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.

24 pages, 1 figure; version published in Lecture Notes in Physics

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• Theories of Relativistic Dissipative Fluid Dynamics
• Local and global polarization of $\Lambda$ hyperons across RHIC-BES energies: the roles of spin hall effect, initial condition and baryon diffusion
• Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: scalar field
• Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: Dirac field
• Hydrodynamics, spin currents and torsion
• Analytic solutions of relativistic dissipative spin hydrodynamics with radial expansion in Gubser flow
• QCD phase structure under rotation
• Spin polarization induced by magnetic field and the relativistic Barnett effect
• Fluctuating Relativistic hydrodynamics from Crooks theorem
• 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
• Polarization in heavy ion collisions: a theoretical review
• Polarization as a signature of local parity violation in hot QCD matter
• Spin Boltzmann equation for non-relativistic spin-1/2 fermions
• Probing early-time longitudinal dynamics with the $\Lambda$ hyperon's spin polarization in relativistic heavy-ion collisions
• A topological realization of spin polarization through vortex formation in collisions of Bose-Einstein condensates
• An improved formula for Wigner function and spin polarization in a decoupling relativistic fluid at local thermodynamic equilibrium