Related papers: Functional determinant and Green functions for a f…
The Dirac Hamiltonian formalism is applied to a system in $(2+1)$-dimensions consisting of a Dirac field $\psi$ minimally coupled to Chern-Simons $U(1)$ and $SO(2,1)$ connections, $A$ and $\omega$, respectively. This theory is connected to…
Being motivated by applications to the physics of Weyl semimetals we study spectral geometry of Dirac operator with an abelian gauge field and an axial vector field. We impose chiral bag boundary conditions with variable chiral phase…
We prove a Mahoux-Mehta--type theorem for finite-volume partition functions of SU(N_c\geq 3) gauge theories coupled to fermions in the fundamental representation. The large-volume limit is taken with the constraint V << 1/m_{\pi}^4. The…
We study the two-dimensional electron gas in a magnetic field at filling fraction $\nu=\frac{1}{2}$. At this filling the system is in a gapless state which can be interpreted as a Fermi liquid of composite fermions. We construct trial wave…
We investigate Dirac fermions in the antifferomagnetic metallic state of iron-based superconduc- tors. Deriving an effective Hamiltonian for Dirac fermions, we reveal that there exist two Dirac cones carrying the same chirality, contrary to…
The zero mode wave function of a massless Dirac fermion in the presence of a random gauge field is studied. The density correlation function is calculated numerically and found to exhibit power law in the weak randomness with the disorder…
The goal of the present paper is to calculate the determinant of the Dirac operator with a mass in the cylindrical geometry. The domain of this operator consists of functions that realize a unitary one-dimensional representation of the…
We present a fermion model characterized by an anticommuting-parameter shift symmetry. The Hamiltonian formulation exhibits a combination of first-class and second-class constraints. We derive the well-known Dirac equation by fixing the…
We study the effective action associated to the Dirac operator in two dimensional non-commutative Field Theory. Starting from the axial anomaly, we compute the determinant of the Dirac operator and we find that even in the U(1) theory, a…
The fermion determinant and the chiral anomaly of lattice Dirac operator D on a finite lattice are investigated. The condition for D to reproduce correct chiral anomaly at each site of a finite lattice for smooth background gauge fields is…
In this note we study fermionic zero modes in gauge and gravity backgrounds taking a two dimensional compact manifold $T^2$ as extra dimensions. The result is that there exist massless Dirac fermions which have normalizable zero modes under…
A generalized Dirac equation is derived in order to describe charge carriers moving in corrugated graphene, which is the case for temperatures above 10{\deg}K due to the presence of flexural phonons. Such interaction is taken into account…
In this paper, we define the Green function for the Dirac operator under two local boundary conditions: the condition associated with a chirality operator (also called the chiral bag boundary condition) and the $\MIT$ bag boundary…
We use the $\zeta$-function regularization and an integral representation of the complex power of a pseudo differential operator, to give an unambiguous definition of the determinant of the Dirac operator. We bring this definition to a…
Making use of the symmetries of anti-de Sitter space-time, we derive an analytic expression for the bispinor of parallel transport, from which we construct in closed form the vacuum Feynman Green's function of the Dirac field on this…
We study functional determinants for Dirac operators on manifolds with boundary and discuss the ellipticity of boundary problems by using the Calder\'on projector. We give, for local boundary conditions, an explicit formula relating these…
A Dirac fermion model with random axial-vector potential is proposed. At a special strength of randomness, the symmetry of the action is enhanced, which is due to the gauge symmetry \`a la Nishimori. Some exact scaling exponents of…
We study the coupling between mechanical motion and Dirac electrons in a dynamical sheet of graphene. We show that this coupling can be understood in terms of an effective gauge field acting on the electrons, which has two contributions:…
We use a functional approach to calculate the Casimir energy due to Dirac fields in interaction with thin, flat, parallel walls, which implement imperfect bag-like boundary conditions. These are simulated by the introduction of delta-like…
We discuss how to formulate Dirac fermion operator on a finite lattice such that it can provide a nonperturbative regularization for massless fermion interacting with a background gauge field.