Chiral fermions on the lattice

Abstract

An expression for the lattice e ective action induced by chiral fermions in any even dimensions in terms of an overlap of two states is shown to have promising properties in two dimensions: The correct abelian anomaly is reproduced and instantons are suppressed.

Formulation of chiral gauge theories

“…In contrast to the Dirac operators considered previously those in (1) are no longer restricted to one real eigenvalue in addition to zero and also admit more general complex ones. They have nevertheless appropriate realizations which also allow numerical evaluation [4].…”

“…Starting from the basic structure of previous approaches to chiral gauge theories [1,2] we have recently presented a generalization [3] in which the Dirac operator and the chiral projections have been considered as functions of a certain unitary and γ 5 -Hermitian operator. Here we avoid the restrictions introduced by referring to such an operator by determining the possible structures of the chiral projections for given Dirac operator D. …”

Differential equation for spectral flows of hermitean Wilson–Dirac operator

“…The hermitean Wilson-Dirac operator H is a fundamental quantity in the overlap formalism [1,2]. It has been shown there that the difference of the numbers of its positive and negative eigenvalues is related to the index of the massless Dirac operator.…”

Möbius Fermions

“…This work led to two concrete realizations of lattice fermions with chiral symmetry. The domain wall fermions [5,6,7,8] and the overlap fermions [9,10,11,12,13].…”