# Lorentz covariant and gauge invariant description of orbital and spin angular momentum and the non-symmetric energy momentum tensor

## TL;DR

This paper presents a covariant, gauge-invariant method to separate orbital and spin angular momentum in electrodynamics, resolving longstanding paradoxes and deriving a consistent spin vector from the non-symmetric energy-momentum tensor.

## Contribution

It introduces a covariant, gauge-invariant framework for decomposing electromagnetic angular momentum, addressing issues with the non-symmetric energy-momentum tensor.

## Key findings

- Derived a covariant gauge-invariant spin vector
- Resolved the paradox of plane wave spin angular momentum
- Provided a gauge-independent separation of angular momentum components

## Abstract

Starting from covariant expressions, a gauge independent separation of orbital and spin angular momentum for electrodynamics is presented. This results from the non-symmetric canonical energy momentum tensor of the electromagnetic field. The origin of the difficulty is discussed and a covariant gauge invariant spin vector is derived. The paradox concerning the spin angular momentum of a plane wave finds a natural solution.