Towards a Nonperturbative Path Integral in Gauge Theories
arXiv:hep-th/9902017 · doi:10.1016/S0370-2693(99)00493-1
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.
plain Latex, 12 pages, a few changes made and some comments added, a final version to appear in Phys. Lett. B
References in corpus (5)
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- Lattice Coulomb Hamiltonian and Static Color-Coulomb Field
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Cited by in corpus (6)
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- Impact of the strong electromagnetic field on the QCD effective potential for homogeneous Abelian gluon field configurations
- Gribov Problem for Gauge Theories: a Pedagogical Introduction
- Domain wall network as QCD vacuum and the chromomagnetic trap formation under extreme conditions
- Quantisation without Gauge Fixing: Avoiding Gribov Ambiguities through the Physical Projector
- Energy-driven disorder in the mean field QCD