Quantum Kinetic Equation for Fluids of Spin-1/2 Fermions

TL;DR

This paper develops a quantum kinetic framework for spin-1/2 fermion fluids, deriving covariant equations that incorporate noninertial effects and electromagnetic interactions, and explores their nonrelativistic and massless limits.

Contribution

It introduces a new covariant quantum kinetic equation for fermions that accounts for noninertial and electromagnetic effects, unifying massless and massive cases.

Findings

Derived covariant kinetic equations for fermions including noninertial effects.

Established nonrelativistic limit leading to a novel 3D transport theory.

Confirmed consistency of the 3D chiral transport with the chiral anomaly.

Abstract

Fluid of spin-1/2 fermions is represented by a complex scalar field and a four-vector field coupled both to the scalar and the Dirac fields. We present the underlying action and show that the resulting equations of motion are identical to the (hydrodynamic) Euler equations in the presence of Coriolis force. As a consequence of the gauge invariances of this action we established the quantum kinetic equation which takes account of noninertial properties of the fluid in the presence of electromagnetic fields. The equations of the field components of Wigner function in Clifford algebra basis are employed to construct new semiclassical covariant kinetic equations of the vector and axial-vector field components for massless as well as massive fermions. Nonrelativistic limit of the chiral kinetic equation is studied and shown that it generates a novel three-dimensional transport theory which does not depend on spatial variables explicitly and possesses a Coriolis force term. We demonstrated that the three-dimensional chiral transport equations are consistent with the chiral anomaly. For massive fermions the three-dimensional kinetic transport theory generated by the new covariant kinetic equations is established in small mass limit. It possesses the Coriolis force and the massless limit can be obtained directly.