On the existence of star products on quotient spaces of linear Hamiltonian torus actions

TL;DR

This paper proves that reduced spaces from linear Hamiltonian torus actions admit continuous star products by analyzing the BFV deformation quantization and the acyclicity of the Koszul complex on the moment map.

Contribution

It demonstrates the existence of star products on quotient spaces of linear Hamiltonian torus actions using BFV quantization and Koszul complex analysis.

Findings

Koszul complex on the moment map is acyclic for effective linear actions

Rephrases nonpositivity condition for linear Hamiltonian torus actions

Reduced spaces admit continuous star products

Abstract

We discuss BFV deformation quantization of singular symplectic quotient spaces in the special case of linear Hamiltonian torus actions. In particular, we show that the Koszul complex on the moment map of an effective linear Hamiltonian torus action is acyclic. We rephrase the nonpositivity condition of Arms, Gotay and Jennings for linear Hamiltonian torus actions. It follows that reduced spaces of such actions admit continuous star products.