Defining 〈A2〉 in the finite volume Hamiltonian formalism

It is shown how in principle for non-Abelian gauge theories it is possible in the finite volume Hamiltonian framework to make sense of calculating the expectation value of ‖A‖2=∫d3x (Aai(x→))2. Gauge invariance requires one to replace ‖A‖2 by its minimum over the gauge orbit, which makes it a highly non-local quantity. We comment on the difficulty of finding an expression for ‖A‖2min analogous to that found for the Abelian case, and the relation of this question to Gribov copies. We deal with these issues by implementing the Hamiltonian on the so-called fundamental domain, with appropriate boundary conditions in field space, essential to correctly represent the physics of the problem.