The metaplectic correction in 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 construction of metaplectic covers of GLn in characteristic zero

This paper presents a new construction of the m-fold metaplectic cover of GLn over an algebraic number field k, where k contains a primitive m-th root of unity. A 2-cocycle on GLn(A) representing this extension is given and the splitting of the cocycle on GLn(k) is found explicitly. The cocycle is smooth at almost all places of k. As a consequence, a formula for the Kubota symbol on SLn is obta...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

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...

Coherent States in Geometric Quantization

In this paper we study overcomplete systems of coherent states associated to compact integral symplectic manifolds by geometric quantization. Our main goals are to give a systematic treatment of the construction of such systems and to collect some recent results. We begin by recalling the basic constructions of geometric quantization in both the Kähler and non-Kähler cases. We then study the re...