Spin-dependent distribution functions for relativistic hydrodynamics of spin-1/2 particles

Understand

Recently advocated expressions for the phase-space dependent spin-1/2 density matrices of particles and antiparticles are analyzed in detail and reduced to the forms linear in the Dirac spin operator.

• This allows for a natural determination of the spin polarization vectors of particles and antiparticles by the trace of products of the spin density matrices and the Pauli matrices.
• We demonstrate that the total spin polarization vector obtained in this way agrees with the Pauli-Lubanski four-vector, constructed from an appropriately chosen spin tensor and boosted to the particle rest frame.
• We further show that several forms of the spin tensor used in the literature give the same Pauli-Lubanski four-vector.