$C^*$-algebraic approach to interacting quantum field theory: Inclusion of Fermi fields

TL;DR

This paper extends the $C^*$-algebraic framework for interacting quantum field theory to include Fermi fields by employing auxiliary Grassmann variables in a systematic, functorial manner.

Contribution

It introduces a novel method to incorporate Fermi fields into the $C^*$-algebraic approach using auxiliary Grassmann variables.

Findings

Successful extension of the $C^*$-algebraic approach to Fermi fields

Development of a functorial method with Grassmann variables

Framework compatibility with existing quantum field theories

Abstract

We extend the $C^*$-algebraic approach to interacting quantum field theory, proposed recently by Detlev Buchholz and one of us (KF) to Fermi fields. The crucial feature of our approach is the use of auxiliary Grassmann variables in a functorial way.