Background field quantization and non-commutative Maxwell theory

We quantize non-commutative Maxwell theory canonically in the background field gauge for weak and slowly varying background fields. We determine the complete basis for expansion under such an approximation. As an application, we derive the Wigner function which determines the leading order high temperature behavior of the perturbative amplitudes of noncommutative Maxwell theory. To leading order, we also give a closed form expression for the distribution function for the non-commutative U(1) gauge theory at high temperature. (C) 2003 Published by Elsevier B.V.