Lattice theories of chiral fermions

Abstract

We present a Hamiltonian formulation for gauged nonanomalous chiral theories on a spatial lattice. The formulation has the desirable properties that it provides exact chiral symmetry in the massless limit, with a correct fermion spectrum and correct weak-coupling perturbation theory for QED. It can be generalized to non-Abelian theories. The disadvantage of the formalism is that it is complicated and nonlocal (on the lattice) and hence not easily implemented in practical calculations. However, it does provide an existence proof for a satisfactory chiral lattice gauge theory in the Hamiltonian formulation.