Theoretical Physics(DTP)
Physique théorique (DPT)
Jedrzej SNIATYCKI
University of Calgary
Gauge Symmetries in Yang-Mills Theory
For Yang-Mills equations on the Minkowski space-time, we identify a space P of Cauchy data which admit global solutions, the gauge symmetry GS(P) group of P, and its connected subgroup GS0(P) consisting of the localized gauge transformations that give rise to the constraints of the theory. We show that the constraint set C has a manifold structure, but it is not a submanifold of P. The group GS0(P) acts freely and properly on P. The reduced phase space R=C/GS0(P), consisting of GS0(P) orbits in C is a quotient manifold of C and it inherits the structure of a symplectic manifold with an exact symplectic form. The colour group GS(P)/GS0(P) has a Hamiltonian action on R.
We conclude that, for the Yang-Mills theory in the Minkowski space, geometric quantization commutes with reduction.