Subtleties and Fancies in Gauge Theory Non Trivial Vacuum

Abstract

The one loop effective potential for a non-Abelian gauge configuration is analyzed using the background field method. The Savvidy result and the non-Abelian ansatz, the other alternative possible background that generates a constant color magnetic field configuration, are compared. This second possibility is very interesting because it avoids the possible coordinate singularity, ${\rm Det}B_i^a=0$, and it is easy to implement in lattice simulations. We emphasize the interesting dependence of the potential by the gauge fixing parameter $α$, when the loop expansion is performed around a non trivial background configuration. Finally, we point out some crucial differences in analyzing the vacuum structure between non-Abelian gauge theories and the cases of scalar and Abelian gauge theories.