The Weyl quantization and the quantum group quantization of the moduli space of flat SU(2)-connections on the torus are the same

Details The Weyl quantization and the quantum group quantization of the moduli space of flat SU(2)-connections on the torus are the same The Weyl quantization and the quantum group quantization of the moduli space of flat SU(2)-connections on the torus are the same

2002-01-28

arxiv.org/abs/math-ph/0201059v1

Commun.Math.Phys. 233 (2003) 493-512

Physics

Mathematical Physics

18 pages, latex format, 2 figures

Scientific paper

10.1007/s00220-002-0759-3

We prove that, for the moduli space of flat SU(2)-connections on the torus, the Weyl quantization and the quantization using the quantum group of SL(2,C) are unitarily equivalent. This is done by comparing the matrices of the operators associated by the two quantization to cosine functions. We also discuss the *-product of the Weyl quantization and show that it satisfies the product-to-sum formula for noncommutative cosines on the noncommutative torus.

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