Abstract
Statistical average of the axial current is evaluated on the basis of the covariant Wigner function. In the resulting formula, chemical potential $\mu$, angular velocity $\Omega$ and acceleration $a$ enter in combination $\mu \pm (\Omega \pm ia)/2$. The limiting cases of zero mass and zero temperature are investigated in detail. In the zero-mass limit, the axial current is described by a smooth function only at temperatures higher than the Unruh temperature. At zero temperature, the axial current, as a function of the angular velocity and chemical potential, vanishes in a two-dimensional plane region.
Highlights
Many remarkable effects related to the properties of relativistic fluids have been discovered at the theoretical level
In the resulting formula, chemical potential μ, angular velocity Ω and acceleration jaj enter in combination μ Æ ðΩ Æ ijajÞ=2
The zero-mass limit (2.8), (2.10), which is consistent in the linear approximation with the standard formula for the chiral vortical effect (CVE), was studied
Summary
Many remarkable effects related to the properties of relativistic fluids have been discovered at the theoretical level. The appearance of the Unruh temperature in Eq (2.8) is a direct consequence of the fact that in (2.5) and (2.6) the acceleration enters as an imaginary chemical potential If both acceleration and angular velocity are nonzero and directed arbitrarily, the boundary temperature is generalized to TU → T UðΩ; jaj; θÞ, where θ is the angle between a and Ω in the comoving reference system. A similar result on the existence of a boundary temperature proportional to the Unruh temperature on the basis of the same Wigner function [16] was recently obtained in [18] by considering the energy-momentum tensor and the condition of positivity of the energy density. Þωμ is consistent with the results of [1,2] (see [31] for recent progress in the geometric approach, developed in [1])
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