Loop space Hamiltonians and numerical methods for large- N gauge theories

Abstract

We consider large- N gauge theories in the hamiltonian, collective field approach. We derive an alternative collective representation which leads to significant reduction when translation invariance is invoked. It allows for a simplified computer simulation of loop rearrangements and the development of numerical techniques in the hamiltonian, loop space formalism. We proceed to give numerical evidence for validity of our representation and outline a general numerical approach for solving large- N QCD in terms of gauge-invariant Wilson loop variables.