Phase space structure and the path integral for gauge theories on a cylinder

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 ${\mathbf{R}}^{2r}/W_A,$ $r$ a rank of the gauge group, $W_A$ the affine Weyl group. The 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.

Saclay-T93/078

References in corpus (1)

• Gribov ambiguity and non-trivial vacuum structure of gauge theories on a cylinder

Cited by in corpus (13)

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• The Configuration Space of Low-dimensional Yang-Mills Theories
• Towards a Nonperturbative Path Integral in Gauge Theories
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• The Path Integral for 1+1-dimensional QCD