Effects of rotation and acceleration in the axial current: density operator vs Wigner function

George Y Prokhorov,Oleg V Teryaev,Valentin I Zakharov

doi:10.1007/jhep02(2019)146

Abstract

The hydrodynamic coefficients in the axial current are calculated on the basis of the equilibrium quantum statistical density operator in the third order of perturbation theory in thermal vorticity tensor both for the case of massive and massless fermions. The coefficients obtained describe third-order corrections to the Chiral Vortical Effect and include the contribution from local acceleration. We show that the methods of the Wigner function and the statistical density operator lead to the same result for an axial current in describing effects associated only with vorticity when the local acceleration is zero, but differ in describing mixed effects for which both acceleration and vorticity are significant simultaneously.

Highlights

JHEP02(2019)146 anomaly [2,3,4], higher-order terms should be related to other anomalies in quantum field theory, in particular, to the gravitational anomaly [23, 24]
The hydrodynamic coefficients in the axial current are calculated on the basis of the equilibrium quantum statistical density operator in the third order of perturbation theory in thermal vorticity tensor both for the case of massive and massless fermions
We will be interested in two recently developed methods for investigation of chiral effects: the first of them is based on the ansatz of the Wigner function [11, 12, 28,29,30], the second approach is based on the equilibrium quantum statistical density operator [10, 26, 27, 31,32,33,34,35,36]

Summary

Introduction

JHEP02(2019)146 anomaly [2,3,4], higher-order terms should be related to other anomalies in quantum field theory, in particular, to the gravitational anomaly [23, 24]. The study of corrections of higher orders will make it possible to improve our understanding of the effect of the anomalies of quantum field theory to relativistic hydrodynamics Another open question relates to the study of effects associated with acceleration in chiral phenomena. In [12] the exact nonperturbative expression for the axial current was obtained In this expression, the angular velocity and acceleration play the role of additional chemical potentials, and the acceleration corresponds to an imaginary chemical potential. In [11, 12], corrections of higher orders to CVE were investigated, and it was shown that the axial current contains a third-order term with respect to the angular velocity. Note that the third order was the highest - all higher-order terms are zero

Objectives

Discussion

Conclusion