A Counter Example of Invariant Deformation Quantization

TL;DR

This paper presents a specific example demonstrating that certain Hamiltonian Lie algebra actions do not admit an invariant star product, challenging assumptions about invariant deformation quantization.

Contribution

It provides the first explicit counterexample showing the non-existence of invariant star products for some Hamiltonian Lie algebra actions.

Findings

Identifies a Hamiltonian Lie algebra action with no invariant star product

Challenges previous beliefs about invariant deformation quantization

Provides insight into limitations of deformation quantization methods

Abstract

In this note, we will show one example of hamiltonian Lie algebra action which has no invariant star product.