Pseudogauge freedom and the SO(3) algebra of spin operators. (English) Zbl 1528.81196
Summary: 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 \(\frac{1}{2}\) 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.
MSC:
| 81T32 | Matrix models and tensor models for quantum field theory |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 70S15 | Yang-Mills and other gauge theories in mechanics of particles and systems |
| 76Y05 | Quantum hydrodynamics and relativistic hydrodynamics |
| 81-10 | Mathematical modeling or simulation for problems pertaining to quantum theory |
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