Prequantization, Geometric Quantization, Corrected Geometric Quantization

Weyl Quantization from Geometric Quantization

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...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

Geometric Quantization; a Crash Course

Early in 2011 Sam Evens acting on behalf of the organizers of a summer school on quantization at Notre Dame asked me to give a short series of lectures on geometric quantization. These lectures were meant to prepare a group of graduate mathematics students for talks at the conference on quantization which were to follow the summer school. I was told to assume that the students had attended an i...

Geometric Quantization for Proper Actions

We first introduce an invariant index for G-equivariant elliptic differential operators on a locally compact manifold M admitting a proper cocompact action of a locally compact group G. It generalizes the Kawasaki index for orbifolds to the case of proper cocompact actions. Our invariant index is used to show that an analog of the Guillemin-Sternberg geometric quantization conjecture holds if M...

Geometric Quantization on the Superdisc

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 superhomogeneous manifold: a super-disc. We show that it has a natural symplectic form, it...