Magnetic moment, vorticity-spin coupling and parity-odd conductivity of chiral fermions in 4-dimensional Wigner functions

TL;DR

This paper explores how 4D Wigner functions describe magnetic moments, spin-vorticity coupling, and parity-odd conductivity of chiral fermions, unifying various physical phenomena in electromagnetic fields.

Contribution

It demonstrates the emergence of magnetic moments and spin-vorticity coupling in 4D Wigner functions and derives parity-odd conductivity in linear response theory, connecting to known loop results.

Findings

Magnetic moment and spin-vorticity coupling are captured by 4D Wigner functions.

Parity-odd electric conductivity is derived consistent with loop calculations.

Wigner functions provide a comprehensive description of chiral fermion physics in electromagnetic fields.

Abstract

We demonstrate the emergence of the magnetic moment and spin-vorticity coupling of chiral fermions in 4-dimensional Wigner functions. In linear response theory with space-time varying electromagnetic fields, the parity-odd part of the electric conductivity can also be derived which reproduces results of the one-loop and the hard-thermal or hard-dense loop. All these properties show that the 4-dimensional Wigner functions capture comprehensive aspects of physics for chiral fermions in electromagnetic fields.