Geometric Quantization on the Super-Disc

Details Geometric Quantization on the Super-Disc Geometric Quantization on the Super-Disc

2000-11-11

arxiv.org/abs/math-ph/0011018v1

Physics

Mathematical Physics

17 pages, Latex file. Subject: Mathematical physics, geometric quantization

Scientific paper

In this article we discuss the geometric quantization on a certain type of infinite dimensional super-disc. Such systems are quite natural when we analyze coupled bosons and fermions. The large-N limit of a system like that corresponds to a certain super-homogeneous space. First, we define an example of a super-homogeneous manifold: a super-disc. We show that it has a natural symplectic form, it can be used to introduce classical dynamics once a Hamiltonian is chosen. Existence of moment maps provide a Poisson realization of the underlying symmetry super-group. These are the natural operators to quantize via methods of geometric quantization, and we show that this can be done.

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