Higgs phase in non-Abelian gauge theories

Abstract

June 1981 LBL-12840 HIGGS PHASE IN NON-ABELIAN GAUGE THEORIES* Omer Sefik Kaymakcalan Lawrence Berkeley Laboratory University of California Berkeley, California 94720 ABSTRACT In this work, we consider a non-Abeliai gauge theory involving scalar fields with non-tachyonic mass te 5 in the Lagrangian and we wish to construct a finite energy density trial vacuum for this theory. The usual scalar potential arguments suggest that the vacuum of such a theory would be in the perturba- tive phase. However, the obvious choices for a vacuum in this phase, the Axial gauge and the Coulomb gauge bare vacua, do not have finite energy densities even with an ultraviolet cutoff. Indeed it is a non-trivial problem to construct finite energy density vacua for non-Abelian gauge theories and this is intimately connected with the gauge fixing degeneracies of these theories. Since the gauge fixing is achieved in the Unitary gauge, this suggests that the Unitary gauge bare vacuum might be a finite energy trial vacuum and, despite the form of the scalar potential, the vacuum of this theory might be in a Higgs phase rather than the perturbative phase. In the first Chapter, we give a general discussion of the phases of a gauge theory and its gauge fixing degeneracies. This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract Number W-740S-ENG-48. v