The Weyl Quantization and the Quantum Group Quantization of the Moduli Space of Flat SU(2)-Connections on the Torus are the Same

Abstract:

 We prove that, for the moduli space of flat SU(2)-connections on the 2-dimensional torus, the Weyl quantization and the quantization performed using the quantum group of SL(2,C) are the same. This is done by comparing the matrices of the operators associated through the two quantizations 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.