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Single-particle quantum mechanics of the free Klein–Gordon equation with Lorentz violation

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Abstract

In spite of its problems with interactions, the first-quantized Klein–Gordon equation is a satisfactory theory of free spinless particles. Moreover, the usual theory may be extended to describe Lorentz-violating behavior, of the same types that exist can in second-quantized scalar field theories. However, because the construction of the theory requires a restriction to positive-energy modes, the Hilbert space inner product and the position operator depend explicitly on the form of the Lorentz violation.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The paper was based entirely on analytical calculations, with no numerical data collected or created].

References

  1. D. Colladay, V.A. Kostelecký, Phys. Rev. D 55, 6760 (1997)

    Article  ADS  Google Scholar 

  2. D. Colladay, V.A. Kostelecký, Phys. Rev. D 58, 116002 (1998)

    Article  ADS  Google Scholar 

  3. O.W. Greenberg, Phys. Rev. Lett. 89, 231602 (2002)

    Article  ADS  Google Scholar 

  4. K. Bakke, H. Belich, Ann. Phys. 360, 596 (2015)

    Article  Google Scholar 

  5. R.L.L. Vitória, H. Belich, K. Bakke, Eur. Phys. J. Plus 132, 25 (2017)

    Article  Google Scholar 

  6. R.L.L. Vitória, H. Belich, Eur. Phys. J. C 78, 999 (2018)

    Article  ADS  Google Scholar 

  7. R.L.L. Vitória, H. Belich, Adv. High Energy Phys. 2019, 8462973 (2019)

    Google Scholar 

  8. R.L.L. Vitória, H. Belich, Eur. Phys. J. D 75, 291 (2021)

    Article  ADS  Google Scholar 

  9. F. Ahmed, Int. J. Geom. Meth. Mod. Phys. 19, 2250059 (2022)

    Article  MathSciNet  Google Scholar 

  10. E.-Q. Wang, H. Chen, Y. Yang, Z.-W. Long, H. Hassanabadi, Acta Phys. Sin 71, 060301 (2022)

    Article  Google Scholar 

  11. S. Zare, H. Hassanabadi, G. Junker, Mod. Phys. Lett. A 37, 2250113 (2022)

    Article  ADS  Google Scholar 

  12. V.A. Kostelecký, Phys. Rev. D 69, 105009 (2004)

    Article  ADS  Google Scholar 

  13. R. Bluhm, Phys. Rev. D 91, 065034 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  14. R. Bluhm, Phys. Rev. D 92, 085015 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  15. R. Bluhm, A. Šehić, Phys. Rev. D 94, 104034 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  16. R. Bluhm, H. Bossi, Y. Wen, Phys. Rev. D 100, 084022 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  17. V.A. Kostelecký, R. Lehnert, Phys. Rev. D 63, 065008 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  18. V.A. Kostelecký, N. Russell, Phys. Lett. B 693, 443 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  19. V.A. Kostelecký, Phys. Lett. B 701, 137 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  20. D. Colladay, P. McDonald, Phys. Rev. D 85, 044042 (2012)

    Article  ADS  Google Scholar 

  21. V.A. Kostelecký, N. Russell, R. Tso, Phys. Lett. B 716, 470 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  22. N. Russell, Phys. Rev. D 91, 045008 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  23. M. Schreck, Eur. Phys. J. C 75, 187 (2015)

    Article  ADS  Google Scholar 

  24. B.R. Edwards, V.A. Kostelecký, Phys. Lett. B 786, 319 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  25. M. Voicu, Prog. Electromag. Res. 113, 83102 (2011)

    Article  Google Scholar 

  26. C. Pfeifer, M.N.R. Wohlfarth, Phys. Rev. D 84, 044039 (2011)

    Article  ADS  Google Scholar 

  27. M. Hohmann, C. Pfeifer, N. Voicu, J. Math. Phys. 63, 032503 (2022)

    Article  ADS  Google Scholar 

  28. M.S. Berger, V.A. Kostelecký, Phys. Rev. D 65, 091701 (2002)

    Article  ADS  Google Scholar 

  29. S.L. Schweber, An Introduction to Relativistic Quantum Field Theory (Harper and Row, New York, 1961), pp.54–64

    Google Scholar 

  30. M.H.L. Pryce, Proc. Roy. Soc. A (London) 195, 62 (1948)

    ADS  Google Scholar 

  31. C. Møller, Comm. Dublin Inst. Adv. Stud. 4, 5 (1949)

    Google Scholar 

  32. T.D. Newton, E.P. Wigner, Rev. Mod. Phys. 21, 400 (1949)

    Article  ADS  Google Scholar 

  33. L.L. Foldy, S.A. Wouthuysen, Phys. Rev. 78, 29 (1950)

    Article  ADS  Google Scholar 

  34. J.R. Ellis, G. Siopsis, J. Phys. A: Math. Gen. 15, L259 (1982)

    Article  ADS  Google Scholar 

  35. B. Altschul, D. Colladay, Phys. Rev. D 71, 125015 (2005)

    Article  ADS  Google Scholar 

  36. O.I. Zavialov, Theor. Math. Phys. 141, 1631 (2004)

    Article  Google Scholar 

  37. B. Altschul, Phys. Lett. B 639, 679 (2006)

    Article  ADS  Google Scholar 

  38. D. Colladay, V.A. Kostelecký, Phys. Lett. B 511, 209 (2001)

    Article  ADS  Google Scholar 

  39. B. Altschul, Phys. Rev. D 70, 056005 (2004)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of South Carolina, Columbia, SC, 29208, USA

    Brett Altschul

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  1. Brett Altschul
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Correspondence to Brett Altschul.

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Altschul, B. Single-particle quantum mechanics of the free Klein–Gordon equation with Lorentz violation. Eur. Phys. J. Plus 138, 648 (2023). https://doi.org/10.1140/epjp/s13360-023-04285-7

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