The universal C*-algebra of the electromagnetic field

TL;DR

This paper constructs a universal C*-algebra for the electromagnetic field that can be embedded in any quantum field theory with electromagnetism, capturing fundamental features like Maxwell's equations and causality.

Contribution

It introduces a universal algebra framework for the electromagnetic field that encodes topological and dynamical properties across quantum theories.

Findings

The algebra encodes Maxwell's equations and causality.

Representation theory focuses on vacuum states.

Topological properties lead to central commutation relations.

Abstract

A universal C*-algebra of the electromagnetic field is constructed. It is represented in any quantum field theory which incorporates electromagnetism and expresses basic features of this field such as Maxwell's equations, Poincar\'e covariance and Einstein causality. Moreover, topological properties of the field resulting from Maxwell's equations are encoded in the algebra, leading to commutation relations with values in its center. The representation theory of the algebra is discussed with focus on vacuum representations, fixing the dynamics of the field.