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

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.

Solitons in spin-tensor–momentum-coupled Bose–Einstein condensates

Recently spin-tensor–momentum coupling (STMC) has been proposed to realize in the Bose–Einstein condensate (BEC). Here, we study the bright soliton in spin-1 three components BEC with STMC. The properties of the bright solitons are discussed by the analytical solutions and numerical solutions. In addition, we also study its dynamic evolution and discover the spontaneous motion, which is different from the spin-orbit-coupled solitons.