Berezin expectation and Clifford trace

TL;DR

This paper demonstrates a correspondence between Berezin expectation on exterior algebras and trace on Clifford algebras in finite dimensions, using a form of antinormal ordering to establish the connection.

Contribution

It introduces a novel link between Berezin expectation and Clifford trace through a specific ordering technique in finite-dimensional algebras.

Findings

Berezin expectation corresponds to Clifford trace in finite dimensions

Antinormal ordering mediates the correspondence

Provides a new perspective on algebraic structures in mathematical physics

Abstract

We show that in finite dimensions, the Berezin expectation on an exterior algebra corresponds to the trace on a Clifford algebra, the correspondence being mediated by what is effectively a version of antinormal ordering.