Histories Electromagnetism

TL;DR

This paper develops a histories-based classical and quantum theory of electromagnetism within the HPO formalism, emphasizing foliation dependence and Poincare group actions, extending prior work on field and constrained systems.

Contribution

It introduces a histories formulation of electromagnetism, incorporating foliation dependence and Poincare symmetries, building on previous histories approaches to field and constrained systems.

Findings

Histories phase space and Hilbert space depend on foliation choices.

The theory incorporates two Poincare groups acting on the histories.

Quantisation follows the Dirac scheme for constrained systems.

Abstract

Working within the HPO (History Projection Operator) Consistent Histories formalism, we follow the work of Savvidou on (scalar) field theory and that of Savvidou and Anastopolous on (first-class) constrained systems to write a histories theory (both classical and quantum) of Electromagnetism. We focus particularly on the foliation-dependence of the histories phase space/Hilbert space and the action thereon of the two Poincare groups that arise in histories field theory. We quantise in the spirit of the Dirac scheme for constrained systems.