Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-02-01
Phys.Lett. B456 (1999) 38-47
Physics
High Energy Physics
High Energy Physics - Theory
plain Latex, 12 pages, a few changes made and some comments added, a final version to appear in Phys. Lett. B
Scientific paper
10.1016/S0370-2693(99)00493-1
We propose a modification of the Faddeev-Popov procedure to construct a path integral representation for the transition amplitude and the partition function for gauge theories whose orbit space has a non-Euclidean geometry. Our approach is based on the Kato-Trotter product formula modified appropriately to incorporate the gauge invariance condition, and thereby equivalence to the Dirac operator formalism is guaranteed by construction. The modified path integral provides a solution to the Gribov obstruction as well as to the operator ordering problem when the orbit space has curvature. A few explicit examples are given to illustrate new features of the formalism developed. The method is applied to the Kogut-Susskind lattice gauge theory to develop a nonperturbative functional integral for a quantum Yang-Mills theory. Feynman's conjecture about a relation between the mass gap and the orbit space geometry in gluodynamics is discussed in the framework of the modified path integral.
Klauder John R.
Shabanov Sergei V.
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