Electromagnetic field with constraints and Papapetrou equation

TL;DR

This paper derives a geometric optical description of polarized electromagnetic waves in curved space-time from a variational principle, revealing connections to Papapetrou equations for massless particles with helicity.

Contribution

It introduces a novel variational framework that reduces electromagnetic fields to locally plane monochromatic waves, linking polarization, local frames, and null-curves to Papapetrou equations.

Findings

Derivation of geometric optics from variational principle

Introduction of constraints leading to local frame variables

Connection between electromagnetic wave dynamics and Papapetrou equations

Abstract

It is shown that geometric optical description of electromagnetic wave with account of its polarization in curved space-time can be obtained straightforwardly from the classical variational principle for electromagnetic field. For this end the entire functional space of electromagnetic fields must be reduced to its subspace of locally plane monochromatic waves. We have formulated the constraints under which the entire functional space of electromagnetic fields reduces to its subspace of locally plane monochromatic waves. These constraints introduce variables of another kind which specify a field of local frames associated to the wave and contain some congruence of null-curves. The Lagrangian for constrained electromagnetic field contains variables of two kinds, namely, a congruence of null-curves and the field itself. This yields two kinds of Euler-Lagrange equations. Equations of first kind are trivial due to the constraints imposed. Variation of the curves yields the Papapetrou equations for a classical massless particle with helicity 1.