Classical History Theory of Vector Fields

TL;DR

This paper extends classical history theory to vector fields, revealing additional degrees of freedom and gauge structures, and analyzing the constraints and symmetries in massive and electromagnetic cases.

Contribution

It introduces a five-component formulation of vector fields in classical history theory, uncovering new gauge structures and constraints.

Findings

Five-component vector fields arise from Poincare group considerations.

Extra degrees of freedom lead to additional second class constraints.

Extended gauge group includes internal and external U(1) transformations.

Abstract

We consider the extension of classical history theory to the massive vector field and electromagnetism. It is argued that the action of the two Poincare groups introduced by Savvidou suggests that the history fields should have five components. The extra degrees of freedom introduced to make the fields five-dimensional result in an extra pair of second class constraints in the case of the massive vector field, and in an extended gauge group in the case of electromagnetism. The total gauge transformations depend on two arbitrary parameters, and contain `internal' and `external' U(1) gauge transformations as subgroups.