Subtleties and Fancies in Gauge Theory Non Trivial Vacuum

Details Subtleties and Fancies in Gauge Theory Non Trivial Vacuum Subtleties and Fancies in Gauge Theory Non Trivial Vacuum

1994-09-06

arxiv.org/abs/hep-lat/9409002v1

Physics

High Energy Physics

High Energy Physics - Lattice

21 pages, BU-HEP-94-23

Scientific paper

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 $\alpha$, 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.

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