English

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

Mathematical Physics 2009-11-07 v1 math.MP Quantum Algebra

Abstract

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.

Keywords

Cite

@article{arxiv.math-ph/0201059,
  title  = {The Weyl quantization and the quantum group quantization of the moduli space of flat SU(2)-connections on the torus are the same},
  author = {Razvan Gelca and Alejandro Uribe},
  journal= {arXiv preprint arXiv:math-ph/0201059},
  year   = {2009}
}

Comments

18 pages, latex format, 2 figures