Abstract

We show that spin polarization of a fermion in a relativistic fluid at local thermodynamic equilibrium can be generated by the symmetric derivative of the four-temperature vector, defined as thermal shear. As a consequence, besides vorticity, acceleration and temperature gradient, also the shear tensor contributes to the polarization of particles in a fluid. This contribution to the spin polarization vector, which is entirely non-dissipative, adds to the well known term proportional to thermal vorticity and may thus have important consequences for the solution of the local polarization puzzles observed in relativistic heavy ion collisions.

Highlights

  • In a rotating fluid at global thermodynamic equilibrium, particle spin gets polarized along the direction of the angular velocity vector by an amount which is proportional to ω/KT

  • In a relativistic fluid at local thermodynamic equilibrium, the covariant form of statistical mechanics dictates that spin polarization is driven by thermal vorticity: μν

  • We will show that the symmetric gradient of β contributes to the spin at local thermodynamic equilibrium at the leading order. This term is non-dissipative as well as non-local for it depends on a specific 3D integration hypersurface and implies a new relativistic effect, namely a coupling between spin and the shear tensor in a relativistic fluid

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Summary

INTRODUCTION

In a rotating fluid at global thermodynamic equilibrium, particle spin gets polarized along the direction of the angular velocity vector by an amount which is proportional to ω/KT. This phenomenon is the essence of the Barnett effect [1] and it has been known for a long time. We will show that the symmetric gradient of β contributes to the spin at local thermodynamic equilibrium at the leading order This term is non-dissipative as well as non-local for it depends on a specific 3D integration hypersurface and implies a new relativistic effect, namely a coupling between spin and the shear tensor in a relativistic fluid. Operators in Hilbert space will be denoted by a wide upper hat, e.g. H, except the Dirac field operator which is denoted by a Ψ

LOCAL THERMODYNAMIC EQUILIBRIUM AND ITS GRADIENT EXPANSION
SPIN AND THERMAL SHEAR TENSOR
DISCUSSION AND CONCLUSIONS
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