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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 inertia. Finally, we consider the Einstein–Cartan theory, an extension of conventional general relativity, which allows for a natural definition of the spin tensor.
Virtual photon polarization and dilepton anisotropy in relativistic nucleus–nucleus collisions
(2018)
The polarization of virtual photons produced in relativistic nucleus–nucleus collisions provides information on the conditions in the emitting medium. In a hydrodynamic framework, the resulting angular anisotropy of the dilepton final state depends on the flow as well as on the transverse momentum and invariant mass of the photon. We illustrate these effects in dilepton production from quark–antiquark annihilation in the QGP phase and π+π− annihilation in the hadronic phase for a static medium in global equilibrium and for a longitudinally expanding system.
It is shown that the description of a relativistic fluid at local thermodynamic equilibrium depends on the particular quantum stress-energy tensor operator chosen, e.g., the canonical or symmetrized Belinfante stress-energy tensor. We argue that the Belinfante tensor is not appropriate to describe a relativistic fluid whose macroscopic polarization relaxes slowly to thermodynamic equilibrium and that a spin tensor, like the canonical spin tensor, is required. As a consequence, the description of a polarized relativistic fluid involves an extension of relativistic hydrodynamics including a new antisymmetric rank-two tensor as a dynamical field. We show that the canonical and Belinfante tensors lead to different predictions for measurable quantities such as spectrum and polarization of particles produced in relativistic heavy-ion collisions.