Finite-element quantum electrodynamics: Canonical formulation, unitarity, and the magnetic moment of the electron.

Abstract

This is the first in a series of papers dealing with four-dimensional quantum electrodynamics on a finite-element lattice. We begin by studying the canonical structure of the theory without interactions. This tells us how to construct momentum expansions for the field operators. Next we examine the interaction term in the Dirac equation. We construct the transfer matrix explicitly in the temporal gauge, and show that it is unitary. Therefore, fermion canonical anticommutation relations hold at each lattice site. Finally, we expand the interaction term to second order in the temporal-lattice spacing and deduce the magnetic moment of the electron in a background field, consistent with the continuum value of {ital g}=2.