Abstract
Based on the Wigner function for an medium with thermal vorticity, an exact non-perturbative formula for axial current was obtained. It is confirmed that the Chiral Vortical Effect results from the Wigner function. It is shown that the angular velocity and acceleration play the role of new chemical potentials, which is expressed in the appearance of combination $$\mu \pm \,(\Omega \pm i\left| a \right|)/2$$. It is shown that acceleration enters in the form of imaginary chemical potential and the consequences of this fact are investigated. An expression for the boundary temperature for a medium of fermions, which simultaneously has acceleration and rotation, is derived. This temperature in the particular case coincides with the temperature of Unruh.
Highlights
A variety of remarkable effects have been discovered, which lie on the border of relativistic hydrodynamics and quantum field theory
It is shown that the angular velocity and acceleration play the role of new chemical potentials, which is expressed in the appearance of combination μ ± (Ω ± i|a|)/2
It was shown that the rotation of a liquid of massless fermions - a chiral fluid - leads to the appearance of an axial current along an angular velocity, which is the essence of the CVE
Summary
A variety of remarkable effects have been discovered, which lie on the border of relativistic hydrodynamics and quantum field theory. We will use a quantumstatistical approach based on the covariant Wigner function for a medium with thermal vorticity, proposed in [12] This Wigner function was used in analysing the effects of non-stationary motion of a medium in the energy-momentum tensor, vector and axial current, and other observable quantities [6, 12, 13]. We derive a formula for the axial current in the general case of massive fermions [16] For this purpose we summarize the full series in thermal vorticity, and the expression obtained is non-perturbative. The following sections will explore the consequences of this curious fact
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