Defining < A^2 > in the finite volume hamiltonian formalism
Abstract
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=\int d^3x(A^a_i(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 a gauge invariant expression for ||A||^2_{min} 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.
Keywords
Cite
@article{arxiv.hep-th/0210204,
title = {Defining < A^2 > in the finite volume hamiltonian formalism},
author = {L. Stodolsky and Pierre van Baal and V. I. Zakharov},
journal= {arXiv preprint arXiv:hep-th/0210204},
year = {2008}
}
Comments
13 pages, 2 figures (in 3 parts). Amended references. Modified introduction. Version accepted for publication