Weyl Quantization from Geometric Quantization

نویسنده

  • P. de M. Rios
چکیده

In [23] a nice looking formula is conjectured for a deformed product of functions on a symplectic manifold in case it concerns a hermitian symmetric space of non-compact type. We derive such a formula for simply connected symmetric symplectic spaces using ideas from geometric quantization and prequantization of symplectic groupoids. We compute the result explicitly for the natural 2-dimensional symplectic manifolds R2, H2, and S2. For R2 we obtain the well known Moyal-Weyl product. The other cases show that the original idea in [23] should be interpreted with care.

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تاریخ انتشار 2008