It is shown that for a gauge theory with a semisimple Lie group, all gauge orbits intersect a hyperplane in A-space in a convex region Ω which is bounded in every direction. This bounded region is the configuration space of the theory and is the support of the euclidean or Coulomb gauge functional measure. It is shown that the domain of definition of the effective action Γ is Ω, and that it is a real concave function in Ω which approaches +∞ on the boundary of Ω. It is shown that flat and partially flat configurations, including the naive vacuum F(A) = 0, lie on the boundary of Ω and have effective action +∞.
ASJC Scopus subject areas
- Nuclear and High Energy Physics