Deformation quantization of rank I Bergman domain

Details Deformation quantization of rank I Bergman domain Deformation quantization of rank I Bergman domain

2011-10-12

arxiv.org/abs/1110.2632v1

Physics

Mathematical Physics

20 pages

Scientific paper

In this paper we present a harmonic oscillator realization of the most degenerate discrete series representations of the $SU(m,1)$ group and the deformation quantization of the coset space $D=SU(m,1)/U(m)$ with the method of coherent state quantization. We study in more detail the case of $m=2$ and give an explicit expression of the star product. Finally we consider a quantum field theory model over the quantized domain $\hat D$.

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