The Lorentz Force Law and Spacetime Symmetries

TL;DR

This paper demonstrates that, under flat spacetime assumptions, the Lorentz force law naturally emerges from the most general Poincare group representation, linking spacetime symmetries to charged particle trajectories.

Contribution

It shows that the Lorentz force law can be derived from spacetime symmetry principles using Poincare group representations, without assuming electromagnetic fields a priori.

Findings

Curves with parallel transported tangent vectors have accelerations as scalar products with an antisymmetric tensor.

Charged particle paths in electromagnetic fields follow from spacetime symmetry considerations.

The Lorentz force law is consistent with the most general Poincare group representation.

Abstract

Assume that arc length is measured with the flat spacetime metric. Then, for the most general Poincare group representation for translating 4-vectors, curves with parallel translated tangent vectors must have accelerations that are the scalar product of the tangent vector with an antisymmetric tensor. Such curves are the paths of charged particles in an electromagnetic field.