THE t-EXPANSION AND HAMILTONIAN LATTICE QCD

Abstract

The t-expansion is a tool designed to improve on any variational calculation of a quantum theory. It is designed to produce the correct volume behavior of operators appearing in lattice models. We review its formulation and discuss the techniques used for its analysis by testing it on the solvable Heisenberg model in 1+1 dimensions. We discuss its application to the SU(3) lattice gauge theory in 3+1 space-time dimensions. Starting with strong coupling wave functions we investigate the pure glue sector. We review the calculations of the energy-density, the string-tension and several glueball masses. The scalar 0++ glueball follows from the same calculation as the energy-density. The other glueballs which. we study, with the JPC quantum numbers of 1+−, 0−−, 1−− and 2−− are constructed by using wave-functions corresponding to appropriate representations of the cubic symmetry group. Estimates of their physical masses, as obtained from studies of scaling ratios, are presented and discussed. It is quite straightforward to incorporate dynamical quarks in the model. We point out some qualitative features of the structure of the vacuum and the phase transition at high baryon density. Spectra of hadrons including quarks have not yet been calculated with these techniques but the glueball results indicate that this is a viable analytic method for the study of lattice QCD.