Electromagnetic energy-momentum in dispersive media

TL;DR

This paper derives an exact energy-momentum tensor for electromagnetic fields in dispersive media using an action principle, clarifying the correct momentum density beyond traditional formulas like Minkowski's.

Contribution

It introduces an action-based method to obtain precise energy and momentum densities in dispersive media, resolving ambiguities in classical approaches.

Findings

Time-averaged energy density matches Brillouin's formula for monochromatic fields.

Momentum density differs from Minkowski's expression, even for monochromatic fields.

Results are robust against debates on light-matter momentum transfer.

Abstract

The standard derivations of electromagnetic energy and momentum in media take Maxwell's equations as the starting point. It is well known that for dispersive media this approach does not directly yield exact expressions for the energy and momentum densities. Although Maxwell's equations fully describe electromagnetic fields, the general approach to conserved quantities in field theory is not based on the field equations, but rather on the action. Here an action principle for macroscopic electromagnetism in dispersive, lossless media is used to derive the exact conserved energy-momentum tensor. The time-averaged energy density reduces to Brillouin's simple formula when the fields are monochromatic. The momentum density is not given by the familiar Minkowski expression $\mathbf{D}\times\mathbf{B}$, even for time-averaged monochromatic fields. The results are unaffected by the debate over momentum balance in light-matter interactions.