An intermediate-coupling expansion for hamiltonian lattice gauge theory

Abstract

An intermediate-coupling expansion for the Hamiltonian formulation of lattice gauge theory without matter fields is developed. The expansion is an alternative to the conventional strong-coupling methods and is applicable to both finite and continuous gauge groups. The set of plaquettes of the lattice contains two complementary subsets, which are identified as even and odd plaquettes. In (2+1)-dimensions they are like the black and white squares of a chess board. The even plaquettes include all the links of the lattice and thus all the degrees of freedom. A zero-order Hamiltonian, written in terms of operators which act on single even plaquette states, is defined. It includes both the link terms and the even plaquette terms of the Kogut-Susskind Hamiltonian, and thus all the degrees of freedom, and is separated into terms involving independent even plaquette states. The odd plaquette terms, which are also written in terms of even plaquette operators, are treated as a perturbation. The vacuum energy density, mass gap and string tension of the (2+1)-dimensional Z(2) lattice gauge theory are calculated as an illustration of the expansion. Results are obtained which compare favourably with those of the corresponding strong-coupling expansions. A diagrammatic method for the enumeration and evaluation of the terms of the expansion is presented and a computer program based on this scheme is discussed. A class of models with inhomogeneous coupling strengths is introduced. These models provide a valuable tool for the study of the phase diagram of the homogeneous-coupling model, onto which they may be mapped smoothly. Several applications and extensions are considered.