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

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.

6 pages

References in corpus (5)

• Thermodynamical inequivalence of quantum stress-energy and spin tensors
• Pseudogauge dependence of the spin polarization and of the axial vortical effect
• Pseudo-gauges and relativistic spin hydrodynamics for interacting Dirac and Proca fields
• Relativistic corrections to the algebra of position variables and spin-orbital interaction
• Pseudo-gauge dependence of quantum fluctuations of energy in a hot relativistic gas of fermions

Cited by in corpus (9)

• Theories of Relativistic Dissipative Fluid Dynamics
• Emergent Canonical Spin Tensor in the Chiral-Symmetric Hot QCD
• Euler-Poisson equations of a dancing spinning top, integrability and examples of analytical solutions
• Dynamical constraints on pseudo-gauge transformations
• Mean free path of photons in relativistic heavy ion collisions
• Polarization of spin-1/2 particles with effective spacetime dependent masses
• Application range of perfect spin hydrodynamics
• Dynamics on a submanifold: intermediate formalism versus Hamiltonian reduction of Dirac bracket, and integrability
• On the non-uniqueness of the energy-momentum and spin currents