Geometric quantization on the super-disk

In this article we discuss the geometric quantization on a certain type of infinite dimensional super-disk. 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-disk. We show that it has a natural symplectic form, and 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. (C) 2001 American Institute of Physics.