Equivalence of canonical and phenomenological formulations of spin hydrodynamics

Abstract

Two formulations of relativistic hydrodynamics of particles with spin 1/2 are compared. The first one uses expressions for the energy-momentum and spin tensors that have properties that follow a direct application of Noether's theorem, including a totally antisymmetric spin tensor. The other one is based on a simplified form of the spin tensor that is commonly used in the current literature under the name of phenomenological pseudo-gauge. We show that these two frameworks are equivalent, since they can be directly connected by a suitably defined pseudogauge transformation. Our analysis uses arguments related to the positivity of entropy production. The latter turns out to be independent of the pseudo-gauge provided the canonical energy-momentum tensor is properly improved.

Gyrohydrodynamics: Relativistic spinful fluid with strong vorticity

“…As we will demonstrate, the constitutive relations in gyrohydrodynamics have much richer structure than those in spin hydrodynamics [32,34,35,43,45,46,[51][52][53]. Firstly, the leading-order constitutive relation describes the anisotropic pressure induced by strong vorticity.…”

New developments in relativistic magnetohydrodynamics

“…Then, in a similar manner as we present in this article, one can construct the spin hydrodynamics in an order-by-order analysis in the derivative expansion (see, e.g., Refs. [122,124,[264][265][266][267][268][269][270][271][272][273][274][275][276][277][278]).…”

Boost invariant spin hydrodynamics within the first order in derivative expansion

“…In this work, we present an analysis of boost-invariant solutions of the spin hydrodynamic equations formulated by Hattori et al in Ref. [13] and investigated later in a series of publications [14,18,19,51,52]. The approach of Ref.…”

“…Several approaches for describing relativistic hydrodynamics for spin-polarized fluids have been developed as a result of the successes of the relativistic dissipative hydrodynamic framework in heavyion phenomenological research [11,12]. Different frameworks have been constructed using entropy current analysis [13][14][15][16][17][18][19], relativistic kinetic theory [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], effective Lagrangian approach [36][37][38][39], quantum statistical density operators [40][41][42][43][44], equilibrium partition functions [45], and holography [46,47]. To allow for future dynamic simulations of spin polarization [48][49][50], a consistent framework of relativistic hydrodynamics with spin degrees of freedom (spin hydrodynamics) is currently being built.…”