Staggered Fermion Approach to Chiral Gauge Theories on the Lattice *

An important open problem in lattice field theory is to find a satisfactory method to describe chiral fermions. There exist several attempts and proposals, for an overview see [1], but none of these has so far been shown to work. Here we shall discuss and test an approach [2] based on the staggered fermion method. Note that in this approach the notorious species doublers need not be decoupled, since they are used as physical spinflavor degrees of freedom. Staggered fermion fields, denoted by χx, do not carry explicit flavor and Dirac labels since these components are ‘spread out’ over the lattice. In the classical continuum limit one can see the usual Dirac and flavor structure in momentum space [3], and an equivalent method can also be given in position space. Thereto one introduces 4 × 4 matrices Ψ x defined as, Ψx = 1 8 ∑