Hamiltonian Electric/Magnetic Duality and Lorentz Invariance

TL;DR

This paper explores the Hamiltonian formulation of electric/magnetic duality, revealing how Lorentz invariance constraints lead to duality conditions in gauge theories like Maxwell and Born-Infeld.

Contribution

It demonstrates the connection between Hamiltonian duality invariance and Lorentz invariance constraints, providing a Hamiltonian perspective on gauge theory dualities.

Findings

Hamiltonian form clarifies duality conditions

Lorentz invariance imposes differential constraints

Duality invariance applies to Maxwell and Born-Infeld theories

Abstract

In (3+1) Hamiltonian form, the conditions for the electric/magnetic invariance of generic self-interacting gauge vector actions and the definition of the duality generator are obvious. Instead, (3+1) actions are not intrinsically Lorentz invariant. Imposing the Dirac-Schwinger stress tensor commutator requirement to enforce the latter yields a differential constraint on the Hamiltonian which translates into the usual Lagrangian form of the duality invariance condition obeyed by Maxwell and Born-Infeld theories. We also discuss covariance properties of some analogous scalar models.