New formulation of the Dirac equation on a Minkowski lattice

Abstract

The Dirac equation is formulated on (1+{ital D})-dimensional discrete Minkowski space-time. We find that the minimum number of components of the fermion field is 2{sup D{minus}1} in the massless case, which is smaller than 2{sup D+1} of the Kogut-Susskind fermion. There exist no extra poles in the fermion propagator. The action is not Hermitian but the quantization can be performed consistently. In the (1+3)-dimensional massless case the equation describes a single species of Dirac particle in the continuous space-time limit. In the (1+1)-dimensional massless case the equation is the same as the automaton equation by {close_quote}t Hooft and describes a chiral fermion. The time evolution operator is unitary and the norm is conserved. For interacting fermions with gauge fields the evolution operator is not unitary. But in the continuum limit the unitarity will be recovered. The consequences of loosening the unitarity condition on the time evolution operator are discussed. {copyright} {ital 1997} {ital The American Physical Society}