Skip to main content

Advertisement

SpringerLink
Log in

Thermodynamic Properties in Higher-Derivative Electrodynamics

  • Particles and Fields
  • Published:
Brazilian Journal of Physics Aims and scope Submit manuscript

Abstract

In this work, we study the thermodynamic properties of a photon gas in a heat bath within the context of higher-derivative electrodynamics. Specifically, we analyze Podolsky’s theory and its extension involving the Lorentz symmetry violation recently proposed in the literature. First, we use the concept of the number of available states of the system in order to construct the partition function. Next, we calculate the main thermodynamic functions: Helmholtz free energy, mean energy, entropy, and heat capacity. In particular, we verify that there exist significant changes in heat capacity and mean energy due to Lorentz violation. Additionally, the modification of the black body radiation and the correction to the Stefan–Boltzmann law in the context of the primordial inflationary universe are provided for both theories as well.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. P.W. Higgs, Broken symmetries and the masses of gauge bosons. Phys. Rev. Lett. 13, 508 (1964). https://doi.org/10.1103/PhysRevLett.13.508

  2. P.W. Higgs, Spontaneous Symmetry Breakdown without Massless Bosons. Phys. Rev. 145, 1156 (1966). https://doi.org/10.1103/PhysRev.145.1156

    Article  ADS  MathSciNet  Google Scholar 

  3. L.H. Ryder, Quantum field theory (Cambridge University Press, 1996)

  4. A. Das, Lectures on quantum field theory (World Scientific, 2008)

  5. L.C. Tu, J. Luo, and G. T. Gillies, ”The mass of the photon”, Rep. Prog. Phys. 68, 77–130, (2005) https://doi.org/10.1088/0034-4885/68/1/R02.

  6. B. Podolsky, A generalized electrodynamics part Inon-quantum. Phys. Rev. 62, 68 (1942). https://doi.org/10.1103/PhysRev.62.68

  7. B. Podolsky, C. Kikuchi, A generalized electrodynamics part II quantum. Phys. Rev. 65, 228 (1944). https://doi.org/10.1103/PhysRev.65.228

  8. B. Podolsky, P. Schwed, Review of a generalized electrodynamics. Rev. Mod. Phys. 20, 40 (1948). https://doi.org/10.1103/RevModPhys.20.40

  9. A. Accioly, E. Scatena, Limits on the coupling constant of higher-derivative electromagnetism. Mod. Phys. Lett. A 25, 269–276 (2010). https://doi.org/10.1142/S0217732310031610

    Article  ADS  MATH  Google Scholar 

  10. C.A. Galvao, B. Pimentel, The canonical structure of Podolsky generalized electrodynamics. Can. J. Phys. 66, 460–466 (1988). https://doi.org/10.1139/p88-075

  11. R. Casana, M.M. Ferreira Jr., L. Lisboa-Santos, F.E. dos Santos, M. Schreck, Maxwell electrodynamics modified by CPT-even and Lorentz-violating dimension-6 higher-derivative terms. Phys. Rev. D 97, 115043 (2018). https://doi.org/10.1103/PhysRevD.97.115043

    Article  ADS  Google Scholar 

  12. R. Bufalo, B. Pimentel, G. Zambrano, Renormalizability of generalized quantum electrodynamics. Phys. Rev. D 86, 125023 (2012). https://doi.org/10.1103/PhysRevD.86.125023

  13. R. Bufalo, B.M. Pimentel, G.E.R. Zambrano, Path integral quantization of generalized quantum electrodynamics. Phys. Rev. D 83, 045007 (2011). https://doi.org/10.1103/PhysRevD.83.045007

    Article  ADS  Google Scholar 

  14. P. Gaete, Some considerations about Podolsky-axionic electrodynamics. Int. J. Mod. Phys. A 27, 1250061 (2012). https://doi.org/10.1142/S0217751X12500613

  15. C. Bonin, R. Bufalo, B. Pimentel, G. Zambrano, Podolsky electromagnetism at finite temperature: Implications on the Stefan-Boltzmann law. Phys. Rev. D 81, 025003 (2010). https://doi.org/10.1103/PhysRevD.81.025003

    Article  ADS  Google Scholar 

  16. C. Bonin, B. Pimentel, P. Ortega, Multipole expansion in generalized electrodynamics. Int. J. Mod. Phys. A 34, 1950134 (2019). https://doi.org/10.1142/S0217751X19501343

    Article  ADS  MathSciNet  Google Scholar 

  17. R.R. Cuzinatto, C.A.M. de Melo, L.G. Medeiros, B.M. Pimentel, P.J. Pompeia, Bopp-Podolsky black holes and the no-hair theorem. Eur. Phys. J. C 78, 43 (2018). https://doi.org/10.1140/epjc/s10052-018-5525-6

    Article  ADS  Google Scholar 

  18. R.R. Cuzinatto, E.M. de Morais, L.G. Medeiros, C. Naldoni de Souza, B.M. Pimentel, ”de Broglie-Proca and Bopp-Podolsky massive photon gases in cosmology”, EPL (Europhysics Letters) 118, 19001 (2017) https://doi.org/10.1209/0295-5075/118/19001.

  19. S.I. Kruglov, Solutions of Podolsky’s Electrodynamics Equation in the First-Order Formalism. J. Phys. A 43, 245403 (2010). https://doi.org/10.1088/1751-8113/43/24/245403

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. R. Cuzinatto, C. De Melo, L. Medeiros, P. Pompeia, How can one probe Podolsky Electrodynamics? Int. J. Mod. Phys. A 26, 3641 (2011). https://doi.org/10.1142/S0217751X11053961

    Article  ADS  Google Scholar 

  21. A.E. Zayats, Self-interaction in the Bopp-Podolsky electrodynamics: Can the observable mass of a charged particle depend on its acceleration? Ann. Phys. 342, 11 (2014). https://doi.org/10.1016/j.aop.2013.12.005

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. D. Granado, A. Carvalho, A. Y. Petrov, and P. Porfirio, arXiv: 1912.00855 [hep-th] (2019)

  23. A. Nogueira, C. Palechor, A. Ferrari, Reduction of order and Fadeev-Jackiw formalism in generalized electrodynamics. Nucl. Phys. B 939, 372 (2019). https://doi.org/10.1016/j.nuclphysb.2018.12.026

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. L. Borges, F. Barone, C. de Melo, F. Barone, Higher order derivative operators as quantum corrections. Nucl. Phys. B 944, 114634 (2019). https://doi.org/10.1016/j.nuclphysb.2019.114634

  25. L. Bonetti, L. R. dos Santos Filho, J. A. Helayël-Neto, and A. D. Spallicci, ”Effective photon mass by Super and Lorentz symmetry breaking”, Phys. Lett. B 764, 203 (2017) https://doi.org/10.1016/j.physletb.2016.11.023

  26. V.A. Kosteleckyỳ, M. Mewes, Fermions with Lorentz-violating operators of arbitrary dimension. Phys. Rev. D 88, 096006 (2013). https://doi.org/10.1103/PhysRevD.88.096006

    Article  ADS  Google Scholar 

  27. F. Reif, Fundamentals of statistical and thermal physics (Waveland Press, 2009)

  28. A. Camacho, A. Maciás, Thermodynamics of a photon gas and deformed dispersion relations. Gen. Relativ. Gravit. 39, 1175 (2007). https://doi.org/10.1007/s10714-007-0419-1

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. M. Anacleto, F. Brito, E. Maciel, A. Mohammadi, E. Passos, W. Santos, J. Santos, Lorentz-violating dimension-five operator contribution to the black body radiation. Phys. Lett. B 785, 191 (2018). https://doi.org/10.1016/j.physletb.2018.08.043

  30. R. R. Oliveira, A. A. Araújo Filho, F. C. Lima, R. V. Maluf, and C. A. Almeida, ”Thermodynamic properties of an Aharonov-Bohm quantum ring”, Eur. Phys. J. Plus 134, 495 (2019) https://doi.org/10.1140/epjp/i2019-12880-x.

  31. R. Oliveira and A. Arauújo Filho, ”Thermodynamic properties of neutral Dirac particles in the presence of an electromagnetic field”, Eur. Phys. J. Plus 135, 99 (2020) https://doi.org/10.1140/epjp/s13360-020-00146-9.

  32. H. Hassanabadi, M. Hosseinpour, Thermodynamic properties of neutral particle in the presence of topological defects in magnetic cosmic string background. Eur. Phys. J. C 76, 553 (2016). https://doi.org/10.1140/epjc/s10052-016-4392-2

    Article  ADS  Google Scholar 

  33. M. Pacheco, R. Maluf, C. Almeida, R. Landim, Three-dimensional Dirac oscillator in a thermal bath. Europhys. Lett. 108, 10005 (2014). https://doi.org/10.1209/0295-5075/108/10005

    Article  ADS  Google Scholar 

  34. W. Yao, C. Yang, J. Jing, Holographic insulator/superconductor transition with exponential nonlinear electrodynamics probed by entanglement entropy. Eur. Phys. J. C 78, 353 (2018). https://doi.org/10.1140/epjc/s10052-018-5836-7

  35. N. Zettili, Quantum mechanics: concepts and applications (Wiley, Chichester, 2003)

    Google Scholar 

  36. R. Maluf, A. Araújo Filho, W. Cruz, and C. Almeida, ”Antisymmetric tensor propagator with spontaneous Lorentz violation”, Europhys. Lett. 124, 61001 (2019)  https://doi.org/10.1209/0295-5075/124/61001.

  37. A.B. Scarpelli, H. Belich, J. Boldo, J.A. Helayël-Neto, Aspects of causality and unitarity and comments on vortexlike configurations in an Abelian model with a Lorentz-breaking term. Phys. Rev. D 67, 085021 (2003). https://doi.org/10.1103/PhysRevD.67.085021

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for financial support. R. V. Maluf thanks CNPq grants 307556/2018-2 for supporting this project. A.A.A.F thanks D.M. Dantas for help with the computer calculations and L.L. Mesquita for the careful reading of this manuscript.

Author information

Authors and Affiliations

  1. Departamento de Física, Campus do Pici, Universidade Federal do Ceará (UFC), Ceara, C.P. 6030, 60455-760, Fortaleza, Brazil

    A. A. Araújo Filho & R. V. Maluf

Authors
  1. A. A. Araújo Filho
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. V. Maluf
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Araújo Filho.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Araújo Filho, A.A., Maluf, R.V. Thermodynamic Properties in Higher-Derivative Electrodynamics. Braz J Phys 51, 820–830 (2021). https://doi.org/10.1007/s13538-021-00880-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13538-021-00880-0

Keywords

Search

Navigation