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Title: Disentangling covariant Wigner functions for chiral fermions

Abstract

Here, we develop a general formalism for the quantum kinetics of chiral fermions in a background electromagnetic field based on a semiclassical expansion of covariant Wigner functions in the Planck constant ℏ. We demonstrate to any order of ℏ that only the time-component of the Wigner function is independent while other components are explicit derivative. We further demonstrate to any order of ℏ that a system of quantum kinetic equations for multiple-components of Wigner functions can be reduced to one chiral kinetic equation involving only the single-component distribution function. These are remarkable properties of the quantum kinetics of chiral fermions and will significantly simplify the description and simulation of chiral effects in heavy ion collisions and Dirac/Weyl semimetals. We present the unintegrated chiral kinetic equations in four-momenta up to O(ℏ 2) and the integrated ones in three-momenta up to O(ℏ). We find that some singular terms emerge in the integration over the time component of the four-momentum, which result in a new source term contributing to the chiral anomaly, in contrast to the well-known scenario of the Berry phase term. Finally we rewrite our results in any Lorentz frame with a reference four-velocity and show how the non-trivial transformation ofmore » the distribution function in different frames emerges in a natural way.« less

Authors:
; ; ;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1467150
Alternate Identifier(s):
OSTI ID: 1480794
Grant/Contract Number:  
[AC02-05CH11231; 2014CB845400; 2015CB856902]
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
[Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 3]; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats

Gao, Jian-Hua, Liang, Zuo-Tang, Wang, Qun, and Wang, Xin-Nian. Disentangling covariant Wigner functions for chiral fermions. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.98.036019.
Gao, Jian-Hua, Liang, Zuo-Tang, Wang, Qun, & Wang, Xin-Nian. Disentangling covariant Wigner functions for chiral fermions. United States. doi:10.1103/PhysRevD.98.036019.
Gao, Jian-Hua, Liang, Zuo-Tang, Wang, Qun, and Wang, Xin-Nian. Tue . "Disentangling covariant Wigner functions for chiral fermions". United States. doi:10.1103/PhysRevD.98.036019.
@article{osti_1467150,
title = {Disentangling covariant Wigner functions for chiral fermions},
author = {Gao, Jian-Hua and Liang, Zuo-Tang and Wang, Qun and Wang, Xin-Nian},
abstractNote = {Here, we develop a general formalism for the quantum kinetics of chiral fermions in a background electromagnetic field based on a semiclassical expansion of covariant Wigner functions in the Planck constant ℏ. We demonstrate to any order of ℏ that only the time-component of the Wigner function is independent while other components are explicit derivative. We further demonstrate to any order of ℏ that a system of quantum kinetic equations for multiple-components of Wigner functions can be reduced to one chiral kinetic equation involving only the single-component distribution function. These are remarkable properties of the quantum kinetics of chiral fermions and will significantly simplify the description and simulation of chiral effects in heavy ion collisions and Dirac/Weyl semimetals. We present the unintegrated chiral kinetic equations in four-momenta up to O(ℏ2) and the integrated ones in three-momenta up to O(ℏ). We find that some singular terms emerge in the integration over the time component of the four-momentum, which result in a new source term contributing to the chiral anomaly, in contrast to the well-known scenario of the Berry phase term. Finally we rewrite our results in any Lorentz frame with a reference four-velocity and show how the non-trivial transformation of the distribution function in different frames emerges in a natural way.},
doi = {10.1103/PhysRevD.98.036019},
journal = {Physical Review D},
number = [3],
volume = [98],
place = {United States},
year = {2018},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.98.036019

Citation Metrics:
Cited by: 7 works
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    Works referencing / citing this record:

    Anomalous magnetohydrodynamics with longitudinal boost invariance and chiral magnetic effect
    journal, June 2019