Inequivalent Quantizations of Yang-Mills Theory on a Cylinder

Details Inequivalent Quantizations of Yang-Mills Theory on a Cylinder Inequivalent Quantizations of Yang-Mills Theory on a Cylinder

1993-09-10

arxiv.org/abs/hep-th/9309065v2

Nucl.Phys. B426 (1994) 94-106

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/0550-3213(94)90127-9

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.

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