
Gaugeinvariant dressed fermion propagator in massless QED3
International Nuclear Information System (INIS)
Mitra, Indrajit; Ratabole, Raghunath; Sharatchandra, H.S.
20060101
The infrared behaviour of the gaugeinvariant 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 fieldtheoretical requirement

Exact onefermionloop contributions in (1+1)dimensional solitons
International Nuclear Information System (INIS)
Shepard, J.R.; Price, C.E.; Ferree, T.C.
19930101
We find solutions to the (1+1)dimensional scalaronly linear σ model. A new method is used to compute onefermionloop contributions exactly, and agreemment with published results employing other methods is excellent. A renormalization scheme which differs from that commonly used in such calculations but is similar to that required in 1+3 dimensions is also presented. We compare ''kink'' versus ''shallow bag'' solutions, paying careful attention to the implications of the onefermionloop contributions for the stability of the former. We find that, for small fermion multiplicities, selfconsistent shallow bag solutions are always more bound than their metastable kink counterparts. However, as the fermion multiplicity increases, shallow bags evolve into kinks which eventually are the only selfconsistent configurations. This situation is qualitatively the same for the two renormalization schemes considered. When we construct ''baryons,'' each containing three fermions, the kink configuration is typically more bound than the shallow bag when onefermionloop contributions are included

Quantum Hall effect of massless Dirac fermions and free fermions in Hofstadter's butterfly
International Nuclear Information System (INIS)
Yoshioka, Nobuyuki; Matsuura, Hiroyasu; Ogata, Masao
20160101
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 selfsimilar 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)

Hints of hybridizing Majorana fermions in a nanowire coupled to superconducting leads
Science.gov (United States)
Finck, A. D. K.; van Harlingen, D. J.; Mohseni, P. K.; Jung, K.; Li, X.
20130301
It has been proposed that a nanowire with strong spinorbit coupling that is contacted with a conventional superconductor and subjected to a large magnetic field can be driven through a topological phase transition. In this regime, the two ends of the nanowire together host a pair of quasiparticles known as Majorana fermions (MFs). A key feature of MFs is that they are pinned to zero energy when the topological nanowire is long enough such that the wave functions of the two MFs do not overlap significantly, resulting in a zero bias anomaly (ZBA). It has been recently predicted that changes in external parameters can vary the wave function overlap and cause the MFs to hybridize in an oscillatory fashion. This would lead to a nonmonotonic splitting or broadening of the ZBA and help distinguish MF transport signatures from a Kondo effect. Here, we present transport studies of an InAs nanowire contacted with niobium nitride leads in high magnetic fields. We observe a number of robust ZBAs that can persist for a wide range of back gate bias and magnetic field strength. Under certain conditions, we find that the height and width of the ZBA can oscillate with back gate bias or magnetic field. This work was supported by Microsoft Project Q.

Wigner functions for fermions in strong magnetic fields
Science.gov (United States)
Sheng, Xinli; Rischke, Dirk H.; Vasak, David; Wang, Qun
20180201
We compute the covariant Wigner function for spin(1/2) fermions in an arbitrarily strong magnetic field by exactly solving the Dirac equation at nonzero fermionnumber and chiralcharge 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 Wignerfunction operator. The Wigner function is obtained by taking the ensemble average of the Wignerfunction operator in global thermodynamical equilibrium, i.e., at constant temperature T and nonzero fermionnumber and chiralcharge chemical potentials μ and μ_5, respectively. Extracting the vector and axialvector components of the Wigner function, we reproduce the currents of the chiral magnetic and separation effect in an arbitrarily strong magnetic field.

Hierarchy spectrum of SM fermions: from top quark to electron neutrino
International Nuclear Information System (INIS)
Xue, SheSheng
20160101
In the SM gauge symmetries and fermion content of neutrinos, charged leptons and quarks, we study the effective fourfermion operators of EinsteinCartan type and their contributions to the SchwingerDyson equations of fermion selfenergy functions. The study is motivated by the speculation that these fourfermion operators are probably originated due to the quantum gravity, which provides the natural regularization for chiralsymmetric gauge field theories. In the chiralgauge symmetry breaking phase, as to achieve the energetically favorable ground state, only the topquark mass is generated via the spontaneous symmetry breaking, and other fermion masses are generated via the explicit symmetry breaking induced by the topquark mass, fourfermion interactions and fermionflavor mixing matrices. A phase transition from the symmetry breaking phase to the chiralgauge symmetric phase at TeV scale occurs and the drastically finetuning problem can be resolved. In the infrared fixedpoint domain of the fourfermion coupling for the SM at low energies, we qualitatively obtain the hierarchy patterns of the SM fermion Dirac masses, Yukawa couplings and familyflavor mixing matrices with three additional righthanded neutrinos ν_R"f. Large Majorana masses and leptonnumber symmetry breaking are originated by the fourfermion interactions among ν_R"f and their lefthanded conjugated fields ν_R"f"c. Light masses of gauged Majorana neutrinos in the normal hierarchy (10"−"5−10"−"2 eV) are obtained consistently with neutrino oscillations. We present some discussions on the composite Higgs phenomenology and forwardbackward asymmetry of tt̄production, as well as remarks on the candidates of light and heavy dark matter particles (fermions, scalar and pseudoscalar bosons).

Hierarchy spectrum of SM fermions: from top quark to electron neutrino
Energy Technology Data Exchange (ETDEWEB)
Xue, SheSheng [ICRANet,Piazza della Repubblica 10, 65122 Pescara (Italy); Physics Department, Sapienza University of Rome,Piazzale Aldo Moro 5, 00185 Roma (Italy)
20161110
In the SM gauge symmetries and fermion content of neutrinos, charged leptons and quarks, we study the effective fourfermion operators of EinsteinCartan type and their contributions to the SchwingerDyson equations of fermion selfenergy functions. The study is motivated by the speculation that these fourfermion operators are probably originated due to the quantum gravity, which provides the natural regularization for chiralsymmetric gauge field theories. In the chiralgauge symmetry breaking phase, as to achieve the energetically favorable ground state, only the topquark mass is generated via the spontaneous symmetry breaking, and other fermion masses are generated via the explicit symmetry breaking induced by the topquark mass, fourfermion interactions and fermionflavor mixing matrices. A phase transition from the symmetry breaking phase to the chiralgauge symmetric phase at TeV scale occurs and the drastically finetuning problem can be resolved. In the infrared fixedpoint domain of the fourfermion coupling for the SM at low energies, we qualitatively obtain the hierarchy patterns of the SM fermion Dirac masses, Yukawa couplings and familyflavor mixing matrices with three additional righthanded neutrinos ν{sub R}{sup f}. Large Majorana masses and leptonnumber symmetry breaking are originated by the fourfermion interactions among ν{sub R}{sup f} and their lefthanded conjugated fields ν{sub R}{sup fc}. Light masses of gauged Majorana neutrinos in the normal hierarchy (10{sup −5}−10{sup −2} eV) are obtained consistently with neutrino oscillations. We present some discussions on the composite Higgs phenomenology and forwardbackward asymmetry of tt̄production, as well as remarks on the candidates of light and heavy dark matter particles (fermions, scalar and pseudoscalar bosons).

Fermion field as inflaton, dark energy and dark matter
International Nuclear Information System (INIS)
Grams, Guilherme; Souza, Rudinei C de; Kremer, Gilberto M
20140101
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 nonminimally 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 nonminimal 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 nonminimal coupling is allowed, it mediates a powerlaw inflation. (paper)

Light fermions in quantum gravity
International Nuclear Information System (INIS)
Eichhorn, Astrid; Gies, Holger
20110101
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 nonGaußian 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 asymptoticsafety 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)

Symmetry between bosons and fermions
International Nuclear Information System (INIS)
Ohnuki, Y.; Kamefuchi, S.
19860101
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 gnumbers. 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, gsymmetry transformations. 6 references, 1 table

Grassmann phase space methods for fermions. II. Field theory
Energy Technology Data Exchange (ETDEWEB)
Dalton, B.J., Email: 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)
20170215
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 cnumber phase space variables, with the density operator equivalent to a distribution function of these variables. The anticommutation rules for fermion annihilation, creation operators suggests the possibility of using anticommuting 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 quantumatom 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 anticommuting 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 multicomponent Fermi gases with nonzero 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.

Grassmann phase space methods for fermions. II. Field theory
International Nuclear Information System (INIS)
Dalton, B.J.; Jeffers, J.; Barnett, S.M.
20170101
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 cnumber phase space variables, with the density operator equivalent to a distribution function of these variables. The anticommutation rules for fermion annihilation, creation operators suggests the possibility of using anticommuting 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 quantumatom 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 anticommuting 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 multicomponent Fermi gases with nonzero 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.

Axial gravity, massless fermions and trace anomalies
International Nuclear Information System (INIS)
Bonora, L.; Cvitan, M.; Giaccari, S.; Stemberga, T.; Prester, P.D.; Pereira, A.D.; UFFUniv. Federal Fluminense, Niteroi
20170101
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.)

Axial gravity, massless fermions and trace anomalies
Energy Technology Data Exchange (ETDEWEB)
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. [UERJUniv. Estadual do Rio de Janeiro (Brazil). Dept. de Fisica Teorica; UFFUniv. Federal Fluminense, Niteroi (Brazil). Inst. de Fisica
20170815
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.)

Interactingstring picture of the fermionic string
International Nuclear Information System (INIS)
Mandelstam, S.
19860101
This report gives a review of the interactingstring picture of the Bose string. In the present lecture, the author outlines a similar treatment of the Fermionic string. The quantization of the free Fermionic string is carried out to the degrees of freedom x, representing the displacement of the string. Also presented are Grassman degrees of freedom S distributed along the string. The report pictures the fermionic string as a string of dipoles. The general picture of the interaction of such strings by joining and splitting is the same as for the Bose string. The author does not at present have the simplest formula for fermion string scattering amplitudes. A less detailed treatment is given than for the Bose string. The report sets up the functionalintegration formalism, derives the analog mode, and indicates in general, terms how the conformal transformation to the zplane may be performed. The paper concludes by stating without proof the formula for the Narticle tree amplitude in the manifestly supersymmetric formalism

Disordered 2d quasiparticles in class D: Dirac fermions with random mass, and dirty superconductors
International Nuclear Information System (INIS)
Bocquet, M.; Serban, D.; Zirnbauer, M.R.
20000101
Disordered noninteracting quasiparticles that are governed by a Majoranatype Hamiltonian  prominent examples are dirty superconductors with broken timereversal and spinrotation symmetry, or the fermionic representation of the 2d Ising model with fluctuating bond strengths  are called class D . In two dimensions, weakly disordered systems of this kind may possess a metallic phase beyond the insulating phases expected for strong disorder. We show that the 2d metal phase emanates from the free Majorana fermion point, in the direction of the RG trajectory of a perturbed WZW model. To establish this result, we develop a supersymmetric extension of the method of nonabelian bosonization. On the metallic side of the metalinsulator transition, the density of states becomes nonvanishing at zero energy, by a mechanism akin to dynamical mass generation. This feature is explored in a model of N species of disordered Dirac fermions, via the mapping on a nonlinear sigma model, which encapsulates a Z 2 spin degree of freedom. We compute the density of states in a finite system, and obtain agreement with the randommatrix prediction for class D , in the ergodic limit. Vortex disorder, which is a relevant perturbation at the freefermion point, changes the density of states at low energy and suppresses the local Z 2 degree of freedom, thereby leading to a different symmetry class, BD

Anomalous diffusion of fermions in superlattices
International Nuclear Information System (INIS)
Drozdz, S.; Okolowicz, J.; Srokowski, T.; Ploszajczak, M.
19960301
Diffusion of fermions in the periodic twodimensional 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)

Global WellPosedness of the NLS System for Infinitely Many Fermions
Science.gov (United States)
Chen, Thomas; Hong, Younghun; Pavlović, Nataša
20170401
In this paper, we study the mean field quantum fluctuation dynamics for a system of infinitely many fermions with delta pair interactions in the vicinity of an equilibrium solution (the Fermi sea) at zero temperature, in dimensions d = 2, 3, and prove global wellposedness of the corresponding Cauchy problem. Our work extends some of the recent important results obtained by Lewin and Sabin in [33,34], who addressed this problem for more regular pair interactions.

Ladder physics in the spin fermion model
Science.gov (United States)
Tsvelik, A. M.
20170501
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 largeN 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.

Ladder physics in the spin fermion model
International Nuclear Information System (INIS)
Tsvelik, A. M.
20170101
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 largeN 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 dMott 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.