Relativistic observer and Maxwell equations

TL;DR

This paper explores the geometric structure of Maxwell's equations in Minkowski space using Ehresmann connections, introducing concepts like curvature and torque to describe observer-dependent effects.

Contribution

It introduces a geometric framework for Maxwell's equations based on anholonomic observers and defines the novel concept of torque as a measure of connection deviation.

Findings

Connection curvature relates to electromagnetic field geometry

Torque quantifies deviation from principal connections

Geometric terms influence Maxwell's equations in observer-dependent settings

Abstract

The Ehresmann connection on a fiber bundle that is not compatible with a (possible) Lie group structure is illustrated by the geometry of a general anholonomic observer in the Minkowski space. The 3D split of Maxwell's equations induces geometric terms that are the (generalized) curvature and torque of the connection. The notion of torque is introduced here as a Lie coalgebra-valued endomorphism field and measures the deviation of a connection from being principal.