Abstract
We derive the Wigner functions of polarized photons in the Coulomb gauge with the ħ expansion applied to quantum field theory, and identify side-jump effects for massless photons. We also discuss the photonic chiral vortical effect for the Chern-Simons current and zilch vortical effect for the zilch current in local thermal equilibrium as a consistency check for our formalism. The results are found to be in agreement with those obtained from different approaches. Moreover, using the real-time formalism, we construct the quantum kinetic theory (QKT) for polarized photons. By further adopting a specific power counting scheme for the distribution functions, we provide a more succinct form of an effective QKT. This photonic QKT involves quantum corrections associated with self-energy gradients in the collision term, which are analogous to the side-jump corrections pertinent to spin-orbit interactions in the chiral kinetic theory for massless fermions. The same theoretical framework can also be directly applied to weakly coupled gluons in the absence of background color fields.
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References
K.Y. Bliokh and Y.P. Bliokh, Topological spin transport of photons: The Optical Magnus Effect and Berry Phase, Phys. Lett. A 333 (2004) 181 [physics/0402110] [INSPIRE].
M. Onoda, S. Murakami and N. Nagaosa, Hall Effect of Light, Phys. Rev. Lett. 93 (2004) 083901 [cond-mat/0405129] [INSPIRE].
A. Avkhadiev and A.V. Sadofyev, Chiral Vortical Effect for Bosons, Phys. Rev. D 96 (2017) 045015 [arXiv:1702.07340] [INSPIRE].
N. Yamamoto, Photonic chiral vortical effect, Phys. Rev. D 96 (2017) 051902 [arXiv:1702.08886] [INSPIRE].
V.A. Zyuzin, Landau levels for an electromagnetic wave, Phys. Rev. A 96 (2017) 043830.
X.-G. Huang and A.V. Sadofyev, Chiral Vortical Effect For An Arbitrary Spin, JHEP 03 (2019) 084 [arXiv:1805.08779] [INSPIRE].
G.Y. Prokhorov, O.V. Teryaev and V.I. Zakharov, Chiral vortical effect: Black-hole versus flat-space derivation, Phys. Rev. D 102 (2020) 121702 [arXiv:2003.11119] [INSPIRE].
M.N. Chernodub, A. Cortijo and K. Landsteiner, Zilch vortical effect, Phys. Rev. D 98 (2018) 065016 [arXiv:1807.10705] [INSPIRE].
C. Copetti and J. Fernández-Pendás, Higher spin vortical Zilches from Kubo formulae, Phys. Rev. D 98 (2018) 105008 [arXiv:1809.08255] [INSPIRE].
D.M. Lipkin, Existence of a New Conservation Law in Electromagnetic Theory, J. Math. Phys. 5 (1964) 696.
T.A. Morgan, Two classes of new conservation laws for the electromagnetic field and for other massless fields, J. Math. Phys. 5 (1964) 1659.
T.W.B. Kibble, Conservation Laws for Free Fields, J. Math. Phys. 6 (1965) 1022.
Y. Tang and A.E. Cohen, Optical Chirality and Its Interaction with Matter, Phys. Rev. Lett. 104 (2010) 163901.
D.T. Son and N. Yamamoto, Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids, Phys. Rev. Lett. 109 (2012) 181602 [arXiv:1203.2697] [INSPIRE].
M.A. Stephanov and Y. Yin, Chiral Kinetic Theory, Phys. Rev. Lett. 109 (2012) 162001 [arXiv:1207.0747] [INSPIRE].
D.T. Son and N. Yamamoto, Kinetic theory with Berry curvature from quantum field theories, Phys. Rev. D 87 (2013) 085016 [arXiv:1210.8158] [INSPIRE].
J.-W. Chen, S. Pu, Q. Wang and X.-N. Wang, Berry Curvature and Four-Dimensional Monopoles in the Relativistic Chiral Kinetic Equation, Phys. Rev. Lett. 110 (2013) 262301 [arXiv:1210.8312] [INSPIRE].
C. Manuel and J.M. Torres-Rincon, Kinetic theory of chiral relativistic plasmas and energy density of their gauge collective excitations, Phys. Rev. D 89 (2014) 096002 [arXiv:1312.1158] [INSPIRE].
J.-Y. Chen, D.T. Son, M.A. Stephanov, H.-U. Yee and Y. Yin, Lorentz Invariance in Chiral Kinetic Theory, Phys. Rev. Lett. 113 (2014) 182302 [arXiv:1404.5963] [INSPIRE].
J.-Y. Chen, D.T. Son and M.A. Stephanov, Collisions in Chiral Kinetic Theory, Phys. Rev. Lett. 115 (2015) 021601 [arXiv:1502.06966] [INSPIRE].
Y. Hidaka, S. Pu and D.-L. Yang, Relativistic Chiral Kinetic Theory from Quantum Field Theories, Phys. Rev. D 95 (2017) 091901 [arXiv:1612.04630] [INSPIRE].
Y. Hidaka, S. Pu and D.-L. Yang, Nonlinear Responses of Chiral Fluids from Kinetic Theory, Phys. Rev. D 97 (2018) 016004 [arXiv:1710.00278] [INSPIRE].
N. Mueller and R. Venugopalan, The chiral anomaly, Berry’s phase and chiral kinetic theory, from world-lines in quantum field theory, Phys. Rev. D 97 (2018) 051901 [arXiv:1701.03331] [INSPIRE].
N. Mueller and R. Venugopalan, Worldline construction of a covariant chiral kinetic theory, Phys. Rev. D 96 (2017) 016023 [arXiv:1702.01233] [INSPIRE].
A. Huang, S. Shi, Y. Jiang, J. Liao and P. Zhuang, Complete and Consistent Chiral Transport from Wigner Function Formalism, Phys. Rev. D 98 (2018) 036010 [arXiv:1801.03640] [INSPIRE].
S. Carignano, C. Manuel and J.M. Torres-Rincon, Consistent relativistic chiral kinetic theory: A derivation from on-shell effective field theory, Phys. Rev. D 98 (2018) 076005 [arXiv:1806.01684] [INSPIRE].
O.F. Dayi and E. Kilinçarslan, Quantum Kinetic Equation in the Rotating Frame and Chiral Kinetic Theory, Phys. Rev. D 98 (2018) 081701 [arXiv:1807.05912] [INSPIRE].
Y.-C. Liu, L.-L. Gao, K. Mameda and X.-G. Huang, Chiral kinetic theory in curved spacetime, Phys. Rev. D 99 (2019) 085014 [arXiv:1812.10127] [INSPIRE].
S. Lin and A. Shukla, Chiral Kinetic Theory from Effective Field Theory Revisited, JHEP 06 (2019) 060 [arXiv:1901.01528] [INSPIRE].
S. Carignano, C. Manuel and J.M. Torres-Rincon, Chiral kinetic theory from the on-shell effective field theory: Derivation of collision terms, Phys. Rev. D 102 (2020) 016003 [arXiv:1908.00561] [INSPIRE].
N. Mueller and R. Venugopalan, Constructing phase space distributions with internal symmetries, Phys. Rev. D 99 (2019) 056003 [arXiv:1901.10492] [INSPIRE].
N. Weickgenannt, X.-L. Sheng, E. Speranza, Q. Wang and D.H. Rischke, Kinetic theory for massive spin-1/2 particles from the Wigner-function formalism, Phys. Rev. D 100 (2019) 056018 [arXiv:1902.06513] [INSPIRE].
J.-H. Gao and Z.-T. Liang, Relativistic Quantum Kinetic Theory for Massive Fermions and Spin Effects, Phys. Rev. D 100 (2019) 056021 [arXiv:1902.06510] [INSPIRE].
K. Hattori, Y. Hidaka and D.-L. Yang, Axial Kinetic Theory and Spin Transport for Fermions with Arbitrary Mass, Phys. Rev. D 100 (2019) 096011 [arXiv:1903.01653] [INSPIRE].
Z. Wang, X. Guo, S. Shi and P. Zhuang, Mass Correction to Chiral Kinetic Equations, Phys. Rev. D 100 (2019) 014015 [arXiv:1903.03461] [INSPIRE].
D.E. Kharzeev, M.A. Stephanov and H.-U. Yee, Anatomy of chiral magnetic effect in and out of equilibrium, Phys. Rev. D 95 (2017) 051901 [arXiv:1612.01674] [INSPIRE].
A. Huang, Y. Jiang, S. Shi, J. Liao and P. Zhuang, Out-of-equilibrium chiral magnetic effect from chiral kinetic theory, Phys. Lett. B 777 (2018) 177 [arXiv:1703.08856] [INSPIRE].
Y. Sun and C.M. Ko, Λ hyperon polarization in relativistic heavy ion collisions from a chiral kinetic approach, Phys. Rev. C 96 (2017) 024906 [arXiv:1706.09467] [INSPIRE].
Y. Hidaka and D.-L. Yang, Nonequilibrium chiral magnetic/vortical effects in viscous fluids, Phys. Rev. D 98 (2018) 016012 [arXiv:1801.08253] [INSPIRE].
Y. Sun and C.M. Ko, Chiral kinetic approach to the chiral magnetic effect in isobaric collisions, Phys. Rev. C 98 (2018) 014911 [arXiv:1803.06043] [INSPIRE].
D.-L. Yang, Side-Jump Induced Spin-Orbit Interaction of Chiral Fluids from Kinetic Theory, Phys. Rev. D 98 (2018) 076019 [arXiv:1807.02395] [INSPIRE].
S.Y.F. Liu, Y. Sun and C.M. Ko, Spin Polarizations in a Covariant Angular-Momentum-Conserved Chiral Transport Model, Phys. Rev. Lett. 125 (2020) 062301 [arXiv:1910.06774] [INSPIRE].
S. Shi, C. Gale and S. Jeon, Relativistic Viscous Spin Hydrodynamics from Chiral Kinetic Theory, arXiv:2008.08618 [INSPIRE].
D.T. Son and B.Z. Spivak, Chiral Anomaly and Classical Negative Magnetoresistance of Weyl Metals, Phys. Rev. B 88 (2013) 104412 [arXiv:1206.1627] [INSPIRE].
G. Basar, D.E. Kharzeev and H.-U. Yee, Triangle anomaly in Weyl semimetals, Phys. Rev. B 89 (2014) 035142 [arXiv:1305.6338] [INSPIRE].
K. Landsteiner, Anomalous transport of Weyl fermions in Weyl semimetals, Phys. Rev. B 89 (2014) 075124 [arXiv:1306.4932] [INSPIRE].
E.V. Gorbar, V.A. Miransky, I.A. Shovkovy and P.O. Sukhachov, Consistent Chiral Kinetic Theory in Weyl Materials: Chiral Magnetic Plasmons, Phys. Rev. Lett. 118 (2017) 127601 [arXiv:1610.07625] [INSPIRE].
N. Yamamoto and D.-L. Yang, Chiral Radiation Transport Theory of Neutrinos, Astrophys. J. 895 (2020) 56 [arXiv:2002.11348] [INSPIRE].
N. Yamamoto, Magnetic monopoles and fermion number violation in chiral matter, arXiv:2005.05028 [INSPIRE].
A. Vilenkin, Macroscopic parity violating effects: neutrino fluxes from rotating black holes and in rotating thermal radiation, Phys. Rev. D 20 (1979) 1807 [INSPIRE].
J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].
N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Dutta, R. Loganayagam and P. Surowka, Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].
D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].
K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational Anomaly and Transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].
X.-G. Huang, P. Mitkin, A.V. Sadofyev and E. Speranza, Zilch Vortical Effect, Berry Phase, and Kinetic Theory, JHEP 10 (2020) 117 [arXiv:2006.03591] [INSPIRE].
R. Kleiss and W.J. Stirling, Spinor Techniques for Calculating \( p\overline{p} \) → W±/Z0 + Jets, Nucl. Phys. B 262 (1985) 235 [INSPIRE].
J.F. Gunion and Z. Kunszt, Improved Analytic Techniques for Tree Graph Calculations and the \( Ggq\overline{q}\mathrm{\ell}\overline{\mathrm{\ell}} \) Subprocess, Phys. Lett. B 161 (1985) 333 [INSPIRE].
Z. Xu, D.-H. Zhang and L. Chang, Helicity Amplitudes for Multiple Bremsstrahlung in Massless Nonabelian Gauge Theories, Nucl. Phys. B 291 (1987) 392 [INSPIRE].
M.E. Peskin, Simplifying Multi-Jet QCD Computation, arXiv:1101.2414 [INSPIRE].
D.-L. Yang, K. Hattori and Y. Hidaka, Effective quantum kinetic theory for spin transport of fermions with collsional effects, JHEP 07 (2020) 070 [arXiv:2002.02612] [INSPIRE].
STAR collaboration, Global Λ hyperon polarization in nuclear collisions: evidence for the most vortical fluid, Nature 548 (2017) 62 [arXiv:1701.06657] [INSPIRE].
STAR collaboration, Global polarization of Λ hyperons in Au+Au collisions at \( \sqrt{s_{NN}} \) = 200 GeV, Phys. Rev. C 98 (2018) 014910 [arXiv:1805.04400] [INSPIRE].
STAR collaboration, Global polarization measurement in Au+Au collisions, Phys. Rev. C 76 (2007) 024915 [Erratum ibid. 95 (2017) 039906] [arXiv:0705.1691] [INSPIRE].
J.-j. Zhang, R.-h. Fang, Q. Wang and X.-N. Wang, A microscopic description for polarization in particle scatterings, Phys. Rev. C 100 (2019) 064904 [arXiv:1904.09152] [INSPIRE].
S. Li and H.-U. Yee, Quantum Kinetic Theory of Spin Polarization of Massive Quarks in Perturbative QCD: Leading Log, Phys. Rev. D 100 (2019) 056022 [arXiv:1905.10463] [INSPIRE].
J.I. Kapusta, E. Rrapaj and S. Rudaz, Relaxation Time for Strange Quark Spin in Rotating Quark-Gluon Plasma, Phys. Rev. C 101 (2020) 024907 [arXiv:1907.10750] [INSPIRE].
N. Weickgenannt, E. Speranza, X.-l. Sheng, Q. Wang and D.H. Rischke, Generating spin polarization from vorticity through nonlocal collisions, arXiv:2005.01506 [INSPIRE].
D. Hou and S. Lin, Polarization Rotation of Chiral Fermions in Vortical Fluid, arXiv:2008.03862 [INSPIRE].
S. Bhadury, W. Florkowski, A. Jaiswal, A. Kumar and R. Ryblewski, Dissipative Spin Dynamics in Relativistic Matter, arXiv:2008.10976 [INSPIRE].
Z. Wang, X. Guo and P. Zhuang, Local Equilibrium Spin Distribution From Detailed Balance, arXiv:2009.10930 [INSPIRE].
W. Florkowski, B. Friman, A. Jaiswal and E. Speranza, Relativistic fluid dynamics with spin, Phys. Rev. C 97 (2018) 041901 [arXiv:1705.00587] [INSPIRE].
D. Montenegro, L. Tinti and G. Torrieri, Ideal relativistic fluid limit for a medium with polarization, Phys. Rev. D 96 (2017) 056012 [Addendum ibid. 96 (2017) 079901] [arXiv:1701.08263] [INSPIRE].
W. Florkowski, A. Kumar and R. Ryblewski, Relativistic hydrodynamics for spin-polarized fluids, Prog. Part. Nucl. Phys. 108 (2019) 103709 [arXiv:1811.04409] [INSPIRE].
K. Hattori, M. Hongo, X.-G. Huang, M. Matsuo and H. Taya, Fate of spin polarization in a relativistic fluid: An entropy-current analysis, Phys. Lett. B 795 (2019) 100 [arXiv:1901.06615] [INSPIRE].
K. Fukushima and S. Pu, Spin Hydrodynamics and Symmetric Energy-Momentum Tensors — A current induced by the spin vorticity, arXiv:2010.01608 [INSPIRE].
F. Becattini, V. Chandra, L. Del Zanna and E. Grossi, Relativistic distribution function for particles with spin at local thermodynamical equilibrium, Annals Phys. 338 (2013) 32 [arXiv:1303.3431] [INSPIRE].
F. Becattini, W. Florkowski and E. Speranza, Spin tensor and its role in non-equilibrium thermodynamics, Phys. Lett. B 789 (2019) 419 [arXiv:1807.10994] [INSPIRE].
F. Becattini, M. Buzzegoli and A. Palermo, Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: scalar field, arXiv:2007.08249 [INSPIRE].
F. Becattini and M.A. Lisa, Polarization and Vorticity in the Quark-Gluon Plasma, Ann. Rev. Nucl. Part. Sci. 70 (2020) 395 [arXiv:2003.03640] [INSPIRE].
M. Le Bellac, Thermal field theory, Cambridge University Press (2000).
E. Leader and C. Lorcé, The angular momentum controversy: What’s it all about and does it matter?, Phys. Rept. 541 (2014) 163 [arXiv:1309.4235] [INSPIRE].
K. Fukushima and S. Pu, Relativistic decomposition of the orbital and the spin angular momentum in chiral physics and Feynman’s angular momentum paradox, arXiv:2001.00359 [INSPIRE].
J.-P. Blaizot and E. Iancu, The quark gluon plasma: Collective dynamics and hard thermal loops, Phys. Rept. 359 (2002) 355 [hep-ph/0101103] [INSPIRE].
J.-P. Blaizot and E. Iancu, A Boltzmann equation for the QCD plasma, Nucl. Phys. B 557 (1999) 183 [hep-ph/9903389] [INSPIRE].
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Hattori, K., Hidaka, Y., Yamamoto, N. et al. Wigner functions and quantum kinetic theory of polarized photons. J. High Energ. Phys. 2021, 1 (2021). https://doi.org/10.1007/JHEP02(2021)001
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DOI: https://doi.org/10.1007/JHEP02(2021)001