Towards a nonperturbative path integral in gauge theories
Feb, 1999Citations per year
Abstract:
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.Note:
- plain Latex, 12 pages, a few changes made and some comments added, a final version to appear in Phys. Lett. B Subj-class: High Energy Physics - Theory; Mathematical Physics
- gauge field theory: Yang-Mills
- path integral: nonperturbative
- Gribov problem
- lattice field theory
- group theory: orbit
- matrix model
- mass: gap
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