Quantizations of Momentum Maps and G-Systems

TL;DR

This paper introduces a family of deformation quantizations for momentum maps linked to Lie group actions, enabling anomaly-free quantization of classical invariant Hamiltonians using formal G-systems.

Contribution

It provides an explicit formula for these quantizations and demonstrates their ability to produce anomaly-free quantum Hamiltonians.

Findings

Explicit formula for deformation quantizations of momentum maps

Quantizations parametrized by formal G-systems

Classical invariant Hamiltonians quantized without anomalies

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.