Method of Quantum Characters in Equivariant Quantization

Method of quantum characters in equivariant quantization

Let G be a reductive Lie group, g its Lie algebra, and M a G-manifold. Suppose Ah(M) is a Uh(g)-equivariant quantization of the function algebra A(M) on M . We develop a method of restricting Ah(M) to the Uh(g)-equivariant quantization on Gorbits in M . We are concerned with those quantizations that may be simultaneously represented as subalgebras in U∗ h(g) and quotients of Ah(M). It turns out...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

Equivariant Quantization of Orbifolds

Equivariant quantization is a new theory that highlights the role of symmetries in the relationship between classical and quantum dynamical systems. These symmetries are also one of the reasons for the recent interest in quantization of singular spaces, orbifolds, stratified spaces... In this work, we prove existence of an equivariant quantization for orbifolds. Our construction combines an app...

Equivariant Cohomological Chern Characters

We construct for an equivariant cohomology theory for proper equivariant CW -complexes an equivariant Chern character, provided that certain conditions about the coefficients are satisfied. These conditions are fulfilled if the coefficients of the equivariant cohomology theory possess a Mackey structure. Such a structure is present in many interesting examples.

Conformally equivariant quantization

Let (M, g) be a pseudo-Riemannian manifold and Fλ(M) the space of densities of degree λ on M . We study the space D2 λ,μ(M) of second-order differential operators from Fλ(M) to Fμ(M). If (M, g) is conformally flat with signature p− q, then D2 λ,μ(M) is viewed as a module over the group of conformal transformations of M . We prove that, for almost all values of μ− λ, the O(p+1, q+1)-modules D2 λ...