and Global Antiferromagnetism in Strained Graphene
Bitan Roy
2014-05-01
Full Text Available A novel magnetic ground state is reported for the Hubbard Hamiltonian in strained graphene. When the chemical potential lies close to the Dirac point, the ground state exhibits locally both the Néel and ferromagnetic orders, even for weak Hubbard interaction. Whereas the Néel order parameter remains of the same sign in the entire system, the magnetization at the boundary takes the opposite sign from the bulk. The total magnetization vanishes this way, and the magnetic ground state is globally only an antiferromagnet. This peculiar ordering stems from the nature of the strain-induced single-particle zero-energy states, which have support on one sublattice of the honeycomb lattice in the bulk, and on the other sublattice near the boundary of a finite system. We support our claim with the self-consistent numerical calculation of the order parameters, as well as by the Monte Carlo simulations of the Hubbard model in both uniformly and nonuniformly strained honeycomb lattice. The present result is contrasted with the magnetic ground state of the same Hubbard model in the presence of a true magnetic field (and for vanishing Zeeman coupling, which is exclusively Néel ordered, with zero local magnetization everywhere in the system.
Field space entanglement entropy, zero modes and Lifshitz models
Huffel, Helmuth; Kelnhofer, Gerald
2017-12-01
The field space entanglement entropy of a quantum field theory is obtained by integrating out a subset of its fields. We study an interacting quantum field theory consisting of massless scalar fields on a closed compact manifold M. To this model we associate its Lifshitz dual model. The ground states of both models are invariant under constant shifts. We interpret this invariance as gauge symmetry and subject the models to proper gauge fixing. By applying the heat kernel regularization one can show that the field space entanglement entropies of the massless scalar field model and of its Lifshitz dual are agreeing.
Field space entanglement entropy, zero modes and Lifshitz models
Helmuth Huffel
2017-12-01
Full Text Available The field space entanglement entropy of a quantum field theory is obtained by integrating out a subset of its fields. We study an interacting quantum field theory consisting of massless scalar fields on a closed compact manifold M. To this model we associate its Lifshitz dual model. The ground states of both models are invariant under constant shifts. We interpret this invariance as gauge symmetry and subject the models to proper gauge fixing. By applying the heat kernel regularization one can show that the field space entanglement entropies of the massless scalar field model and of its Lifshitz dual are agreeing.
Monopole-fermion and dyon-fermion bound states. Pt. 4
Osland, P.; Harvard Univ., Cambridge, MA; Tai Tsun Wu
1985-01-01
In the first part of the paper, we give analytic, approximate results for dyon-fermion binding energies and wave functions, valid for large values of A = 1/2 Zvertical strokeegvertical strokeK, where K is the magnetic moment. In the second part, more general results are obtained for the same problem that are valid when either A is large or the binding is weak. Numerical results for the binding energy are tabulated and compared. The case of very strong binding is also discussed. (orig.)
Monopole-fermion and dyon-fermion bound states. Pt. 5
Osland, P.; Harvard Univ., Cambridge, MA; Schultz, C.L.; Wu, T.T.
1985-02-01
We present explicit, approximate, remarkably precise results for the Kazama-Yang hamiltonian, which describes a Dirac monopole interacting with a spin-1/2 fermion that has an extra magnetic moment. The results are valid for bound states of angular momentum j >= Zvertical strokeegvertical stroke+1/2, where the radial wave functions are determined by four coupled differential equations. These equations have been solved analytically for M - E << M, which is a limit of considerable practical interest. Binding energies and wave functions are given. (orig.)
Spin-dependent level density in interacting Boson-Fermion-Fermion model of the Odd-Odd Nucleus 196Au
Kabashi, S.; Bekteshi, S.; Ahmetaj, S.; Shaqiri, Z.
2009-01-01
The level density of the odd-odd nucleus 196 Au is investigated in the interacting boson-fermion-fermion model (IBFFM) which accounts for collectivity and complex interaction between quasiparticle and collective modes.The IBFFM spin-dependent level densities show high-spin reduction with respect to Bethe formula.This can be well accounted for by a modified spin-dependent level density formula. (authors)
Fermion bound states in the Kerr-Newman field with magnetic charge
Gal'tsov, D.V.; Ershov, A.A.
1987-01-01
Approximate solutions of Dirac equations for 1/2 spin charged particles in the Kerr-Newman field are constructed. An equation for quasistationary states energy, taking account of their possible decay due to tunnelling in the black hole, is obtained. A problem of existence of zero modes is discussed
The PHMC algorithm for simulations of dynamical fermions; 1, description and properties
Frezzotti, R
1999-01-01
We give a detailed description of the so-called Polynomial Hybrid Monte Carlo (PHMC) algorithm. The effects of the correction factor, which is introduced to render the algorithm exact, are discussed, stressing their relevance for the statistical fluctuations and (almost) zero mode contributions to physical observables. We also investigate rounding-error effects and propose several ways to reduce memory requirements.
Precision calculations for γγ → 4 fermions and H → WW/ZZ → 4 fermions
Bredenstein, A.
2006-02-01
In this work we provide precision calculations for the processes γγ → 4 fermions and H → WW/ZZ → 4 fermions. At a γγ collider precise theoretical predictions are needed for the γγ → WW → 4f processes because of their large cross section. These processes allow a measurement of the gauge-boson couplings γWW and γγWW. Furthermore, the reaction γγ → H → WW/ZZ → 4f arises through loops of virtual charged, massive particles. Thus, the coupling γγH can be measured and Higgs bosons with a relatively large mass could be produced. For masses M H >or #sim# 135 GeV the Higgs boson predominantly decays into W- or Z-boson pairs and subsequently into four leptons. The kinematical reconstruction of these decays is influenced by quantum corrections, especially real photon radiation. Since off-shell effects of the gauge bosons have to be taken into account below M H ∼ 2M W/Z , the inclusion of the decays of the gauge bosons is important. In addition, the spin and the CP properties of the Higgs boson can be determined by considering angular and energy distributions of the decay fermions. For a comparison of theoretical predictions with experimental data Monte Carlo generators are useful tools. We construct such programs for the processes γγ → WW → 4f and H → WW/ZZ → 4f. On the one hand, they provide the complete predictions at lowest order of perturbation theory. On the other hand, they contain quantum corrections, which ca be classified into real corrections, connected with photons bremsstrahlung, and virtual corrections. Whereas the virtual quantum corrections to γγ → WW → 4f are calculated in the double-pole approximation, i.e. only doubly-resonant contributions are taken into account, we calculate the complete O(α) corrections for the H → WW/ZZ → 4f processes. The infrared (soft and collinear) divergences in the virtual and real corrections are treated either with the dipole-subtraction method or with the phase-space slicing
Conduction properties of strongly interacting Fermions
Brantut, Jean-Philippe; Stadler, David; Krinner, Sebastian; Meineke, Jakob; Esslinger, Tilman
2013-05-01
We experimentally study the transport process of ultracold fermionic atoms through a mesoscopic, quasi two-dimensional channel connecting macroscopic reservoirs. By observing the current response to a bias applied between the reservoirs, we directly access the resistance of the channel in a manner analogous to a solid state conduction measurement. The resistance is further controlled by a gate potential reducing the atomic density in the channel, like in a field effect transistor. In this setup, we study the flow of a strongly interacting Fermi gas, and observe a striking drop of resistance with increasing density in the channel, as expected at the onset of superfluidity. We relate the transport properties to the in-situ evolution of the thermodynamic potential, providing a model independant thermodynamic scale. The resistance is compared to that of an ideal Fermi gas in the same geometry, which shows an order of magnitude larger resistance, originating from the contact resistance between the channel and the reservoirs. The extension of this study to a channel containing a tunable disorder is briefly outlined.
Algorithms for Monte Carlo calculations with fermions
Weingarten, D.
1985-01-01
We describe a fermion Monte Carlo algorithm due to Petcher and the present author and another due to Fucito, Marinari, Parisi and Rebbi. For the first algorithm we estimate the number of arithmetic operations required to evaluate a vacuum expectation value grows as N 11 /msub(q) on an N 4 lattice with fixed periodicity in physical units and renormalized quark mass msub(q). For the second algorithm the rate of growth is estimated to be N 8 /msub(q) 2 . Numerical experiments are presented comparing the two algorithms on a lattice of size 2 4 . With a hopping constant K of 0.15 and β of 4.0 we find the number of operations for the second algorithm is about 2.7 times larger than for the first and about 13 000 times larger than for corresponding Monte Carlo calculations with a pure gauge theory. An estimate is given for the number of operations required for more realistic calculations by each algorithm on a larger lattice. (orig.)
Free fermion resolution of supergroup WZNW models
Quella, T.; Schomerus, V.
2007-06-15
Extending our earlier work on PSL(2 vertical stroke 2), we explain how to reduce the solution of WZNW models on general type I supergroups to those defined on the bosonic subgroup. The new analysis covers in particular the supergroups GL(M vertical stroke N) along with several close relatives such as PSL(N vertical stroke N), certain Poincar'e supergroups and the series OSP(2 vertical stroke 2N). This remarkable progress relies on the use of a special Feigin-Fuchs type representation. In preparation for the field theory analysis, we shall exploit a minisuperspace analogue of a free fermion construction to deduce the spectrum of the Laplacian on type I supergroups. The latter is shown to be non-diagonalizable. After lifting these results to the full WZNW model, we address various issues of the field theory, including its modular invariance and the computation of correlation functions. In agreement with previous findings, supergroup WZNW models allow to study chiral and non-chiral aspects of logarithmic conformal field theory within a geometric framework. We shall briefly indicate how insights from WZNW models carry over to non-geometric examples, such as e.g. the W(p) triplet models.
Fermionic greybody factors in dilaton black holes
Abedi, Jahed; Arfaei, Hessamaddin
2014-01-01
In this paper the question of the emission of fermions in the process of dilaton black hole evolution and its characteristics for different dilaton coupling constants α are studied. The main quantity of interest, the greybody factors, are calculated both numerically and in analytical approximation. The dependence of the rates of evaporation and behaviour on the dilaton coupling constant is analysed. Having calculated the greybody factors, we are able to address the question of the final fate of the dilaton black hole. For that we also need to perform dynamical treatment of the solution by considering the backreaction, which will show a crucial effect on the final result. We find a transition line in the (Q/M,α) plane that separates the two regimes for the fate of the black hole, decay regime and extremal regime. In the decay regime the black hole completely evaporates, while in the extremal regime the black hole approaches the extremal limit by radiation and becomes stable. (paper)
On heterotic vacua with fermionic expectation values
Minasian, Ruben [Institut de Physique Theorique, Universite Paris Saclay, CEA, CNRS, Gif-sur-Yvette (France); Petrini, Michela [Sorbonne Universites, CNRS, LPTHE, UPMC Paris 06, UMR 7589, Paris (France); Svanes, Eirik Eik [Sorbonne Universites, CNRS, LPTHE, UPMC Paris 06, UMR 7589, Paris (France); Sorbonne Universites, Institut Lagrange de Paris, Paris (France)
2017-03-15
We study heterotic backgrounds with non-trivial H-flux and non-vanishing expectation values of fermionic bilinears, often referred to as gaugino condensates. The gaugini appear in the low energy action via the gauge-invariant three-form bilinear Σ{sub MNP} = tr anti χΓ{sub MNP}χ. For Calabi-Yau compactifications to four dimensions, the gaugino condensate corresponds to an internal three-form Σ{sub mnp} that must be a singlet of the holonomy group. This condition does not hold anymore when an internal H-flux is turned on and O(α{sup '}) effects are included. In this paper we study flux compactifications to three and four-dimensions on G-structure manifolds. We derive the generic conditions for supersymmetric solutions. We use integrability conditions and Lichnerowicz type arguments to derive a set of constraints whose solution, together with supersymmetry, is sufficient for finding backgrounds with gaugino condensate. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Langevin simulations of QCD, including fermions
Kronfeld, A.S.
1986-02-01
We encounter critical slow down in updating when xi/a -> infinite and in matrix inversion (needed to include fermions) when msub(q)a -> 0. A simulation that purports to solve QCD numerically will encounter these limits, so to face the challenge in the title of this workshop, we must cure the disease of critical slow down. Physically, this critical slow down is due to the reluctance of changes at short distances to propagate to large distances. Numerically, the stability of an algorithm at short wavelengths requires a (moderately) small step size; critical slow down occurs when the effective long wavelength step size becomes tiny. The remedy for this disease is an algorithm that propagates signals quickly throughout the system; i.e. one whose effective step size is not reduced for the long wavelength conponents of the fields. (Here the effective ''step size'' is essentially an inverse decorrelation time.) To do so one must resolve various wavelengths of the system and modify the dynamics (in CPU time) of the simulation so that all modes evolve at roughly the same rate. This can be achieved by introducing Fourier transforms. I show how to implement Fourier acceleration for Langevin updating and for conjugate gradient matrix inversion. The crucial feature of these algorithms that lends them to Fourier acceleration is that they update the lattice globally; hence the Fourier transforms are computed once per sweep rather than once per hit. (orig./HSI)
Veselago focusing of anisotropic massless Dirac fermions
Zhang, Shu-Hui; Yang, Wen; Peeters, F. M.
2018-05-01
Massless Dirac fermions (MDFs) emerge as quasiparticles in various novel materials such as graphene and topological insulators, and they exhibit several intriguing properties, of which Veselago focusing is an outstanding example with a lot of possible applications. However, up to now Veselago focusing merely occurred in p-n junction devices based on the isotropic MDF, which lacks the tunability needed for realistic applications. Here, motivated by the emergence of novel Dirac materials, we investigate the propagation behaviors of anisotropic MDFs in such a p-n junction structure. By projecting the Hamiltonian of the anisotropic MDF to that of the isotropic MDF and deriving an exact analytical expression for the propagator, precise Veselago focusing is demonstrated without the need for mirror symmetry of the electron source and its focusing image. We show a tunable focusing position that can be used in a device to probe masked atom-scale defects. This study provides an innovative concept to realize Veselago focusing relevant for potential applications, and it paves the way for the design of novel electron optics devices by exploiting the anisotropic MDF.
Electron scattering by trapped fermionic atoms
Wang Haijun; Jhe, Wonho
2002-01-01
Considering the Fermi gases of alkali-metal atoms that are trapped in a harmonic potential, we study theoretically the elastic and inelastic scattering of the electrons by the trapped Fermi atoms and present the corresponding differential cross sections. We also obtain the stopping power for the cases that the electronic state as well as the center-of-mass state are excited both separately and simultaneously. It is shown that the elastic scattering process is no longer coherent in contrast to the electron scattering by the atomic Bose-Einstein condensate (BEC). For the inelastic scattering process, on the other hand, the differential cross section is found to be proportional to the 2/3 power of the number of the trapped atoms. In particular, the trapped fermionic atoms display the effect of ''Fermi surface,'' that is, only the energy levels near the Fermi energy have dominant contributions to the scattering process. Moreover, it is found that the stopping power scales as the 7/6 power of the atomic number. These results are fundamentally different from those of the electron scattering by the atomic BEC, mainly due to the different statistics obeyed by the trapped atomic systems
Decaying fermionic dark matter search with CALET
Bhattacharyya, S.; Torii, S. [Graduate School of Advanced Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku, Tokyo, 169-8555 (Japan); Motz, H. [International Center for Science and Engineering Programs, Waseda University, 3-4-1, Okubo, Shinjuku, Tokyo, 169-8555 (Japan); Asaoka, Y., E-mail: saptashwab@ruri.waseda.jp, E-mail: motz@aoni.waseda.jp, E-mail: torii.shoji@waseda.jp, E-mail: yoichi.asaoka@aoni.waseda.jp [Research Institute for Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku, Tokyo, 169-8555 (Japan)
2017-08-01
The ISS-based CALET (CALorimetric Electron Telescope) detector can play an important role in indirect search for Dark Matter (DM), measuring the electron+positron flux in the TeV region for the first time directly. With its fine energy resolution of approximately 2% and good proton rejection ratio (1:10{sup 5}) it has the potential to search for fine structures in the Cosmic Ray (CR) electron spectrum. In this context we discuss the ability of CALET to discern between signals originating from astrophysical sources and DM decay. We fit a parametrization of the local interstellar electron and positron spectra to current measurements, with either a pulsar or 3-body decay of fermionic DM as the extra source causing the positron excess. The expected CALET data for scenarios in which DM decay explains the excess are calculated and analyzed. The signal from this particular 3-body DM decay which can explain the recent measurements from the AMS−02 experiment is shown to be distinguishable from a single pulsar source causing the positron excess by 5 years of observation with CALET, based on the shape of the spectrum. We also study the constraints from diffuse γ-ray data on this DM-only explanation of the positron excess and show that especially for the possibly remaining parameter space a clearly identifiable signature in the CR electron spectrum exists.
Free fermion resolution of supergroup WZNW models
Quella, T; Schomerus, V
2007-06-15
Extending our earlier work on PSL(2 vertical stroke 2), we explain how to reduce the solution of WZNW models on general type I supergroups to those defined on the bosonic subgroup. The new analysis covers in particular the supergroups GL(M vertical stroke N) along with several close relatives such as PSL(N vertical stroke N), certain Poincar'e supergroups and the series OSP(2 vertical stroke 2N). This remarkable progress relies on the use of a special Feigin-Fuchs type representation. In preparation for the field theory analysis, we shall exploit a minisuperspace analogue of a free fermion construction to deduce the spectrum of the Laplacian on type I supergroups. The latter is shown to be non-diagonalizable. After lifting these results to the full WZNW model, we address various issues of the field theory, including its modular invariance and the computation of correlation functions. In agreement with previous findings, supergroup WZNW models allow to study chiral and non-chiral aspects of logarithmic conformal field theory within a geometric framework. We shall briefly indicate how insights from WZNW models carry over to non-geometric examples, such as e.g. the W(p) triplet models.
Illuminating the chirality of Weyl fermions
Ma, Qiong; Xu, Su-Yang; Chan, Ching-Kit; Zhang, Cheng-Long; Chang, Guoqing; Lin, Hsin; Jia, Shuang; Lee, Patrick; Gedik, Nuh; Jarillo-Herrero, Pablo
In particle physics, Weyl fermions (WF) are elementary particles that travel at the speed of light and have a definite chirality. In condensed matter, it has been recently realized that WFs can arise as magnetic monopoles in the momentum space of a novel topological metal, the Weyl semimetal (WSM). Their chirality, given by the sign of the monopole charge, is the defining property of a WSM, since it directly serves as the topological number and gives rise to exotic properties such as Fermi arcs and the chiral anomaly. Moreover, the two chiralities, analogous to the two valleys in 2D materials, lead to a new degree of freedom in a 3D crystal, suggesting novel pathways to store and carry information. By shining circularly polarized light on the WSM TaAs, we illuminate the chirality of the WFs and achieve an electrical current that is highly controllable based on the WFs' chirality. Our results open up a wide range of new possibilities for experimentally studying and controlling the WFs and their associated quantum anomalies by optical and electrical means, which suggest the exciting prospect of ``Weyltronics''.
The low-temperature phase of the Heisenberg antiferromagnet in a fermionic representation
Azakov, S.; Dilaver, M.; Oztas, A.M.
1999-09-01
Thermal properties of the ordered phase of the spin 1/2 isotropic Heisenberg Antiferromagnet on a d-dimensional hypercubical lattice are studied within the fermionic representation when the constraint of a single occupancy condition is taken into account by the method suggested by Popov and Fedotov. Using a saddle point approximation in the path integral approach we discuss not only the leading order but also the fluctuations around the saddle point at one-loop level. The influence of taking into account the single occupancy condition is discussed at all steps. (author)
Dynamical twisted mass fermions and baryon spectroscopy
Drach, V.
2010-06-01
The aim of this work is an ab initio computation of the baryon masses starting from quantum chromodynamics (QCD). This theory describes the interaction between quarks and gluons and has been established at high energy thanks to one of its fundamental properties: the asymptotic freedom. This property predicts that the running coupling constant tends to zero at high energy and thus that perturbative expansions in the coupling constant are justified in this regime. On the contrary the low energy dynamics can only be understood in terms of a non perturbative approach. To date, the only known method that allows the computation of observables in this regime together with a control of its systematic effects is called lattice QCD. It consists in formulating the theory on an Euclidean space-time and to evaluating numerically suitable functional integrals. First chapter is an introduction to the QCD in the continuum and on a discrete space time. The chapter 2 describes the formalism of maximally twisted fermions used in the European Twisted Mass (ETM) collaboration. The chapter 3 deals with the techniques needed to build hadronic correlator starting from gauge configuration. We then discuss how we determine hadron masses and their statistical errors. The numerical estimation of functional integral is explained in chapter 4. It is stressed that it requires sophisticated algorithm and massive parallel computing on Blue-Gene type architecture. Gauge configuration production is an important part of the work realized during my Ph.D. Chapter 5 is a critical review on chiral perturbation theory in the baryon sector. The two last chapter are devoted to the analysis in the light and strange baryon sector. Systematics and chiral extrapolation are extensively discussed. (author)
Issues related to the Fermion mass problem
Murakowski, Janusz Adam
1998-09-01
This thesis is divided into three parts. Each illustrates a different aspect of the fermion mass issue in elementary particle physics. In the first part, the possibility of chiral symmetry breaking in the presence of uniform magnetic and electric fields is investigated. The system is studied nonperturbatively with the use of basis functions compatible with the external field configuration, the parabolic cylinder functions. It is found that chiral symmetry, broken by a uniform magnetic field, is restored by electric field. Obtained result is nonperturbative in nature: even the tiniest deviation of the electric field from zero restores chiral symmetry. In the second part, heavy quarkonium systems are investigated. To study these systems, a phenomenological nonrelativistic model is built. Approximate solutions to this model are found with the use of a specially designed Pade approximation and by direct numerical integration of Schrodinger equation. The results are compared with experimental measurements of respective meson masses. Good agreement between theoretical calculations and experimental results is found. Advantages and shortcommings of the new approximation method are analysed. In the third part, an extension of the standard model of elementary particles is studied. The extension, called the aspon model, was originally introduced to cure the so called strong CP problem. In addition to fulfilling its original purpose, the aspon model modifies the couplings of the standard model quarks to the Z boson. As a result, the decay rates of the Z boson to quarks are altered. By using the recent precise measurements of the decay rates Z → bb and Z /to [/it c/=c], new constraints on the aspon model parameters are found.
Algebraic fermion models and nuclear structure physics
Troltenier, Dirk; Blokhin, Andrey; Draayer, Jerry P.; Rompf, Dirk; Hirsch, Jorge G.
1996-01-01
Recent experimental and theoretical developments are generating renewed interest in the nuclear SU(3) shell model, and this extends to the symplectic model, with its Sp(6,R) symmetry, which is a natural multi-(ℎ/2π)ω extension of the SU(3) theory. First and foremost, an understanding of how the dynamics of a quantum rotor is embedded in the shell model has established it as the model of choice for describing strongly deformed systems. Second, the symplectic model extension of the 0-(ℎ/2π)ω theory can be used to probe additional degrees of freedom, like core polarization and vorticity modes that play a key role in providing a full description of quadrupole collectivity. Third, the discovery and understanding of pseudo-spin has allowed for an extension of the theory from light (A≤40) to heavy (A≥100) nuclei. Fourth, a user-friendly computer code for calculating reduced matrix elements of operators that couple SU(3) representations is now available. And finally, since the theory is designed to cope with deformation in a natural way, microscopic features of deformed systems can be probed; for example, the theory is now being employed to study double beta decay and thereby serves to probe the validity of the standard model of particles and their interactions. A subset of these topics will be considered in this course--examples cited include: a consideration of the origin of pseudo-spin symmetry; a SU(3)-based interpretation of the coupled-rotor model, early results of double beta decay studies; and some recent developments on the pseudo-SU(3) theory. Nothing will be said about other fermion-based theories; students are referred to reviews in the literature for reports on developments in these related areas
Superconducting gap anomaly in heavy fermion systems
Rout, G.C.; Ojha, M.S.; Behera, S.N.
2008-01-01
The heavy fermion system (HFS) is described by the periodic Anderson model (PAM), treating the Coulomb correlation between the f-electrons in the mean-field Hartree-Fock approximation. Superconductivity is introduced by a BCS-type pairing term among the conduction electrons. Within this approximation the equation for the superconducting gap is derived, which depends on the effective position of the energy level of the f-electrons relative to the Fermi level. The latter in turn depends on the occupation probability n f of the f-electrons. The gap equation is solved self-consistently with the equation for n f ; and their temperature dependences are studied for different positions of the bare f-electron energy level, with respect to the Fermi level. The dependence of the superconducting gap on the hybridization leads to a re-entrant behaviour with increasing strength. The induced pairing between the f-electrons and the pairing of mixed conduction and f-electrons due to hybridization are also determined. The temperature dependence of the hybridization parameter, which characterizes the number of electrons with mixed character and represents the number of heavy electrons is studied. This number is shown to be small. The quasi-particle density of states (DOS) shows the existence of a pseudo-gap due to superconductivity and the signature of a hybridization gap at the Fermi level. For the choice of the model parameters, the DOS shows that the HFS is a metal and undergoes a transition to the gap-less superconducting state. (author)
Three-dimensional Majorana fermions in chiral superconductors.
Kozii, Vladyslav; Venderbos, Jörn W F; Fu, Liang
2016-12-01
Using a systematic symmetry and topology analysis, we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-nondegenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum J formed by Bloch electrons with angular momentum j in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the nonunitary nature of chiral pairing in spin-orbit-coupled superconductors. We address experimental signatures of Majorana fermions and find that the nuclear magnetic resonance spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface, which form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs 4 Sb 12 and related materials as promising candidates for nonunitary chiral superconductors hosting three-dimensional Majorana fermions.
Majorana and Majorana-Weyl fermions in lattice gauge theory
Inagaki, Teruaki; Suzuki, Hiroshi
2004-01-01
In various dimensional Euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In 8n and 1 + 8n dimensions, we find a difficulty to decompose a classical lattice action of the Dirac fermion into a system of the Majorana fermion and thus to obtain a factorized form of the Dirac determinant. Similarly, in 2 + 8n dimensions, there is a difficulty to decompose a classical lattice action of the Weyl fermion into a system of the Majorana-Weyl fermion and thus to obtain a factorized form of the Weyl determinant. Prescriptions based on the overlap formalism do not remove these difficulties. We argue that these difficulties are reflections of the global gauge anomaly associated to the real Weyl fermion in 8n dimensions. For this reason (besides other well-known reasons), a lattice formulation of the N = 1 super Yang-Mills theory in these dimensions is expected to be extremely difficult to find. (author)
Belvedere, L.V.; Souza Dutra, A. de; Natividade, C.P.; Queiroz, A.F. de
2002-01-01
Using a synthesis of the functional integral and operator approaches we discuss the fermion-boson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In QED 2 with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In anomalous chiral QED 2 with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of Θ-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content
Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion
Sannomiya, Noriaki; Katsura, Hosho; Nakayama, Yu
2017-03-01
We introduce a lattice fermion model in one spatial dimension with supersymmetry (SUSY) but without particle number conservation. The Hamiltonian is defined as the anticommutator of two nilpotent supercharges Q and Q†. Each supercharge is built solely from spinless fermion operators and depends on a parameter g . The system is strongly interacting for small g , and in the extreme limit g =0 , the number of zero-energy ground states grows exponentially with the system size. By contrast, in the large-g limit, the system is noninteracting and SUSY is broken spontaneously. We study the model for modest values of g and show that under certain conditions spontaneous SUSY breaking occurs in both finite and infinite chains. We analyze the low-energy excitations both analytically and numerically. Our analysis suggests that the Nambu-Goldstone fermions accompanying the spontaneous SUSY breaking have cubic dispersion at low energies.
Magnetotransport in Layered Dirac Fermion System Coupled with Magnetic Moments
Iwasaki, Yoshiki; Morinari, Takao
2018-03-01
We theoretically investigate the magnetotransport of Dirac fermions coupled with localized moments to understand the physical properties of the Dirac material EuMnBi2. Using an interlayer hopping form, which simplifies the complicated interaction between the layers of Dirac fermions and the layers of magnetic moments in EuMnBi2, the theory reproduces most of the features observed in this system. The hysteresis observed in EuMnBi2 can be caused by the valley splitting that is induced by the spin-orbit coupling and the external magnetic field with the molecular field created by localized moments. Our theory suggests that the magnetotransport in EuMnBi2 is due to the interplay among Dirac fermions, localized moments, and spin-orbit coupling.
Fermionic corrections to fluid dynamics from BTZ black hole
Gentile, L.G.C. [DISIT, Università del Piemonte Orientale,via T. Michel, 11, Alessandria, 15120 (Italy); Dipartimento di Fisica “Galileo Galilei”,Università di Padova, via Marzolo 8, 35131 Padova (Italy); INFN - Sezione di Padova,via Marzolo 8, 35131, Padova (Italy); Grassi, P.A. [DISIT, Università del Piemonte Orientale,via T. Michel, 11, Alessandria, 15120 (Italy); INFN - Gruppo Collegato di Alessandria, Sezione di Torino,Alessandria (Italy); PH-TH Department, CERN,CH-1211 Geneva 23 (Switzerland); Mezzalira, A. [Dipartimento di Fisica Teorica, Università di Torino,via P. Giuria, 1, Torino, 10125 (Italy); INFN - Gruppo Collegato di Alessandria, Sezione di Torino,Alessandria (Italy)
2015-11-23
We reconstruct the complete fermionic orbit of the non-extremal BTZ black hole by acting with finite supersymmetry transformations. The solution satisfies the exact supergravity equations of motion to all orders in the fermonic expansion and the final result is given in terms of fermionic bilinears. By fluid/gravity correspondence, we derive linearized Navier-Stokes equations and a set of new differential equations from Rarita-Schwinger equation. We compute the boundary energy-momentum tensor and we interpret the result as a perfect fluid with a modified definition of fluid velocity. Finally, we derive the modified expression for the entropy of the black hole in terms of the fermionic bilinears.
Models of light singlet fermion and neutrino phenomenology
Chun, E.J.; Joshipura, A.S.; Smirnov, A.Yu.
1995-05-01
We suggest that a single fermion S exists beyond the standard see-saw structure. It mixes with light neutrinos via interactions with the right-handed neutrino components, so that ν e → S conversion solves the solar neutrino problem. Supersymmetry endowed with R-symmetry is shown to give a natural framework for existence, mass scale (∼ 3 · 10 -3 eV) and mixing (sin 2 2θ es ∼ (0.1 - 1.5) · 10 -2 ) of such a fermion. Models with an approximate horizontal symmetry are constructed, which embed the fermion S and explain simultaneously solar, atmospheric, hot dark matter problems as well as may predict the oscillation ν-bar μ → ν-bar e in the region of sensitivity of KARMEN and LSND experiments. (author). 24 refs
Optical Selection Rule of Excitons in Gapped Chiral Fermion Systems
Zhang, Xiaoou; Shan, Wen-Yu; Xiao, Di
2018-02-01
We show that the exciton optical selection rule in gapped chiral fermion systems is governed by their winding number w , a topological quantity of the Bloch bands. Specifically, in a CN-invariant chiral fermion system, the angular momentum of bright exciton states is given by w ±1 +n N with n being an integer. We demonstrate our theory by proposing two chiral fermion systems capable of hosting dark s -like excitons: gapped surface states of a topological crystalline insulator with C4 rotational symmetry and biased 3 R -stacked MoS2 bilayers. In the latter case, we show that gating can be used to tune the s -like excitons from bright to dark by changing the winding number. Our theory thus provides a pathway to electrical control of optical transitions in two-dimensional material.
Heavy fermion stabilization of solitons in 1+1 dimensions
Farhi, E.; Graham, N.; Jaffe, R.L.; Weigel, H.
2000-01-01
We find static solitons stabilized by quantum corrections in a (1+1) -dimensional model with a scalar field chirally coupled to fermions. This model does not support classical solitons. We compute the renormalized energy functional including one-loop quantum corrections. We carry out a variational search for a configuration that minimizes the energy functional. We find a nontrivial configuration with fermion number whose energy is lower than the same number of free fermions quantized about the translationally invariant vacuum. In order to compute the quantum corrections for a given background field we use a phase-shift parameterization of the Casimir energy. We identify orders of the Born series for the phase shift with perturbative Feynman diagrams in order to renormalize the Casimir energy using perturbatively determined counterterms. Generalizing dimensional regularization, we demonstrate that this procedure yields a finite and unambiguous energy functional
Gauge invariance and anomalous theories at finite fermionic density
Roberge, A.
1990-01-01
We investigate the issue of stability of anomalous matter at finite fermionic density using a two-dimensional toy model. In particular, we pay careful attention to the issue of gauge invariance. We find that, contrary to some recent claims, the effective free energy (obtained by integrating out the fermions) cannot be obtained by the simple inclusion of a Chern-Simons term multiplying the fermionic chemical potential. We obtain some conditions for stability of anomalous charges when some finite density of conserved charge is present as well as for the neutral case. We also show that, under reasonable conditions, no sphaleron-type solution can exist in the toy model unless the anomalous charge density vanishes. We argue that this could be the case for more realistic models as well
On the overlap prescription for lattice regularization of chiral fermions
Randjbar-Daemi, S; Strathdee, J
1995-12-01
Feynman rules for the vacuum amplitude of fermions coupled to external gauge and Higgs fields in a domain wall lattice model are derived using time-dependent perturbation theory. They have a clear and simple structure corresponding to 1-loop vacuum graphs. Their continuum approximations are extracted by isolating the infrared singularities and it is shown that, in each order, they reduce to vacuum contributions for chiral fermions. In this sense the lattice model is seen to constitute a valid regularization of the continuum theory of chiral fermions coupled to weak and slowly varying gauge and Higgs fields. The overlap amplitude, while not gauge invariant, exhibits a well defined (module phase conventions) response to gauge transformations of the background fields. This response reduces in the continuum limit to the expected chiral anomaly, independently of the phase convention. (author). 20 refs.
On the overlap prescription for lattice regularization of chiral fermions
Randjbar-Daemi, S.; Strathdee, J.
1995-12-01
Feynman rules for the vacuum amplitude of fermions coupled to external gauge and Higgs fields in a domain wall lattice model are derived using time-dependent perturbation theory. They have a clear and simple structure corresponding to 1-loop vacuum graphs. Their continuum approximations are extracted by isolating the infrared singularities and it is shown that, in each order, they reduce to vacuum contributions for chiral fermions. In this sense the lattice model is seen to constitute a valid regularization of the continuum theory of chiral fermions coupled to weak and slowly varying gauge and Higgs fields. The overlap amplitude, while not gauge invariant, exhibits a well defined (module phase conventions) response to gauge transformations of the background fields. This response reduces in the continuum limit to the expected chiral anomaly, independently of the phase convention. (author). 20 refs
Two-loop fermionic corrections to massive Bhabha scattering
Actis, S.; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Czakon, M. [Wuerzburg Univ. (Germany). Inst. fuer Theoretische Physik und Astrophysik]|[Institute of Nuclear Physics, NSCR DEMOKRITOS, Athens (Greece); Gluza, J. [Silesia Univ., Katowice (Poland). Inst. of Physics
2007-05-15
We evaluate the two-loop corrections to Bhabha scattering from fermion loops in the context of pure Quantum Electrodynamics. The differential cross section is expressed by a small number of Master Integrals with exact dependence on the fermion masses m{sub e}, m{sub f} and the Mandelstam invariants s, t, u. We determine the limit of fixed scattering angle and high energy, assuming the hierarchy of scales m{sup 2}{sub e}<
Heterotic free fermionic and symmetric toroidal orbifold models
Athanasopoulos, P.; Faraggi, A.E. [Department of Mathematical Sciences, University of Liverpool,Liverpool L69 7ZL (United Kingdom); Nibbelink, S. Groot [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München,80333 München (Germany); Mehta, V.M. [Institute for Theoretical Physics, University of Heidelberg,69120 Heidelberg (Germany)
2016-04-07
Free fermionic models and symmetric heterotic toroidal orbifolds both constitute exact backgrounds that can be used effectively for phenomenological explorations within string theory. Even though it is widely believed that for ℤ{sub 2}×ℤ{sub 2} orbifolds the two descriptions should be equivalent, a detailed dictionary between both formulations is still lacking. This paper aims to fill this gap: we give a detailed account of how the input data of both descriptions can be related to each other. In particular, we show that the generalized GSO phases of the free fermionic model correspond to generalized torsion phases used in orbifold model building. We illustrate our translation methods by providing free fermionic realizations for all ℤ{sub 2}×ℤ{sub 2} orbifold geometries in six dimensions.
Boson representations of fermion systems: Proton-neutron systems
Sambataro, M.
1988-01-01
Applications of a procedure recently proposed to construct boson images of fermion Hamiltonians are shown for proton-neutron systems. First the mapping from SD fermion onto sd boson spaces is discussed and a Q/sub π/xQ/sub ν/ interaction investigated. A Hermitian one-body Q boson operator is derived and analytical expressions for its coefficients are obtained. A (Q/sub π/+Q/sub ν/)x(Q/sub π/+Q/sub ν/) interaction is, then, studied for particle-hole systems and the connections with the SU/sup */(3) dynamical symmetry of the neutron-proton interacting boson model are discussed. Finally, an example of mapping from SDG onto sdg spaces is analyzed. Fermion spectra and E2 matrix elements are well reproduced in the boson spaces
The realization of Majorana fermions in Kitaev Quantum Spin Lattice
Do, Seung-Hwan; Park, Sang-Youn; Yoshitake, Junki; Nasu, Joji; Motome, Yukitoshi; Kwon, Y. S.; Adroja, D. T.; Voneshen, D.; Park, J.-H.; Choi, Kwang-Yong; Ji, Sungdae
The Kitaev honeycomb lattice is envisioned as an ideal host for Majorana fermions that are created out of the spin liquid background. Combining specific heat and neutron scattering experiments with theoretical calculations, here, we establish a hitherto unparalleled spin fractionalization to two species of Majorana fermions in the Kitaev material α-RuCl3. The specific heat data unveil a two-stage release of magnetic entropy by (R/2)ln2 and the T-linear dependence at intermediate temperatures. Our inelastic neutron scattering measurements further corroborate two distinct characters of fractionalized excitations: an Y-like, dispersive, magnetic continuum at higher energies and a dispersionless excitation at low energies around the Brillouin zone center. These dual features are well described by a Ferromagnetic Kitaev model, providing a smoking gun proof of the itinerant and localized Majorana fermions emergent in Kitaev magnets.
A local factorization of the fermion determinant in lattice QCD
Ce, Marco [Scuola Normale Superiore, Pisa (Italy); INFN, Pisa (Italy); Giusti, Leonardo [Milano-Bicocca Univ. (Italy). Dipartimento di Fisica; INFN, Milano-Bicocca (Italy); Schaefer, Stefan [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2016-09-15
We introduce a factorization of the fermion determinant in lattice QCD with Wilson-type fermions that leads to a bosonic action which is local in the block fields. The interaction among gauge fields on distant blocks is mediated by multiboson fields located on the boundaries of the blocks. The resultant multiboson domain-decomposed hybrid Monte Carlo passes extensive numerical tests carried out by measuring standard gluonic observables. The combination of the determinant factorization and of the one of the propagator, that we put forward recently, paves the way for multilevel Monte Carlo integration in the presence of fermions. We test this possibility by computing the disconnected correlator of two flavor-diagonal pseudoscalar densities, and we observe a significant increase of the signal-to-noise ratio due to a two-level integration.
Four-fermion simulation at LEP2 in DELPHI
Ballestrero, A; Cossutti, F; Migliore, E
2003-01-01
We present and discuss the generator setup for $e^+e^-\\rightarrow 4f$ processes chosen by the DELPHI collaboration. The need to combine the most recent theoretical achievements in the CC03 sector with the state of the art description of the remaining part of the 4-fermion processes has led to an original combination of different codes, with the {\\tt WPHACT 2.0} 4-fermion generator and the {\\tt YFSWW} code for the CC03 $\\mathcal{O}(\\alpha)$ corrections as a starting point. The coverage of the 4-fermion phase space is discussed in detail, with particular attention to ensuring the compatibility of {\\tt WPHACT} with dedicated $\\gamma\\gamma$ generators.
Landau Levels of Majorana Fermions in a Spin Liquid.
Rachel, Stephan; Fritz, Lars; Vojta, Matthias
2016-04-22
Majorana fermions, originally proposed as elementary particles acting as their own antiparticles, can be realized in condensed-matter systems as emergent quasiparticles, a situation often accompanied by topological order. Here we propose a physical system which realizes Landau levels-highly degenerate single-particle states usually resulting from an orbital magnetic field acting on charged particles-for Majorana fermions. This is achieved in a variant of a quantum spin system due to Kitaev which is distorted by triaxial strain. This strained Kitaev model displays a spin-liquid phase with charge-neutral Majorana-fermion excitations whose spectrum corresponds to that of Landau levels, here arising from a tailored pseudomagnetic field. We show that measuring the dynamic spin susceptibility reveals the Landau-level structure by a remarkable mechanism of probe-induced bound-state formation.
Shell structure and orbit bifurcations in finite fermion systems
Magner, A. G.; Yatsyshyn, I. S.; Arita, K.; Brack, M.
2011-10-01
We first give an overview of the shell-correction method which was developed by V.M. Strutinsky as a practicable and efficient approximation to the general self-consistent theory of finite fermion systems suggested by A.B. Migdal and collaborators. Then we present in more detail a semiclassical theory of shell effects, also developed by Strutinsky following original ideas of M.C. Gutzwiller. We emphasize, in particular, the influence of orbit bifurcations on shell structure. We first give a short overview of semiclassical trace formulae, which connect the shell oscillations of a quantum system with a sum over periodic orbits of the corresponding classical system, in what is usually called the "periodic orbit theory". We then present a case study in which the gross features of a typical double-humped nuclear fission barrier, including the effects of mass asymmetry, can be obtained in terms of the shortest periodic orbits of a cavity model with realistic deformations relevant for nuclear fission. Next we investigate shell structures in a spheroidal cavity model which is integrable and allows for far-going analytical computation. We show, in particular, how period-doubling bifurcations are closely connected to the existence of the so-called "superdeformed" energy minimum which corresponds to the fission isomer of actinide nuclei. Finally, we present a general class of radial power-law potentials which approximate well the shape of a Woods-Saxon potential in the bound region, give analytical trace formulae for it and discuss various limits (including the harmonic oscillator and the spherical box potentials).
Free expansion of fermionic dark solitons in a boson-fermion mixture
Adhikari, Sadhan K
2005-01-01
We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic dark solitons in a trapped degenerate Fermi gas mixed with a Bose-Einstein condensate in a harmonic as well as a periodic optical-lattice potential. The dark soliton with a 'notch' in the probability density with a zero at the minimum is simulated numerically as a nonlinear continuation of the first vibrational excitation of the linear mean-field-hydrodynamic equations, as suggested recently for pure bosons. We study the free expansion of these dark solitons as well as the consequent increase in the size of their central notch and discuss the possibility of experimental observation of the notch after free expansion
One-dimensional model with fermions in the framework of topological expansion
Azakov, S.I.; Aliev, Eh.S.
1986-01-01
Topological expansion for the one-plaquette U(N) gauge model with fermions is investigated in the leading order for the Wilson and Manton actions. It is shown that the introduction of fermions does not change the phase structure
Ising model of a randomly triangulated random surface as a definition of fermionic string theory
Bershadsky, M.A.; Migdal, A.A.
1986-01-01
Fermionic degrees of freedom are added to randomly triangulated planar random surfaces. It is shown that the Ising model on a fixed graph is equivalent to a certain Majorana fermion theory on the dual graph. (orig.)
The Feynman-Vernon Influence Functional Approach in QED
Biryukov, Alexander; Shleenkov, Mark
2016-01-01
In the path integral approach we describe evolution of interacting electromagnetic and fermionic fields by the use of density matrix formalism. The equation for density matrix and transitions probability for fermionic field is obtained as average of electromagnetic field influence functional. We obtain a formula for electromagnetic field influence functional calculating for its various initial and final state. We derive electromagnetic field influence functional when its initial and final states are vacuum. We present Lagrangian for relativistic fermionic field under influence of electromagnetic field vacuum
Casimir energy of massless fermions in the Slab-bag
Paola, R.D.M. de; Rodrigues, R.B.; Svaiter, N.F.
1999-04-01
The zero-point energy of a massless fermion field in the interior of two parallel plates in a D-dimensional space-time at zero temperature is calculated. In order to regularize the model, a mix between dimensional and zeta function regularization procedure is used and it is founded that the regularized zero-point energy density is finite for any number of space-time dimensions. We present a general expression for the Casimir energy for the fermionic field in such a situation. (author)
Energy-momentum tensor in the fermion-pairing model
Kawati, S.; Miyata, H.
1980-01-01
The symmetric energy-momentum tensor for the self-interacting fermion theory (psi-barpsi) 2 is expressed in terms of the collective mode within the Hartree approximation. The divergent part of the energy-momentum tensor for the fermion theory induces an effective energy-momentum tensor for the collective mode, and this effective energy-momentum tensor automatically has the Callan-Coleman-Jackiw improved form. The renormalized energy-momentum tensor is structurally equivalent to the Callan-Coleman-Jackiw improved tensor for the Yukawa theory
Para-bosons and Para-fermions in Quantum Mechanics
Cattani, M.S.D.; Fernandes, N.C.
1982-01-01
Within the framework of the ordinary quantum mechanics, a detailed study of the energy eigenfunctions of N identical particles using the irreducible representations of the permutation group in the Hilbert space is performed. It is shown that the para-states, as occurs with the boson and fermion states, are compatible with the postulates of quantum mechanics and with the principle of indistinguishability. A mathematical support for the existence of para-bosons and para-fermions is given. Gentile's quantum statistics is, in a certain sense, justified. (Author) [pt
Quantum gravity and Standard-Model-like fermions
Eichhorn, Astrid; Lippoldt, Stefan
2017-01-01
We discover that chiral symmetry does not act as an infrared attractor of the renormalization group flow under the impact of quantum gravity fluctuations. Thus, observationally viable quantum gravity models must respect chiral symmetry. In our truncation, asymptotically safe gravity does, as a chiral fixed point exists. A second non-chiral fixed point with massive fermions provides a template for models with dark matter. This fixed point disappears for more than 10 fermions, suggesting that an asymptotically safe ultraviolet completion for the standard model plus gravity enforces chiral symmetry.
Remarks on Fermion-Boson equivalence in three dimensions
Dutra, A. de Souza; Natividade, C.P.
1998-06-01
Starting from a decomposition of the self-dual field in (2+1) dimensions, we build up an alternative quantum theory which consists of a self-dual model coupled to a Maxwell-generalized Chern-Simons theory. We discuss the fermion-boson equivalence of this quantum theory by comparing it to the Thirring model. Using these results we were able to compute the mass of the bosonized fermions up to third order in (1/m). Some problems related to the number of poles of the effective propagator are also addressed. (author)
Partially quenched gauge theories and an application to staggered fermions
Bernard, C.W.; Golterman, M.F.L.
1994-01-01
We extend our Lagrangian technique for chiral perturbation theory for quenched QCD to include theories in which only some of the quarks are quenched. We discuss the relationship between the partially quenched theory and a theory in which only the unquenched quarks are present. We also investigate the peculiar infrared divergences associated with the η' in the quenched approximation, and find the conditions under which such divergences can appear in a partially quenched theory. We then apply our results to staggered fermion QCD in which the square root of the fermion determinant is taken, using the observation that this should correspond to a theory with four quarks, two of which are quenched
BCS-BEC crossover in spatially modulated fermionic condensates
Sedrakian, Armen
2011-01-01
Several novel multi-component fermionic condensates show universal behavior under imbalance in the number of fermionic species. Here I discuss their phase structure, thermodynamics, and the transition from the weak (BCS) to strong (BEC) coupling regime. The inhomogeneous superconducting phases are illustrated on the example of the Fulde-Ferrell phase which appears in the weak coupling regime, at low temperatures and large asymmetries. The inhomogeneous phases persist through the crossover up to (and possibly beyond) the transition to the strong coupling regime.
BCS-BEC crossover in spatially modulated fermionic condensates
Sedrakian, Armen, E-mail: sedrakian@th.physik.uni-frankfurt.de [Institute for Theoretical Physics, J. W. Goethe-University, Max-von-Laue-Str. 1, 60438 Frankfurt am Main (Germany)
2011-09-16
Several novel multi-component fermionic condensates show universal behavior under imbalance in the number of fermionic species. Here I discuss their phase structure, thermodynamics, and the transition from the weak (BCS) to strong (BEC) coupling regime. The inhomogeneous superconducting phases are illustrated on the example of the Fulde-Ferrell phase which appears in the weak coupling regime, at low temperatures and large asymmetries. The inhomogeneous phases persist through the crossover up to (and possibly beyond) the transition to the strong coupling regime.