A lattice gauge theory for fields in the adjoint representation

Abstract

We present a mathematical formulation for a gauge theory for fields in the adjoint representation of SU n, where the fields are general differential forms living on the lattice objects, like sites, links, plaquettes, etc. By a general definition of covariant derivatives we write down the Lagrangian and Hamiltonian densities for the gauge field. Imposing the unitary condition for the gauge link variable we can obtain the well-known Wilson action and for time continuous the Kogut-Susskind Hamiltonian formalism. Furthermore, we present the gauge formulation for scalar and pseudoscalar fields. © 1984 Società Italiana di Fisica.