Electromagnetic stress-energy tensor is a direct consequence of 3- and 6-dimensional left-and right-helical representations of the Lorentz group

TL;DR

This paper demonstrates that the electromagnetic stress-energy tensor naturally arises from the 3- and 6-dimensional representations of the Lorentz group, linking group theory to electromagnetic energy-momentum distribution.

Contribution

It introduces a 6-dimensional irreducible Lorentz representation for electromagnetic vectors and connects it to the stress-energy tensor via helicity state density matrices.

Findings

Stress-energy tensor derived from helicity state density matrices

New 6-dimensional Lorentz representation for electromagnetic vectors

Link between group representations and electromagnetic energy-momentum

Abstract

We review 3-d reducible representation of the Lorentz group and introduce a 6-d irreducible representation tailored for transforming 6-d electromagnetic vector, and we show that the mixture of the density matrices associated with the left- and right-helical states is equivalent to the electromagnetic stress-energy tensor.