Quantizations of Momentum Maps and G-Systems

Abstract

In this note, we give an explicit formula for a family of deformation quantizations for the momentum map associated with the cotangent lift of a Lie group action on Rd. This family of quantizations is parametrized by the formal G-systems introduced by the authors in a previous paper and allows us to obtain classical invariant Hamiltonians that quantize without anomalies with respect to the quantizations of the action prescribed by the formal G-systems.