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(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 themore »
- Authors:
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (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. https://doi.org/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. https://doi.org/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 = {Tue Aug 28 00:00:00 EDT 2018},
month = {Tue Aug 28 00:00:00 EDT 2018}
}
https://doi.org/10.1103/PhysRevD.98.036019
Web of Science
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