Defining < A^2 > in the finite volume hamiltonian formalism

Details Defining < A^2 > in the finite volume hamiltonian formalism Defining < A^2 > in the finite volume hamiltonian formalism

2002-10-22

arxiv.org/abs/hep-th/0210204v2

Phys.Lett.B552:214-222,2003

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, 2 figures (in 3 parts). Amended references. Modified introduction. Version accepted for publication

Scientific paper

10.1016/S0370-2693(02)03162-3

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.

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