Disentangling covariant Wigner functions for chiral fermions

Gao, Jian-Hua; Liang, Zuo-Tang; Wang, Qun; Wang, Xin-Nian

doi:10.1103/PhysRevD.98.036019

Title: Disentangling covariant Wigner functions for chiral fermions

Journal Article · Tue Aug 28 00:00:00 EDT 2018 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.98.036019· OSTI ID:1467150

Gao, Jian-Hua; Liang, Zuo-Tang; Wang, Qun; Wang, Xin-Nian

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.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC02-05CH11231; 2014CB845400; 2015CB856902

OSTI ID:: 1467150

Alternate ID(s):: OSTI ID: 1480794

Journal Information:: Physical Review D, Journal Name: Physical Review D Vol. 98 Journal Issue: 3; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 64 works

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References (49)

Observation of charge-dependent azimuthal correlations and possible local strong parity violation in heavy-ion collisions Abelev, B. I.; Aggarwal, M. M.; Ahammed, Z. Physical Review C, Vol. 81, Issue 5 https://doi.org/10.1103/PhysRevC.81.054908	journal	May 2010
Testing the Chiral Magnetic and Chiral Vortical Effects in Heavy Ion Collisions Kharzeev, Dmitri E.; Son, Dam T. Physical Review Letters, Vol. 106, Issue 6 https://doi.org/10.1103/PhysRevLett.106.062301	journal	February 2011
Fluid dynamics of R-charged black holes Erdmenger, Johanna; Haack, Michael; Kaminski, Matthias Journal of High Energy Physics, Vol. 2009, Issue 01 https://doi.org/10.1088/1126-6708/2009/01/055	journal	January 2009
Chirally Invariant Transport Equations for Quark Matter Florkowski, W.; Hüfner, J.; Klevansky, S. P. Annals of Physics, Vol. 245, Issue 2 https://doi.org/10.1006/aphy.1996.0016	journal	February 1996
Relativistic Quantum Transport Theory for Electrodynamics Zhuang, P.; Heinz, U. Annals of Physics, Vol. 245, Issue 2 https://doi.org/10.1006/aphy.1996.0011	journal	February 1996
Kinetic theory of chiral relativistic plasmas and energy density of their gauge collective excitations Manuel, Cristina; Torres-Rincon, Juan M. Physical Review D, Vol. 89, Issue 9 https://doi.org/10.1103/PhysRevD.89.096002	journal	May 2014
Chiral magnetic and vortical effects in high-energy nuclear collisions—A status report Kharzeev, D. E.; Liao, J.; Voloshin, S. A. Progress in Particle and Nuclear Physics, Vol. 88 https://doi.org/10.1016/j.ppnp.2016.01.001	journal	May 2016
Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs Huang, Xiaochun; Zhao, Lingxiao; Long, Yujia Physical Review X, Vol. 5, Issue 3 https://doi.org/10.1103/PhysRevX.5.031023	journal	August 2015
The quark–gluon plasma: collective dynamics and hard thermal loops Blaizot, Jean-Paul; Iancu, Edmond Physics Reports, Vol. 359, Issue 5-6 https://doi.org/10.1016/S0370-1573(01)00061-8	journal	March 2002
Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory Manuel, Cristina; Torres-Rincon, Juan M. Physical Review D, Vol. 90, Issue 7 https://doi.org/10.1103/PhysRevD.90.076007	journal	October 2014
Lorentz Invariance in Chiral Kinetic Theory Chen, Jing-Yuan; Son, Dam T.; Stephanov, Mikhail A. Physical Review Letters, Vol. 113, Issue 18 https://doi.org/10.1103/PhysRevLett.113.182302	journal	October 2014
Charge separation relative to the reaction plane in Pb-Pb collisions at $\sqrt{s_{N N}} = 2.76 TeV$ Abelev, B.; Adam, J.; Adamová, D. Physical Review Letters, Vol. 110, Issue 1 https://doi.org/10.1103/PhysRevLett.110.012301	journal	January 2013
Consistent Chiral Kinetic Theory in Weyl Materials: Chiral Magnetic Plasmons Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A. Physical Review Letters, Vol. 118, Issue 12 https://doi.org/10.1103/PhysRevLett.118.127601	journal	March 2017
Chiral Anomaly and Local Polarization Effect from the Quantum Kinetic Approach Gao, Jian-Hua; Liang, Zuo-Tang; Pu, Shi Physical Review Letters, Vol. 109, Issue 23 https://doi.org/10.1103/PhysRevLett.109.232301	journal	December 2012
Global Λ hyperon polarization in nuclear collisions Nature, Vol. 548, Issue 7665, p. 62-65 https://doi.org/10.1038/nature23004	journal	August 2017
A PCAC puzzle: π0→γγ in the σ-model Bell, J. S.; Jackiw, R. Il Nuovo Cimento A, Vol. 60, Issue 1 https://doi.org/10.1007/BF02823296	journal	March 1969
Collisions in Chiral Kinetic Theory Chen, Jing-Yuan; Son, Dam T.; Stephanov, Mikhail A. Physical Review Letters, Vol. 115, Issue 2 https://doi.org/10.1103/PhysRevLett.115.021601	journal	July 2015
Hydrodynamics with Triangle Anomalies Son, Dam T.; Surówka, Piotr Physical Review Letters, Vol. 103, Issue 19 https://doi.org/10.1103/PhysRevLett.103.191601	journal	November 2009
Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids Son, Dam Thanh; Yamamoto, Naoki Physical Review Letters, Vol. 109, Issue 18 https://doi.org/10.1103/PhysRevLett.109.181602	journal	November 2012
Chiral magnetic effect Fukushima, Kenji; Kharzeev, Dmitri E.; Warringa, Harmen J. Physical Review D, Vol. 78, Issue 7 https://doi.org/10.1103/PhysRevD.78.074033	journal	October 2008
Chiral anomaly, Berry phase, and chiral kinetic theory from worldlines in quantum field theory Mueller, Niklas; Venugopalan, Raju Physical Review D, Vol. 97, Issue 5 https://doi.org/10.1103/PhysRevD.97.051901	journal	March 2018
Transport equations for the QCD quark Wigner operator Elze, H. -Th.; Gyulassy, M.; Vasak, D. Nuclear Physics B, Vol. 276, Issue 3-4 https://doi.org/10.1016/0550-3213(86)90072-6	journal	October 1986
Relativistic chiral kinetic theory from quantum field theories Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun Physical Review D, Vol. 95, Issue 9 https://doi.org/10.1103/PhysRevD.95.091901	journal	May 2017
Kinetic equations for massive Dirac fermions in electromagnetic field with non-Abelian Berry phase Chen, Jiunn-Wei; Pang, Jin-yi; Pu, Shi Physical Review D, Vol. 89, Issue 9 https://doi.org/10.1103/PhysRevD.89.094003	journal	May 2014
The effects of topological charge change in heavy ion collisions: “Event by event and violation” Kharzeev, Dmitri E.; McLerran, Larry D.; Warringa, Harmen J. Nuclear Physics A, Vol. 803, Issue 3-4 https://doi.org/10.1016/j.nuclphysa.2008.02.298	journal	May 2008
Kinetic Equation for Gluons in the Background Gauge of QCD Wang, Q.; Redlich, K.; Stöcker, H. Physical Review Letters, Vol. 88, Issue 13 https://doi.org/10.1103/PhysRevLett.88.132303	journal	March 2002
Complete and consistent chiral transport from Wigner function formalism Huang, Anping; Shi, Shuzhe; Jiang, Yin Physical Review D, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevD.98.036010	journal	August 2018
Covariant chiral kinetic equation in the Wigner function approach Gao, Jian-hua; Pu, Shi; Wang, Qun Physical Review D, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevD.96.016002	journal	July 2017
Spin alignment of vector mesons in non-central <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>A</mml:mi></mml:math> collisions Liang, Zuo-Tang; Wang, Xin-Nian Physics Letters B, Vol. 629, Issue 1 https://doi.org/10.1016/j.physletb.2005.09.060	journal	November 2005
Globally Polarized Quark-Gluon Plasma in Noncentral $A + A$ Collisions Liang, Zuo-Tang; Wang, Xin-Nian Physical Review Letters, Vol. 94, Issue 10 https://doi.org/10.1103/PhysRevLett.94.102301	journal	March 2005
Axial-Vector Vertex in Spinor Electrodynamics Adler, Stephen L. Physical Review, Vol. 177, Issue 5 https://doi.org/10.1103/PhysRev.177.2426	journal	January 1969
Erratum: Globally Polarized Quark-Gluon Plasma in Noncentral $A + A$ Collisions [Phys. Rev. Lett. 94 , 102301 (2005)] Liang, Zuo-Tang; Wang, Xin-Nian Physical Review Letters, Vol. 96, Issue 3 https://doi.org/10.1103/PhysRevLett.96.039901	journal	January 2006
Azimuthal Charged-Particle Correlations and Possible Local Strong Parity Violation Abelev, B. I.; Aggarwal, M. M.; Ahammed, Z. Physical Review Letters, Vol. 103, Issue 25 https://doi.org/10.1103/PhysRevLett.103.251601	journal	December 2009
Quantum transport theory for abelian plasmas Vasak, David; Gyulassy, Miklos; Elze, Hans-Thomas Annals of Physics, Vol. 173, Issue 2 https://doi.org/10.1016/0003-4916(87)90169-2	journal	February 1987
Berry Curvature and Four-Dimensional Monopoles in the Relativistic Chiral Kinetic Equation Chen, Jiunn-Wei; Pu, Shi; Wang, Qun Physical Review Letters, Vol. 110, Issue 26 https://doi.org/10.1103/PhysRevLett.110.262301	journal	June 2013
Kinetic Theory for Plasmas with Non-Abelian Interactions Heinz, Ulrich Physical Review Letters, Vol. 51, Issue 5 https://doi.org/10.1103/PhysRevLett.51.351	journal	August 1983
Chiral Kinetic Theory Stephanov, M. A.; Yin, Y. Physical Review Letters, Vol. 109, Issue 16 https://doi.org/10.1103/PhysRevLett.109.162001	journal	October 2012
The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal Nielsen, H. B.; Ninomiya, Masao Physics Letters B, Vol. 130, Issue 6 https://doi.org/10.1016/0370-2693(83)91529-0	journal	November 1983
Magnetic moment, vorticity-spin coupling and parity-odd conductivity of chiral fermions in 4-dimensional Wigner functions Gao, Jian-hua; Wang, Qun Physics Letters B, Vol. 749 https://doi.org/10.1016/j.physletb.2015.08.058	journal	October 2015
Strongly Interacting Matter in Magnetic Fields Kharzeev, Dmitri; Landsteiner, Karl; Schmitt, Andreas Lecture Notes in Physics https://doi.org/10.1007/978-3-642-37305-3	book	January 2013
Gravitational Anomaly and Transport Phenomena Landsteiner, Karl; Megías, Eugenio; Pena-Benitez, Francisco Physical Review Letters, Vol. 107, Issue 2 https://doi.org/10.1103/PhysRevLett.107.021601	journal	July 2011
Chiral anomaly and classical negative magnetoresistance of Weyl metals Son, D. T.; Spivak, B. Z. Physical Review B, Vol. 88, Issue 10 https://doi.org/10.1103/PhysRevB.88.104412	journal	September 2013
Some field theoretic issues regarding the chiral magnetic effect Hou, De-fu; Liu, Hui; Ren, Hai-cang Journal of High Energy Physics, Vol. 2011, Issue 5 https://doi.org/10.1007/JHEP05(2011)046	journal	May 2011
Chiral magnetic effect in ZrTe5 Li, Qiang; Kharzeev, Dmitri E.; Zhang, Cheng Nature Physics, Vol. 12, Issue 6 https://doi.org/10.1038/nphys3648	journal	February 2016
Hydrodynamics from charged black branes Banerjee, Nabamita; Bhattacharya, Jyotirmoy; Bhattacharyya, Sayantani Journal of High Energy Physics, Vol. 2011, Issue 1 https://doi.org/10.1007/JHEP01(2011)094	journal	January 2011
Evidence for Effects of the Chiral Anomaly: Status and Future Sorensen, Paul Nuclear Physics A, Vol. 967 https://doi.org/10.1016/j.nuclphysa.2017.05.100	journal	November 2017
Equilibrium parity-violating current in a magnetic field Vilenkin, Alexander Physical Review D, Vol. 22, Issue 12 https://doi.org/10.1103/PhysRevD.22.3080	journal	December 1980
Kinetic theory with Berry curvature from quantum field theories Son, Dam Thanh; Yamamoto, Naoki Physical Review D, Vol. 87, Issue 8 https://doi.org/10.1103/PhysRevD.87.085016	journal	April 2013
Parity violating currents in thermal radiation Vilenkin, A. Physics Letters B, Vol. 80, Issue 1-2 https://doi.org/10.1016/0370-2693(78)90330-1	journal	December 1978

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