Abstract
The physical phase space of gauge field theories on a cylindrical spacetime with an arbitrary compact simple gauge group is shown to be the quotient R 2r W A , r a rank of the gauge group, W A the affine Weyl group. The path integral (PI) formula resulting from Dirac's operator method contains a symmetrization with respect to W A rather than the integration domain reduction. It gives a natural solution to Gribov's problem. Some features of fermion quantum dynamics caused by the nontrivial phase space geometry are briefly discussed.
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