Dynamical constants for electromagnetic fields with elliptic-cylindrical symmetry

TL;DR

This paper introduces a new dynamical variable for free electromagnetic fields with elliptic-cylindrical symmetry, revealing a conservation law linked to a second-order symmetry generator, impacting atomic interactions with such fields.

Contribution

It identifies a novel dynamical constant for electromagnetic fields with elliptic symmetry, extending understanding beyond standard Noether theorem applications.

Findings

New dynamical variable for elliptic-cylindrical electromagnetic fields

Conservation law associated with second-order symmetry generator

Implications for atomic systems interacting with these fields

Abstract

Taking into account the characteristics of a free scalar field in elliptic coordinates, a new dynamical variable is found for the free electromagnetic field. The conservation law associated to this variable cannot be obtained by direct application of standard Noether theorem since the symmetry generator is of second order. Consequences on the expected mechanical behavior of an atomic system interacting with electromagnetic waves exhibiting such a symmetry are also discussed.