Path Integral Quantization of the Symplectic Leaves of the SU(2)* Poisson-Lie Group

Details Path Integral Quantization of the Symplectic Leaves of the SU(2)* Poisson-Lie Group Path Integral Quantization of the Symplectic Leaves of the SU(2)* Poisson-Lie Group

1997-10-09

arxiv.org/abs/physics/9710010v1

Int.J.Mod.Phys. A14 (1999) 919-936

Physics

Mathematical Physics

24 pages, LaTeX, no figures, full postscript available from http://phyweb.lbl.gov/theorygroup/papers/40890.ps

Scientific paper

10.1142/S0217751X99000452

The Feynman path integral is used to quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U_q(su(2)). This is achieved by finding explicit Darboux coordinates and then using a phase space path integral. I discuss the *-structure of SU(2)* and give a detailed description of its leaves using various parametrizations and also compare the results with the path integral quantization of spin.

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