Extensions of the Duflo map and Chern-Simons expectation values

TL;DR

This paper extends the Duflo map to the entire symmetric algebra and applies it to compute expectation values in Chern-Simons theory, enhancing operator ordering techniques in quantum gauge theories.

Contribution

It introduces new extensions of the Duflo map beyond invariant elements and demonstrates their use in calculating Chern-Simons expectation values.

Findings

Extended Duflo map applicable to full symmetric algebra

Improved methods for operator ordering in quantum gauge theories

Successful computation of Chern-Simons expectation values using the extended map

Abstract

The Duflo map is a valuable tool for operator ordering in contexts in which Kirillov-Kostant brackets and their quantizations play a role. A priori, the Duflo map is only defined on the subspace of the symmetric algebra over a Lie algebra consisting of elements invariant under the adjoint action. Here we discuss extensions to the whole symmetric algebra, as well as their application to the calculation of Chern-Simons theory expectation values.