Hamiltonian dynamics of the parametrized electromagnetic field

TL;DR

This paper explores the Hamiltonian formulation of a parametrized electromagnetic field, revealing how gauge symmetries and parametrization influence the system's dynamics and constraint structure.

Contribution

It introduces a geometric, coordinate-free approach to analyze the interplay between parametrization and gauge symmetries in electromagnetic fields, identifying sectors with varying dynamical degrees of freedom.

Findings

Identification of sectors with different numbers of independent Hamiltonian vector fields

Explanation of non-trivial behavior and pathologies in the system

Clarification of the relationship between parametrization and gauge symmetries

Abstract

We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies.