Inequivalent Quantizations of Yang-Mills Theory on a Cylinder

Abstract

Yang-Mills theories on a 1+1 dimensional cylinder are considered. It is shown that canonical quantization can proceed following different routes, leading to inequivalent quantizations. The problem of the non-free action of the gauge group on the configuration space is also discussed. In particular we re-examine the relationship between ``$\theta$-states" and the fundamental group of the configuration space. It is shown that this relationship does or does not hold depending on whether or not the gauge transformations not connected to the identity act freely on the space of connections modulo connected gauge transformations.

(new references added and minor spelling corrections made) 18 pages, SU-4240-537

References in corpus (3)

• Gauge Theories on a Cylinder
• Gribov ambiguity and non-trivial vacuum structure of gauge theories on a cylinder
• Phase space structure and the path integral for gauge theories on a cylinder

Cited by in corpus (6)

• Dirac Quantization Gravity-Yang-Mills Systems in 1+1 Dimensions
• θ-angle monodromy in two dimensions
• Nonperturbative Stochastic Quantization of the Helix Model
• The Configuration Space of Low-dimensional Yang-Mills Theories
• Topology Change and theta-Vacua in 2D Yang-Mills Theory
• Global Anomalies in Canonical Gravity