The Coupled Cluster Method in the Hamiltonian Lattice Gauge Theory

Abstract

The glueball spectrum for SU(3) Yang-Mills theory in 2+1 dimensions is calculated via the coupled clustermethod in Hamiltonian lattice gauge field theory.<br /> In the Hamiltonian formulation the quantum states are gauge invariant functions of the spatial link variables representing the lattice gauge fields. All calculations presented here have been performed in the infinite volume limit. Within the coupled cluster method the eigenvalue problem of the Kogut-Susskind Hamiltonian is reformulated as a non-linear equation for the ground state correlation function, describing the vacuum state, and as a linear eigenvalue problem for the excitation operator, describing the glueball states. In order to expand the ground state correlation function and the excitation operator a large but finite gauge invariant basis is constructed. This basis is built by plaquette products, as the plaquette is the simplest gauge invariant quantity on the lattice. It is truncated to the order δ (up to δ=5 within this work) by taking all states created by up to d-fold products. Lattice translation and rotation symmetries and the operation of charge conjugation are used to project onto states with definite lattice angular momentum, parity and charge parity. In addition an improved Hamiltonian is implemented. Our results are tested by comparing the calculations in different orders, with and without improvement. The corresponding wave functions are also examined.<br /> Satisfactory convergence is obtained for the vacuum. For the glueball states dimensionless mass ratios are calculated in order to reflect scaling. We observe an approximate scaling window, where the mass values agree with standard lattice Monte Carlo results.