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

L. Stodolsky·Pierre van Baal·V. I. Zakharov
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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.

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L. Stodolsky, Pierre van Baal, V. I. Zakharov. 2002-12-04. Defining < A^2 > in the finite volume hamiltonian formalism. https://doi.org/10.1016/s0370-2693(02)03162-3

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