Advertisement

General thermodynamic equilibrium with axial chemical potential for the free Dirac field

  • M. BuzzegoliEmail author
  • F. Becattini
Open Access
Regular Article - Theoretical Physics

Abstract

We calculate the constitutive equations of the stress-energy tensor and the currents of the free massless Dirac field at thermodynamic equilibrium with acceleration and rotation and a conserved axial charge by using the density operator approach. We carry out an expansion in thermal vorticity to the second order with finite axial chemical potential μA. The obtained coefficients of the expansion are expressed as correlators of angular momenta and boost operators with the currents. We confirm previous observations that the axial chemical potential induces non-vanishing components of the stress-energy tensor at first order in thermal vorticity due to breaking of parity invariance of the density operator with μA ≠ 0. The appearance of these components might play an important role in chiral hydrodynamics.

Keywords

Chiral Lagrangians Thermal Field Theory Quark-Gluon Plasma SpaceTime Symmetries 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    D.E. Kharzeev, J. Liao, S.A. Voloshin and G. Wang, Chiral magnetic and vortical effects in high-energy nuclear collisionsA status report, Prog. Part. Nucl. Phys. 88 (2016) 1 [arXiv:1511.04050] [INSPIRE].CrossRefGoogle Scholar
  2. [2]
    STAR collaboration, L. Adamczyk et al., Global Λ hyperon polarization in nuclear collisions: evidence for the most vortical fluid, Nature 548 (2017) 62 [arXiv:1701.06657] [INSPIRE].
  3. [3]
    F. Becattini, F. Piccinini and J. Rizzo, Angular momentum conservation in heavy ion collisions at very high energy, Phys. Rev. C 77 (2008) 024906 [arXiv:0711.1253] [INSPIRE].Google Scholar
  4. [4]
    F.M. Haehl, R. Loganayagam and M. Rangamani, The eightfold way to dissipation, Phys. Rev. Lett. 114 (2015) 201601 [arXiv:1412.1090] [INSPIRE].CrossRefzbMATHGoogle Scholar
  5. [5]
    Y. Neiman and Y. Oz, Relativistic Hydrodynamics with General Anomalous Charges, JHEP 03 (2011) 023 [arXiv:1011.5107] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    S. Pu, J.-h. Gao and Q. Wang, A consistent description of kinetic equation with triangle anomaly, Phys. Rev. D 83 (2011) 094017 [arXiv:1008.2418] [INSPIRE].Google Scholar
  7. [7]
    K. Landsteiner, E. Megias, L. Melgar and F. Pena-Benitez, Holographic Gravitational Anomaly and Chiral Vortical Effect, JHEP 09 (2011) 121 [arXiv:1107.0368] [INSPIRE].CrossRefzbMATHGoogle Scholar
  8. [8]
    K. Landsteiner, E. Megias and F. Pena-Benitez, Anomalous Transport from Kubo Formulae, Lect. Notes Phys. 871 (2013) 433 [arXiv:1207.5808] [INSPIRE].CrossRefGoogle Scholar
  9. [9]
    S.D. Chowdhury and J.R. David, Anomalous transport at weak coupling, JHEP 11 (2015) 048 [arXiv:1508.01608] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    S. Golkar and D.T. Son, (Non)-renormalization of the chiral vortical effect coefficient, JHEP 02 (2015) 169 [arXiv:1207.5806] [INSPIRE].
  11. [11]
    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].CrossRefGoogle Scholar
  12. [12]
    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].MathSciNetGoogle Scholar
  13. [13]
    N. Abbasi, F. Taghinavaz and K. Naderi, Hydrodynamic Excitations from Chiral Kinetic Theory and the Hydrodynamic Frames, JHEP 03 (2018) 191 [arXiv:1712.06175] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    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].MathSciNetGoogle Scholar
  15. [15]
    P. Glorioso, H. Liu and S. Rajagopal, Global Anomalies, Discrete Symmetries and Hydrodynamic Effective Actions, arXiv:1710.03768 [INSPIRE].
  16. [16]
    X.-G. Huang, K. Nishimura and N. Yamamoto, Anomalous effects of dense matter under rotation, JHEP 02 (2018) 069 [arXiv:1711.02190] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    K. Fukushima, D.E. Kharzeev and H.J. Warringa, The Chiral Magnetic Effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].Google Scholar
  18. [18]
    J. Hernandez and P. Kovtun, Relativistic magnetohydrodynamics, JHEP 05 (2017) 001 [arXiv:1703.08757] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    P. Kovtun and A. Shukla, Kubo formulas for thermodynamic transport coefficients, JHEP 10 (2018) 007 [arXiv:1806.05774] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    V.E. Ambrus and E. Winstanley, Rotating quantum states, Phys. Lett. B 734 (2014) 296 [arXiv:1401.6388] [INSPIRE].CrossRefzbMATHGoogle Scholar
  21. [21]
    F. Becattini, L. Bucciantini, E. Grossi and L. Tinti, Local thermodynamical equilibrium and the beta frame for a quantum relativistic fluid, Eur. Phys. J. C 75 (2015) 191 [arXiv:1403.6265] [INSPIRE].CrossRefGoogle Scholar
  22. [22]
    T. Hayata, Y. Hidaka, T. Noumi and M. Hongo, Relativistic hydrodynamics from quantum field theory on the basis of the generalized Gibbs ensemble method, Phys. Rev. D 92 (2015) 065008 [arXiv:1503.04535] [INSPIRE].Google Scholar
  23. [23]
    C.G. Van Weert, Maximum entropy principle and relativistic hydrodynamics, Ann. Phys. 140 (1982) 133.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    D.N. Zubarev, A.V. Prozorkevich and S.A. Smolyanskii, Derivation of nonlinear generalized equations of quantum relativistic hydrodynamics, Theor. Math. Phys. 40 (1979) 821.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    F. Becattini, Covariant statistical mechanics and the stress-energy tensor, Phys. Rev. Lett. 108 (2012) 244502 [arXiv:1201.5278] [INSPIRE].CrossRefGoogle Scholar
  26. [26]
    F. Becattini and E. Grossi, Quantum corrections to the stress-energy tensor in thermodynamic equilibrium with acceleration, Phys. Rev. D 92 (2015) 045037 [arXiv:1505.07760] [INSPIRE].Google Scholar
  27. [27]
    M. Hongo, Path-integral formula for local thermal equilibrium, Annals Phys. 383 (2017) 1 [arXiv:1611.07074] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    V.E. Ambrus and E. Winstanley, Rotating fermions inside a cylindrical boundary, Phys. Rev. D 93 (2016) 104014 [arXiv:1512.05239] [INSPIRE].MathSciNetGoogle Scholar
  29. [29]
    A. Boyarsky, J. Fröhlich and O. Ruchayskiy, Magnetohydrodynamics of Chiral Relativistic Fluids, Phys. Rev. D 92 (2015) 043004 [arXiv:1504.04854] [INSPIRE].Google Scholar
  30. [30]
    M. Buzzegoli, E. Grossi and F. Becattini, General equilibrium second-order hydrodynamic coefficients for free quantum fields, JHEP 10 (2017) 091 [Erratum ibid. 1807 (2018) 119] [arXiv:1704.02808] [INSPIRE].
  31. [31]
    G. Prokhorov, O. Teryaev and V. Zakharov, Axial current in rotating and accelerating medium, Phys. Rev. D 98 (2018) 071901 [arXiv:1805.12029] [INSPIRE].Google Scholar
  32. [32]
    V.E. Ambrus, Quantum non-equilibrium effects in rigidly-rotating thermal states, Phys. Lett. B 771 (2017) 151 [arXiv:1704.02933] [INSPIRE].CrossRefzbMATHGoogle Scholar
  33. [33]
    L.S. Brown, R.D. Carlitz, D.B. Creamer and C.-k. Lee, Propagation Functions in Pseudoparticle Fields, Phys. Rev. D 17 (1978) 1583 [INSPIRE].Google Scholar
  34. [34]
    K. Landsteiner, Notes on Anomaly Induced Transport, Acta Phys. Polon. B 47 (2016) 2617 [arXiv:1610.04413] [INSPIRE].CrossRefGoogle Scholar
  35. [35]
    K. Jensen, R. Loganayagam and A. Yarom, Thermodynamics, gravitational anomalies and cones, JHEP 02 (2013) 088 [arXiv:1207.5824] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    A. Vilenkin, Macroscopic parity violating effects: neutrino fluxes from rotating black holes and in rotating thermal radiation, Phys. Rev. D 20 (1979) 1807 [INSPIRE].MathSciNetGoogle Scholar
  37. [37]
    A. Vilenkin, Quantum field theory at finite temperature in a rotating system, Phys. Rev. D 21 (1980) 2260 [INSPIRE].Google Scholar
  38. [38]
    A. Vilenkin, Cancellation of equilibrium parity violating currents, Phys. Rev. D 22 (1980) 3067 [INSPIRE].Google Scholar
  39. [39]
    D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  40. [40]
    T. Kalaydzhyan, Temperature dependence of the chiral vortical effects, Phys. Rev. D 89 (2014) 105012 [arXiv:1403.1256] [INSPIRE].Google Scholar
  41. [41]
    A. Flachi and K. Fukushima, Chiral vortical effect with finite rotation, temperature and curvature, Phys. Rev. D 98 (2018) 096011 [arXiv:1702.04753] [INSPIRE].Google Scholar
  42. [42]
    F. Becattini and L. Tinti, Thermodynamical inequivalence of quantum stress-energy and spin tensors, Phys. Rev. D 84 (2011) 025013 [arXiv:1101.5251] [INSPIRE].Google Scholar
  43. [43]
    F. Becattini and L. Tinti, Nonequilibrium Thermodynamical Inequivalence of Quantum Stress-energy and Spin Tensors, Phys. Rev. D 87 (2013) 025029 [arXiv:1209.6212] [INSPIRE].Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Università di Firenze and INFN Sezione di FirenzeSesto Fiorentino (Firenze)Italy

Personalised recommendations