Polarization in relativistic fluids: a quantum field theoretical derivation

Abstract

We review the calculation of polarization in a relativistic fluid within the framework of statistical quantum field theory. We derive the expressions of the spin density matrix and the mean spin vector both for a single quantum relativistic particle and for a quantum free field. After introducing the formalism of the covariant Wigner function for the scalar and the Dirac field, the relation between spin density matrix and the covariant Wigner function is obtained. The formula is applied to the fluid produced in relativistic nuclear collisions by using the local thermodynamic equilibrium density operator and recovering previously known formulae. The dependence of these results on the spin tensor and pseudo-gauge transformations of the stress-energy tensor is addressed.

arXiv comment24 pages, 1 figure; version published in Lecture Notes in Physics

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Cited by in corpus (25)

• Hydrodynamics of spin currents
• Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation
• Spin polarization induced by the hydrodynamic gradients
• Foundations and Applications of Quantum Kinetic Theory
• Spin and polarization: a new direction in relativistic heavy ion physics
• Analytic solutions of relativistic dissipative spin hydrodynamics with Bjorken expansion
• Theories of Relativistic Dissipative Fluid Dynamics
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• Hydrodynamics, spin currents and torsion
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• QCD phase structure under rotation
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• Vector and Tensor Spin Polarization for Vector Bosons at Local Equilibrium
• Local equilibrium and Lambda polarization in high energy heavy ion collisions
• Kubo formulas for spin polarization in dissipative relativistic spin hydrodynamics: a first-order gradient expansion approach
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• Spin Boltzmann equation for non-relativistic spin-1/2 fermions
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• Probing early-time longitudinal dynamics with the $\Lambda$ hyperon's spin polarization in relativistic heavy-ion collisions
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• A topological realization of spin polarization through vortex formation in collisions of Bose-Einstein condensates