A closed expression of the Euclidean Wilson-loop functional is derived for pure Yang-Mills continuum theories with gauge groups SU(N) and U(1) and space-time topologies ℝ1 × ℝ1 and ℝ1 × S1. (For the U(1) theory, we also consider the S1 × S1 topology.) The treatment is rigorous, manifestly gauge invariant, manifestly invariant under area preserving diffeomorphisms and handles all (piecewise analytic) loops in one stroke. Equivalence between the resulting Euclidean theory and and the Hamiltonian framework is then established. Finally, an extension of the Osterwalder-Schrader axioms for gauge theories is proposed. These axioms are satisfied in the present model.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics