The necessity of wheels in universal quantization formulas

TL;DR

This paper proves that in formal deformation quantization, all universal quantization formulas must include graphs with wheels, highlighting a fundamental structural requirement.

Contribution

It offers an elementary proof demonstrating the unavoidable presence of wheels in universal quantization formulas.

Findings

Universal quantization formulas involve graphs with wheels

Wheels are necessary in the structure of these formulas

Elementary proof provided for this necessity

Abstract

In the context of formal deformation quantization, we provide an elementary argument showing that any universal quantization formula necessarily involves graphs with wheels.