Lorentz-covariant kinetic theory for massive spin-1/2 particles

Abstract

We construct a matrix-valued spin-dependent distribution function (MVSD) for massive spin-1/2 fermions and study its properties under Lorentz transformations. Such transformations result in a Wigner rotation in spin space and in a nontrivial matrix-valued shift in space-time, which corresponds to the side jump in the massless case. We express the vector and axial-vector components of the Wigner function in terms of the MVSD and show that they transform in a Lorentz-covariant manner. We then construct a manifestly Lorentz-covariant Boltzmann equation which contains a nonlocal collision term encoding spin-orbit coupling. Finally, we obtain the spin-dependent distribution function in local equilibrium by demanding detailed balance.

7 pages, 1 figure

References in corpus (18)

• Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids
• Lorentz Invariance in Chiral Kinetic Theory
• Shear-induced spin polarization in heavy-ion collisions
• Fate of spin polarization in a relativistic fluid: An entropy-current analysis
• Local polarization and isothermal local equilibrium in relativistic heavy ion collisions
• Spin-thermal shear coupling in a relativistic fluid
• Collisions in Chiral Kinetic Theory
• Spin polarization induced by the hydrodynamic gradients
• Derivation of the nonlocal collision term in the relativistic Boltzmann equation for massive spin-1/2 particles from quantum field theory
• Reexamination of local spin polarization beyond global equilibrium in relativistic heavy ion collisions
• From Kadanoff--Baym to Boltzmann equations for massive spin-1/2 fermions
• Mass Correction to Chiral Kinetic Equations
• Spin polarization evolution in a boost invariant hydrodynamical background
• Pseudogauge dependence of the spin polarization and of the axial vortical effect
• Quantum Kinetic Theory for Quantum Electrodynamics
• Spin Polarization Formula for Dirac Fermions at Local Equilibrium
• Kinetic theory with spin: From massive to massless fermions
• Relativistic spin sum rules and the role of the pivot

Cited by in corpus (7)

• Relativistic second-order spin hydrodynamics: an entropy-current analysis
• Chiral Magnetic Effect in Heavy Ion Collisions: The Present and Future
• Damping of spin waves
• Resummed spin hydrodynamics from quantum kinetic theory
• Collisional corrections to spin polarization from quantum kinetic theory using Chapman-Enskog expansion
• The spin alignment of vector mesons with light front quarks
• Generalized Chiral Kinetic Equations