Pseudogauge freedom and the SO(3) algebra of spin operators

TL;DR

This paper examines the pseudogauge freedom in relativistic hydrodynamics with spin, concluding that the canonical spin tensor uniquely satisfies the SO(3) algebra, making it more suitable for describing spin-polarization observables.

Contribution

It demonstrates that among various pseudogauges, only the canonical spin tensor correctly reproduces the SO(3) algebra of angular momentum, clarifying its importance in physical applications.

Findings

Canonical spin tensor obeys the SO(3) algebra.

Pseudogauge choice affects physical quantity calculations.

Canonical form is better for spin-polarization studies.

Abstract

The energy-momentum and spin tensors for a given theory can be replaced by alternative expressions that obey the same conservation laws for the energy, linear momentum, as well as angular momentum but, however, differ by the local redistribution of such quantities (with global energy, linear momentum, and angular momentum remaining unchanged). This arbitrariness is described in recent literature as the pseudogauge freedom or symmetry. In this letter, we analyze several pseudogauges used to formulate the relativistic hydrodynamics of particles with spin 1/2 and conclude that the canonical version of the spin tensor has an advantage over other forms as only the canonical definition defines the spin operators that fulfill the SO(3) algebra of angular momentum. This result sheds new light on the results encountered in recent papers demonstrating pseudogauge dependence of various physical quantities. It indicates that for spin-polarization observables, the canonical version is fundamentally better suited for building a connection between theory and experiment.