Invariant measure in hot gauge theories 1

We investigate properties of the invariant measure for the A0 gauge field in finite temperature gauge theories both on the lattice and in the continuum theory. We have found the cancellation of the naive measure in both cases. The result is quite general and holds at any finite temperature. We demonstrate, however, that there is no cancellation at any temperature for the invariant measure contribution understood as Z(N ) symmetrical distribution of gauge field configurations. The spontaneous breakdown of Z(N ) global symmetry is entirely due to the potential energy term of the gluonic interaction in the effective potential. The effects of this measure on the effective action, mechanism of confinement and A0 condensation are discussed. Work was partially supported by Bundesministerium für Wissenschaft, Forschung und Kunst of Austria and by International Science Foundation Grant K4W 100. email: [email protected] email: [email protected]