Thermodynamical Inequivalence of Stress-Energy and Spin Tensors

Abstract

It is shown that different pairs of stress-energy-momentum and spin tensors of quantum relativistic fields, which are commonly believed to be equivalent in special relativity, are in fact inequivalent. Different tensors imply different mean values of physical quantities like four-momentum and angular momentum density, and, in non-equilibrium situation, entropy production and transport coefficients. This result implies that specific stress-energy-momentum and spin tensors are physically meaningful even in the absence of gravitational coupling and raises the issue of finding the right pair (or the right class of pairs) of tensors. The existence of a non-vanishing spin tensor and, especially, a non symmetric stress-energy-momentum tensor would have major consequences in hydrodynamics, gravity and cosmology.