QCD on a Torus, and electric flux energies from tunneling

The energy of 't Hooft-type electric flux in pure QCD on the hypertorus is a non-perturbative effect, caused by tunneling through a quantum-induced potential barrier. We calculate the electric flux energy using the semiclassical approximation. The problem of infrared divergences is attacked directly, and we show how to treat them consistently, using Luescher's effective Hamiltonian approach. A toy model is first solved to demonstrate the consistency of our approach. Luescher's effective Hamiltonian for the spatially constant modes in QCD is rederived using a Lagrangian approach with a non-local gauge-fixing term, and we show how this rigorously defines an effective action to all loop orders. The removal of the gauge degrees of freedom from the effective Hamiltonian while avoiding Girbov ambiguities is discussed in detail, as are the numerical methods required to treat this non-integrable system. Some consequences of our final result are noted. copyright 1987 Academic Press, Inc