Spin tensor and pseudo-gauges: from nuclear collisions to gravitational physics

TL;DR

This paper explores the ambiguities in relativistic spin decomposition via pseudo-gauge transformations, analyzing their physical implications in nuclear collisions and gravitational theories, and emphasizing the importance of gauge-invariant operators.

Contribution

It provides a detailed analysis of pseudo-gauge transformations, their impact on spin tensors, and their relevance in relativistic hydrodynamics, quantum kinetics, and gravitational theories.

Findings

Pseudo-gauge transformations affect the decomposition of angular momentum.

The spin vector can be defined as a pseudo-gauge invariant operator.

Connections are established between pseudo-gauge choices and the relativistic center of mass.

Abstract

The relativistic treatment of spin is a fundamental subject which has an old history. In various physical contexts it is necessary to separate the relativistic total angular momentum into an orbital and spin contribution. However, such decomposition is affected by ambiguities since one can always redefine the orbital and spin part through the so-called pseudo-gauge transformations. We analyze this problem in detail by discussing the most common choices of energy-momentum and spin tensors with an emphasis on their physical implications, and study the spin vector which is a pseudo-gauge invariant operator. We review the angular momentum decomposition as a crucial ingredient for the formulation of relativistic spin hydrodynamics and quantum kinetic theory with a focus on relativistic nuclear collisions, where spin physics has recently attracted significant attention. Furthermore, we point out the connection between pseudo-gauge transformations and the different definitions of the relativistic center of mass. Finally, we consider the Einstein-Cartan theory, an extension of conventional general relativity, which allows for a natural definition of the spin tensor.