Study of compact QED with light fermions

We present a numerical study of compact QED including dynamical fermions of mass = 0.10 (lattice units) on a 6⁴ lattice. Staggered lattice fermions and the Wilson action and mixed gauge actions were studied. The simulations used two modified hybrid methods: one with stochastic fields and the other with deterministic ones. Working with a variable number of flavors we found that the chiral transition which separates the strong and weak coupling phases is of first order in all cases. The strength of these discontinuous transitions increase with the number of flavors.     

Spin- and isospin-dependent momentum distributions in Fermi liquids at nonzero temperatures

We explore the structure of momentum distributions of Fermi liquids such as completely polarized ³He, unpolarized liquid ³He, and nuclear matter at nonzero temperatures. The study employs correlated density matrix theory and adapts the algorithm to deal with spin- and isospin-dependent correlations. The analysis is based on the factor decomposition of the one-body reduced density matrix. The decomposition permits to distinguish between statistical correlations and dynamic (direct) correlations. Together with the concept of renormalized fermions the formal results open the pathway to investigate the thermal boundaries of normal Fermi phases within the correlated density matrix theory. We also discuss possible transitions from normal phases to anomalous fermion phases triggered by statistical correlations or by periodic phase-phase structures.     

Plasma oscillations of edge Dirac fermions

The dispersion law of one-dimensional plasmons in a quasi-one-dimensional system of massless Dirac fermions has been calculated. Two model two-dimensional systems where bands of edge states filled with such Dirac fermions appear at the edge have been considered. Edge states in the first system, topological insulator, are due to topological reasons. Edge states in the second system, system of massive Dirac fermions, have Tamm origin. It has been shown that the dispersion laws of plasmons in both systems in the long-wavelength limit differ only in the definition of the parameters (velocity and localization depth of Dirac fermions). The frequency of plasmons is formally quantum (ω ∝ ? ^?1/2) and, in the case of the Coulomb interaction between electrons, depends slightly on the Fermi level E _F. The dependence on E _F is stronger in the case of short-range interaction. The quantum features of oscillations of massless one-dimensional Dirac fermions are removed by introducing the mass of Dirac fermions at the Fermi level and their density. Correspondence to the dispersion law of classical one-dimensional plasma oscillations in a narrow stripe of “Schrödinger” electrons has been revealed.     

Monopole catalysis: The fermion-rotor system

We study Weyl fermions coupled to a rotor in two spacetime dimensions. This system is equivalent to the monopole-fermion system in the limit e²→0, e²M_x→∞. This enables us to clarify the physics of the monopole catalysis process. We rederive results of Rubakov and Callan and discuss attempts to treat the case of massive fermions.     

Separable interactions and liquid 3He: II. Extrema of Landau expansion and phase diagram in the weak-coupling limit

In a previous paper we derived a Landau expansion starting from an exactly solvable model for a system of fermions with an l = 1 pairing interaction in the presence of a magnetic field. The Landau expansion, which can be used to study the phases of liquid ³He, is a complicated function of 9 complex variables, in which it is not obvious a priori that the field dependence of the coefficients of the fourth-order terms can be neglected. In the present paper the extrema of the Landau expansion are analyzed in some detail with the weak-coupling values of the coefficients. The absolute minimum of the Landau expansion can be found by minimizing a three-parameter function Φ_BW, the minimalization of which leads to three possible phases, the A1-phase, the ABM-phase (or two-dimensional 2D-phase) and the proper generalization of the BW-phase in the presence of a magnetic field. The phase diagram is compared with the one given by Ambegaokar and Mermin.     

New fermions ate + e − colliders I. Production and decay

We analyze the production in e⁺e^– collisions of new heavy fermions stemming from extensions of the Standard Model. We write down the most general expression for the production of two heavy fermions and their subsequent decays, allowing for the polarization of thee ⁺ e ^– initial state and taking into account the final polarization of the fermions. We then discuss the various decay modes including cascade and three body decays, and the production mechanisms, both pair production and single production in association with ordinary fermions.     

Metastability range of the Bose condensate in 7Li-fermion mixtures at T = 0

We evaluate the ground state of a mixture of bosons and spin-polarized fermions in the case of attractive boson-boson interactions, using a variational Ansatz for the Bose condensate wave function and the Thomas-Fermi approximation for the fermions in the mean field of the condensate. Within this approximation we show that the presence of the fermions tends to restrict the metastability range of the condensate, irrespectively of the sign of the boson-fermion interactions. Numerical illustrations are reported for mixtures of ⁷Li atoms with fermions having the ⁶Li mass.     

The phase structure of Einstein–Cartan theory

In the Einstein–Cartan theory of torsion-free gravity coupling to massless fermions, the four-fermion interaction is induced and its strength is a function of the gravitational and gauge couplings, as well as the Immirzi parameter. We study the dynamics of the four-fermion interaction to determine whether effective bilinear terms of massive fermion fields are generated. Calculating one-particle-irreducible two-point functions of fermion fields, we identify three different phases and two critical points for phase transitions characterized by the strength of four-fermion interaction: (1) chiral symmetric phase for massive fermions in strong coupling regime; (2) chiral symmetric broken phase for massive fermions in intermediate coupling regime; (3) chiral symmetric phase for massless fermions in weak coupling regime. We discuss the scaling-invariant region for an effective theory of massive fermions coupled to torsion-free gravity in the low-energy limit.     

Fermion zero modes at the boundary of superfluid <Superscript>3</Superscript>He-B

Superfluid ³He-B belongs to the important special class of time-reversal invariant topological superfluids. It has Majorana fermions as edge states on the surface of bulk ³He-B. On the rough wall these fermion zero modes have finite density of states at E = 0. It is possible that Lancaster experiments with a wire vibrating in ³He-B have already probed Majorana fermions living on the surface of the wire.     

Type-III and IV interacting Weyl points

3+1-dimensional Weyl fermions in interacting systems are described by effective quasi-relativistic Green’s functions parametrized by a 16-element matrix e _α ^μ in an expansion around the Weyl point. The matrix e _α ^μ can be naturally identified as an effective tetrad field for the fermions. The correspondence between the tetrad field and an effective quasi-relativistic metric g_μν governing the Weyl fermions allows for the possibility to simulate different classes of metric fields emerging in general relativity in interacting Weyl semimetals. According to this correspondence, there can be four types of Weyl fermions, depending on the signs of the components g ⁰⁰ and g ₀₀ of the effective metric. In addition to the conventional type-I fermions with a tilted Weyl cone and type-II fermions with an overtilted Weyl cone for g ⁰⁰ > 0 and, respectively, g ₀₀ > 0 or g ₀₀ < 0, we find additional “type-III” and “type-IV” Weyl fermions with instabilities (complex frequencies) for g ⁰⁰ < 0 and g ₀₀ > 0 or g ₀₀ < 0, respectively. While the type-I and type-II Weyl points allow us to simulate the black hole event horizon at an interface where g ⁰⁰ changes sign, the type-III Weyl point leads to effective spacetimes with closed timelike curves.     

Stability of the Bose system in Bose-Fermi mixture with attraction between bosons and fermions

An effective Hamiltonian for the Bose system in the mixture of ultracold atomic clouds of bosons and fermions is obtained by integrating out the Fermi degrees of freedom. An instability of the Bose system is found in the case of attractive interaction between components that is in good agreement with an experiment on the bosonic ⁸⁷Rb and fermionic ⁴⁰K mixture.     

Coulomb interaction and semimetal-insulator transition in graphene

The strong Coulomb interaction between massless Dirac fermions can drive a semimetal-insulator transition in single-layer graphene by dynamically generating an excitonic fermion gap. There is a critical interaction strength λc that separates the semimetal phase from the insulator phase. We calculate the specific heat and susceptibility of the system and show that they exhibit distinct behaviors in the semimetal and insulator phases.     

Exotic phases of finite temperature gauge theories

We calculate the phase diagrams at high temperature of SU(N) gauge theories with massive fermions by minimizing the one-loop effective potential. Considering fermions in the adjoint (Adj) representation at various N we observe a variety of phases when N_f2 Majorana flavours and periodic boundary conditions are applied to fermions. Also the confined phase is perturbatively accessible. For N=3, we add Fundamental (F) representation fermions with antiperiodic boundary conditions to adjoint QCD to show how the Z(3)-symmetry breaks in the confined phase.     

Effective functional for the supercoherent state of spinless algebra in the Hubbard model

The supermatrix of a supercoherent state is calculated for deformed nonlinear superalgebra in the mode of spinless fermions for the Hubbard model with strong repulsion in sites. The effective functional is derived for spinless fermions. The superfield Lagrangian is calculated for spinless fermions in the Hubbard model with the help of the simple chiral model with N = 1 and self-action Ф³.     

Cosmological consequences of grand unification beyond SU(5)

We examine the cosmological consequences of new types of fermions generally present in GUTs based on unitary groups larger than SU(5) which break down to SU(5) at ultralarge energies. We find that some SU(5) singlet fermions in such theories tend to have masses small compared to 10¹⁵ GeV. If sufficiently light (or massless) such particles affect He abundance unacceptably. If heavier (but still light compared to 10¹⁵ GeV) the decays of such particles generate entropy and thus greatly suppress n_B/n_γ.Such theories also contain ultraheavy fermions. Their decays are shown to be a prime source of singlet fermions. It is also shown that the decays of ultraheavy fermions generate entropy which tends to suppress the contribution to n_B/n_γ from usual mechanisms. These decays may themselves, however, generate a baryon asymmetry.     

Topological superfluid <Superscript>3</Superscript>He-B in magnetic field and ising variable

The topological superfluid ³He-B provides many examples of the interplay of symmetry and topology. Here we consider the effect of magnetic field on topological properties of ³He-B. Magnetic field violates the time reversal symmetry. As a result, the topological invariant supported by this symmetry ceases to exist; and thus the gapless fermions on the surface of ³He-B are not protected any more by topology: they become fully gapped. Nevertheless, if perturbation of symmetry is small, the surface fermions remain relativistic with mass proportional to symmetry violating perturbation—magnetic field. The ³He-B symmetry gives rise to the Ising variable I = ±1, which emerges in magnetic field and which characterizes the states of the surface of ³He-B. This variable also determines the sign of the mass term of surface fermions and the topological invariant describing their effective Hamiltonian. The line on the surface, which separates the surface domains with different I, contains 1 + 1 gapless fermions, which are protected by combined action of symmetry and topology.     

Dynamics of Dirac and Weyl fermions on a two-dimensional surface

The determinants of Dirac and Weyl fermions coupled to the extrinsic geometry of a two-dimensional surface embedded in a 3D euclidean space are calculated exactly. The effective action produced by chiral fermions contains a Wess-Zumino term with the structure of the Hopf topological invariant of a map S³→S².     

Radially free Higgs-Yukawa model

A radially free scalar model coupled to naive fermions via a Yukawa coupling is studied numerically on a 4⁴ lattice. The phase diagram is similar to the radially fixed case. Some results on a 6⁴ lattice are also presented. The mechanism by which the fermions induce symmetry breaking in the scalar sector is discussed.     

Family unification within SO(15)

We present a model for the unification of fermion families based on the gauge symmetry SO(15). It is a minimal SO(n) model which can accommodate the known fermions within a single irreducible representation. The model predicts four ordinary fermion families and four families of mirror fermions. The latter have V + A weak interactions, and their mass scale is predicted to be 10² GeV/c². We argue that radiative corrections to the fermion masses can cause non-negligible mixing between ordinary and mirror fermions. The implications of these mixings for the weak interaction phenomenology and solar neutrinos are discussed.     

Tunneling effect of Dirac particles from the non-extremal black hole in <Emphasis Type="Italic">D</Emphasis> = 5, <Emphasis Type="Italic">SO</Emphasis>(6) gauged supergravity

Recent research shows that Hawking radiation from black hole horizon can be treated as a quantum tunneling process, and fermions tunneling method can successfully recover Hawking temperature. In this tunneling framework, choosing a set of appropriate matrices γ ^μ is an important technique for fermions tunneling method. In this paper, motivated by Kerner and Man’s fermions tunneling method of 4 dimension black holes, we further improve the analysis to investigate Hawking tunneling radiation from the non-extremal black hole in D = 5, SO(6) gauged supergravity by constructing a set of appropriate matrices γ ^μ for general covariant Dirac equation. Finally, the expected Hawking temperature of the black hole is correctly recovered, which takes the same form as that obtained by other methods.