Related papers: Chiral Dirac Fermions on the Lattice using Geometr…
We propose a nonperturbative formulation of chiral gauge theories. The method involves a `pre-regulation' of the gauge fields, which may be implemented on a lattice, followed by a computation of the chiral fermion determinant in the form of…
We study the large-scale behavior of the height function in the dimer model on the square lattice. Richard Kenyon has shown that the fluctuations of the height function on Temperleyan discretizations of a planar domain converge in the…
A unified classification and analysis is presented of two dimensional Dirac operators of QCD-like theories in the continuum as well as in a naive lattice discretization. Thereby we consider the quenched theory in the strong coupling limit.…
We discuss the quantum computation of dynamical chirality production in lattice gauge theory. Although the chirality of a lattice fermion is complicated in general dimensions, it can be simply formulated on a one-dimensional lattice. The…
The most fundamental characteristics of a physical system can often be deduced from its behaviour under discrete symmetry transformations such as time reversal, parity and chirality. Here we review basic symmetry properties of the…
This article gives a review of the topic of regularising chiral gauge theories and is aimed at a general audience. It begins by clarifying the meaning of chirality and goes on to discussing chiral projections in field theory, parity…
We only require generalized chiral symmetry and $\gamma_5$-hermiticity, which leads to a large class of Dirac operators describing massless fermions on the lattice, and use this framework to give an overview of developments in this field.…
Minimally doubled fermions have been proposed as a strictly local discretization of the QCD quark action, which also preserves chiral symmetry at finite cut-off. We study the renormalization and mixing properties of two particular…
Chiral fermions can (presumably) be constructed by introducing two regulators, one for the gauge fields (e.g. a lattice), and another for the fermion functional integrals in a fixed (regulated) gauge field. This talk discusses cutoff…
Differential calculus on discrete spaces is studied in the manner of non-commutative geometry by representing the differential calculus by an operator algebra on a suitable Krein space. The discrete analogue of a (pseudo-)Riemannian metric…
We report tests and results from a new approach to the spectral density and the mode number distribution of the Dirac operator in lattice gauge theories. The algorithm generates the spectral density of the lattice Dirac operator as a…
Twisted bilayer graphene is a chiral system which has been recently shown to present circular dichroism. In this work we show that the origin of this optical activity is the rotation of the Dirac fermions' helicities in the top and bottom…
The species doubling problem of the lattice fermion is resolved by introducing hopping interactions that mix left- and right-handed fermions around the momentum boundary. Approximate chiral symmetry is realized on the lattice. The deviation…
The utility of lattice discretization technique is demonstrated for solving nonrelativistic quantum scattering problems and specially for the treatment of ultraviolet divergences in these problems with some potentials singular at the origin…
We investigate numerically the effect of regulating fermions in the presence of singular background fields in three dimensions. For this, we couple free lattice fermions to a background compact U(1) gauge field consisting of a…
This paper concerns the question of how chirality is realized for discrete counterparts of the Dirac-K\"{a}hler equation in the Hestenes and Joyce forms. It is shown that left and right chiral states for these discrete equations can be…
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.
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…
For thermodynamics studies it is desirable to simulate two degenerate flavors and retain at least a remnant of the chiral symmetry. Staggered fermions can achieve this at the cost of rooting the determinant. Rooting can be avoided using…
We investigate exact symmetries of a staggered fermion in D dimensions. The Dirac operator is reformulated by SO(2D) Clifford algebra. The chiral symmetry, rotational invariance and parity symmetries are clarified in any dimension. Local…