Covariant Energy Density in Free Massless Field Theory

Abstract

We have discovered a covariant stress tensor for free massless field theories of integer spin. We construct and explicitly give this tensor. Until now, no covariant stress tensor was known in such theories except for the anomalous cases of spins 0 and 1. Indeed, we show that for massless field theories of spin greater than 1, no ordinary second-rank stress tensor can even exist. It is thus significant that the stress tensor we have found belongs to an infinite-dimensional representation of the homogeneous Lorentz group. This infinite-component stress tensor has remarkable properties which we study in detail.