Improvement and Analytic Techniques in Hamiltonian Lattice Gauge Theory

TL;DR

This thesis advances Hamiltonian lattice gauge theory by developing improved lattice Hamiltonians for gluons and extending analytic techniques to compute glueball masses for large N, including feasibility in 3+1 dimensions.

Contribution

It introduces a direct method for improving lattice Hamiltonians and extends analytic techniques to SU(N) for large N, enabling new calculations of glueball masses.

Findings

Improved lattice Hamiltonians reduce discretisation errors.

Analytic techniques allow calculation of glueball masses for N up to 25.

Feasibility of applying these methods in 3+1 dimensions is demonstrated.

Abstract

This thesis is concerned with two topics in Hamiltonian lattice gauge theory: improvement and the application of analytic techniques. On the topic of improvement, we develop a direct method for improving lattice Hamiltonians for gluons, in which linear combinations of gauge invariant lattice operators are chosen to cancel the lowest order discretisation errors. On the topic of analytic methods, we extend the techniques that have been used in 2+1 dimensional SU(2) variational calculations for many years, to the general case of SU(N). For this purpose a number of group integrals are calculated in terms of Toeplitz determinants. As generating functions these group integrals allow the calculation of all matrix elements appearing in variational glueball mass calculations in 2+1 dimensions. Making use of these analytic techniques, glueball masses in various symmetry sectors are calculated with N as large as 25 allowing extrapolations to infinite N to be performed. We finish with a feasibility study of applying analytic Hamiltonian techniques in 3+1 dimensional calculations.