Electromagnetic 2-forms on space-time

TL;DR

This paper explores the mathematical structure of electromagnetic 2-forms on space-time, linking duality, Maxwell equations, and charge quantization within a Hamiltonian framework for relativistic particles with electric and magnetic charges.

Contribution

It introduces a duality-based formulation of electromagnetic 2-forms on space-time and connects them to Maxwell equations, charge quantization, and a Hamiltonian system for relativistic particles.

Findings

Maxwell equations derived from exterior derivatives of 2-forms

Charge quantization conditions from integrality constraints

Classical Hamiltonian system describing energy and wave propagation

Abstract

Two field 2-forms on the space-time manifold, in a relationship of duality, are presented and included in the extended phase-space structure used to describe relativistic particles having both electric and magnetic charges. By exterior derivatives, these forms yield the two groups of Maxwell equations, while specific integrality conditions ensure magnetic monopole or electric charge quantization. Some properties of the common characteristic vector of the dual 2-forms are discussed. It is shown that the coupled energy-density continuity equation and the eikonal equation represent a classical, infinite-dimensional Hamiltonian system.