Kinematic Constraints in Generally Covariant Non-Linear Electrodynamics

TL;DR

This paper explores how the motion of electromagnetic fields in generally covariant non-linear electrodynamics relates to spacetime decomposition, providing a systematic method to derive constraints and connecting it to charged particle dynamics.

Contribution

It introduces a novel parametrization approach to derive kinematic constraints in non-linear electrodynamics within a covariant framework, simplifying the analysis of such theories.

Findings

Derived explicit form of super-Hamiltonian constraints

Developed a plug-and-play method for arbitrary non-linear electrodynamics

Connected parametrization with charged particle dynamics

Abstract

In this paper, we show how the motion of physical fields, in particular the electromagnetic potential, is connected with the choice of a space and time decomposition of the background spacetime manifold. The relation of the field dynamics and its kinematic description is derived with the help of the parametrization approach. In this context, we give an original proof for the main statement of this approach. With regard to generally covariant theories, the arising kinematic constraints are investigated for the class of non-linear electrodynamics. We reduce the problem of finding the explicit form of the super-Hamiltonian constraint to the problem of solving two non-linear equations. By this, we provide a plug-and-play approach to find the whole set of constraints for an arbitrary theory of non-linear electrodynamics and apply it to selected examples. Furthermore, it will be shown that the parametrization approach is connected with the description of a charged point particle within its own electromagnetic field.