×

The covariance of chiral fermions theory. (English) Zbl 1421.83066

Summary: The quasiclassical theory of massless chiral fermions is considered. The effective action is derived using time-dependent variational principle which provides a clear interpretation of relevant canonical variables. As a result their transformation properties under the action of Lorentz group are derived from first principles.

MSC:

83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
81T10 Model quantum field theories
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Son, DT; Surówka, P., Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett., 103, 191601 (2009) · doi:10.1103/PhysRevLett.103.191601
[2] R. Loganayagam, Anomaly Induced Transport in Arbitrary Dimensions, arXiv:1106.0277 [INSPIRE]. · Zbl 1348.83040
[3] Loganayagam, R.; Surowka, P., Anomaly/Transport in an Ideal Weyl gas, JHEP, 04, 097 (2012) · Zbl 1348.83040 · doi:10.1007/JHEP04(2012)097
[4] Dubovsky, S.; Hui, L.; Nicolis, A.; Son, DT, Effective field theory for hydrodynamics: thermodynamics and the derivative expansion, Phys. Rev., D 85, 085029 (2012)
[5] Dubovsky, S.; Hui, L.; Nicolis, A., Effective field theory for hydrodynamics: Wess-Zumino term and anomalies in two spacetime dimensions, Phys. Rev., D 89, 045016 (2014)
[6] Fukushima, K.; Kharzeev, DE; Warringa, HJ, The Chiral Magnetic Effect, Phys. Rev., D 78, 074033 (2008)
[7] Fukushima, K.; Kharzeev, DE; Warringa, HJ, Real-time dynamics of the Chiral Magnetic Effect, Phys. Rev. Lett., 104, 212001 (2010) · doi:10.1103/PhysRevLett.104.212001
[8] Basar, G.; Dunne, GV; Kharzeev, DE, Chiral Magnetic Spiral, Phys. Rev. Lett., 104, 232301 (2010) · doi:10.1103/PhysRevLett.104.232301
[9] Stephanov, MA; Yin, Y.; Theory, CK, No article title, Phys. Rev. Lett., 109, 162001 (2012) · doi:10.1103/PhysRevLett.109.162001
[10] Son, DT; Yamamoto, N.; Curvature, B., Triangle Anomalies and the Chiral Magnetic Effect in Fermi Liquids, Phys. Rev. Lett., 109, 181602 (2012) · doi:10.1103/PhysRevLett.109.181602
[11] Son, DT; Yamamoto, N., Kinetic theory with Berry curvature from quantum field theories, Phys. Rev., D 87, 085016 (2013)
[12] Chen, J-W; Pu, S.; Wang, Q.; Wang, X-N, Berry Curvature and Four-Dimensional Monopoles in the Relativistic Chiral Kinetic Equation, Phys. Rev. Lett., 110, 262301 (2013) · doi:10.1103/PhysRevLett.110.262301
[13] Chen, J-W; Pang, J-y; Pu, S.; Wang, Q., Kinetic equations for massive Dirac fermions in electromagnetic field with non-Abelian Berry phase, Phys. Rev., D 89, 094003 (2014)
[14] Stone, M.; Dwivedi, V., Classical version of the non-Abelian gauge anomaly, Phys. Rev., D 88, 045012 (2013)
[15] Dwivedi, V.; Stone, M., Classical chiral kinetic theory and anomalies in even space-time dimensions, J. Phys., A 47, 025401 (2014) · Zbl 1283.81117
[16] Stone, M.; Dwivedi, V.; Zhou, T.; Phase, B., Lorentz Covariance and Anomalous Velocity for Dirac and Weyl Particles, Phys. Rev., D 91, 025004 (2015)
[17] Stone, M.; Dwivedi, V.; Zhou, T., Wigner Translations and the Observer Dependence of the Position of Massless Spinning Particles, Phys. Rev. Lett., 114, 210402 (2015) · doi:10.1103/PhysRevLett.114.210402
[18] Chen, J-Y; Son, DT; Stephanov, MA; Yee, H-U; Yin, Y., Lorentz Invariance in Chiral Kinetic Theory, Phys. Rev. Lett., 113, 182302 (2014) · doi:10.1103/PhysRevLett.113.182302
[19] Megias, E.; Valle, M., Second-order partition function of a non-interacting chiral fluid in 3+1 dimensions, JHEP, 11, 005 (2014) · doi:10.1007/JHEP11(2014)005
[20] Sohrabi, KA, Microscopic Study of Vorticities in Relativistic Chiral Fermions, JHEP, 03, 014 (2015) · doi:10.1007/JHEP03(2015)014
[21] Manuel, C.; Torres-Rincon, JM, Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory, Phys. Rev., D 90, 076007 (2014)
[22] Zhang, P.; Horváthy, PA, Anomalous Hall Effect for semiclassical chiral fermions, Phys. Lett., A 379, 507 (2014) · Zbl 1342.81761
[23] Duval, C.; Horvathy, PA, Chiral fermions as classical massless spinning particles, Phys. Rev., D 91, 045013 (2015)
[24] Duval, C.; Elbistan, M.; Horváthy, PA; Zhang, PM, Wigner-Souriau translations and Lorentz symmetry of chiral fermions, Phys. Lett., B 742, 322 (2015) · Zbl 1345.81049 · doi:10.1016/j.physletb.2015.01.048
[25] Andrzejewski, K.; Kijanka-Dec, A.; Kosinski, P.; Maslanka, P., Chiral fermions, massless particles and Poincaré covariance, Phys. Lett., B 746, 417 (2015) · Zbl 1343.81144 · doi:10.1016/j.physletb.2015.05.035
[26] J.-M. Souriau, Structure of Dynamical Systems: A Sympletic View of Physics, Birkhäuser, Boston U.S.A. (1997). · Zbl 0884.70001
[27] B.S. Skagerstam, Localization of massless spinning particles and the Berry phase, hep-th/9210054 [INSPIRE]. · Zbl 0942.81550
[28] Newton, TD; Wigner, EP, Localized States for Elementary Systems, Rev. Mod. Phys., 21, 400 (1949) · Zbl 0036.26704 · doi:10.1103/RevModPhys.21.400
[29] Bliokh, KY; Bliokh, YP, Topological spin transport of photons: The Optical Magnus Effect and Berry Phase, Phys. Lett., A 333, 181 (2004) · Zbl 1123.78301 · doi:10.1016/j.physleta.2004.10.035
[30] Onoda, M.; Murakami, S.; Nagaosa, N., Hall Effect of Light, Phys. Rev. Lett., 93, 083901 (2004) · doi:10.1103/PhysRevLett.93.083901
[31] Duval, C.; Horvath, Z.; Horvathy, P., Geometrical spinoptics and the optical Hall effect, J. Geom. Phys., 57, 925 (2007) · Zbl 1124.78002 · doi:10.1016/j.geomphys.2006.07.003
[32] Duval, C.; Horvath, Z.; Horvathy, PA, Fermat principle for spinning light, Phys. Rev., D 74, 021701 (2006)
[33] Bliokh, K.; Niv, A.; Kleiner, V.; Hasman, E., Geometrodynamics of Spinning Light, Nature Photon., 2, 748 (2008) · doi:10.1038/nphoton.2008.229
[34] Bliokh, K., Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium, J. Opt., A 11, 094009 (2009)
[35] Bliokh, KY; Nori, F.; Effect, RH, No article title, Phys. Rev. Lett., 108, 120403 (2012) · doi:10.1103/PhysRevLett.108.120403
[36] Landau, L.; Peierls, R., Time of the Energy Emission in the Hydrogen Atom and Its Electrodynamical Background, Z. Phys., 69, 56 (1931) · doi:10.1007/BF01391513
[37] V.B. Berestetskii, E.M. Lifshitz and L.P. Pitaevskii, Relativistic Quantum Theory 1, Pergamon Press, Oxford U.K. (1971).
[38] Weinberg, S., Feynman Rules for Any Spin, Phys. Rev., 133, b1318 (1964) · Zbl 0134.45904 · doi:10.1103/PhysRev.133.B1318
[39] Weinberg, S., Feynman Rules for Any Spin. 2. Massless Particles, Phys. Rev., 134, b882 (1964) · Zbl 0134.45904 · doi:10.1103/PhysRev.134.B882
[40] Weinberg, S., Photons and Gravitons in s Matrix Theory: Derivation of Charge Conservation and Equality of Gravitational and Inertial Mass, Phys. Rev., 135, b1049 (1964) · Zbl 0144.23702 · doi:10.1103/PhysRev.135.B1049
[41] S. Weinberg, The Quantum Theory of Fields. Vol.I, Cambridge University Press, Cambridge U.K. (1995). · Zbl 0959.81002 · doi:10.1017/CBO9781139644167
[42] Chang, M-C; Niu, Q., Berry phase, hyperorbits and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bands, Phys. Rev., B 53, 7010 (1996) · doi:10.1103/PhysRevB.53.7010
[43] Sundaram, G.; Niu, Q., Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects, Phys. Rev., B 59, 14915 (1999) · doi:10.1103/PhysRevB.59.14915
[44] Culcer, D.; Yao, Y.; Niu, Q., Coherent wave-packet evolution in coupled bands, Phys. Rev., B 72, 085110 (2005) · doi:10.1103/PhysRevB.72.085110
[45] Chang, M-C; Niu, Q., Berry curvature, orbital moment, and effective quantum theory of electrons in electromagnetic fields, J. Phys. Condens. Matter, 20, 193202 (2008) · doi:10.1088/0953-8984/20/19/193202
[46] Yu. V. Novozhilov, Introduction to Elementary Particle Theory, Pergamon Press, Oxford U.K. (1975).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.