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Worldline path integrals for a Dirac particle in a weak gravitational plane wave

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Abstract

The problem of a relativistic spinning particle interacting with a weak gravitational plane wave in (3+1) dimensions is formulated in the frame work of covariant supersymmetric path integrals. The relative Green function is expressed through a functional integral over bosonic trajectories that describe the external motion and fermionic variables that describe the spin degrees of freedom. The (3+1) dimensional problem is reduced to the (1+1) dimensional one by using an identity. Next, the relative propagator is exactly calculated and the wave functions are extracted.

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References

  1. R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals (McGraw Hill, New York, 1965)

    MATH  Google Scholar 

  2. S.W. Hawking, J.B. Hartle, Phys. Rev. D 13, 2188 (1976)

    Article  ADS  Google Scholar 

  3. D.M. Chitre, J.B. Hartle, Phys. Rev. D 16, 251 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  4. L.S. Schulman, Techniques and Applications of Path Integration (John Wiley, New York, 1981)

    MATH  Google Scholar 

  5. H. Kleinert, Path Integral in Quantum Mechanics, Statistics and Polymer Physics (World Scientific, Singapore, 1990)

    Google Scholar 

  6. M. Chaichian, A. Demichev, Path Integrals in Physics, Vol. 1 (IOP Publisher, Bristol UK, 2001)

    MATH  Google Scholar 

  7. M. Chaichian, A. Demichev, Stochastic Processes and Quantum Mechanics, Vol. 2 (IOP Publisher, Bristol UK, 2001)

    MATH  Google Scholar 

  8. M. Chaichian, A. Demichev, Quantum Field Theory, Statistical Physics and other Modern Applications (IOP Publisher, Bristol UK, 2001)

    MATH  Google Scholar 

  9. E.S. Fradkin, D.M. Gitman, Phys. Rev. D 44, 3220 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  10. C. Alexandrou, R. Rosenfelder, A.W. Schreiber, Phys. Rev. A 59, 3 (1998)

    MathSciNet  Google Scholar 

  11. D.M. Gitman, Nucl. Phys. B 488, 490 (1997)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. B. Geyer, D.M. Gitman, I.L. Shapiro, Int. J. Mod. Phys. A 15, 3861 (2000)

    MATH  ADS  MathSciNet  Google Scholar 

  13. S. Haouat, L. Chetouani, Int. J. Theor. Phys. 46, 1528 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  14. S. Haouat, L. Chetouani, J. Phys. A Math. Theor. 40, 1349 (2007)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. A. Barducci, R. Giachetti, J. Phys. A Math. Gen. 38, 1615 (2005)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  16. A.N. Vaidya, C. Farina, M.S. Guimaraes, M. Neves, J. Phys. A Math. Theor. 40, 9149 (2007)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  17. L.D. Landau, E.M. Lifshitz, The Classical Theory Fields (Pergamon Press, Oxford, 1987)

    Google Scholar 

  18. V.I. Pustovoit, L.A. Chernozatonskii, JETP 34, 229 (1981)

    Google Scholar 

  19. B.F. Schutz, A first Course in General Relativity (Cambridge University Press, Cambridge, 1995)

    Google Scholar 

  20. S. Weinberg, Gravitation and Cosmology (John Wiley and Sons, New York, 1972)

    Google Scholar 

  21. F.A. Berezin, M.S. Marinov, JETP Lett. 21, 320 (1975)

    ADS  Google Scholar 

  22. F.A. Berezin, M.S. Marinov, Ann. Phys. 104, 336 (1977)

    Article  MATH  ADS  Google Scholar 

  23. L. Brink, S. Deser, B. Zumino, P. Di Vecchia, P. Howe, Phys. Lett. B 64, 435 (1976)

    Article  ADS  Google Scholar 

  24. L. Brink, P. Di Vecchia, P. Howe, Nucl. Phys. B 118, 76 (1977)

    Article  ADS  Google Scholar 

  25. D.M. Gitman, S.I. Zlatev, Phys. Rev. D 55, 7701 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  26. D.M. Gitman, S.I. Zlatev, W.D. Cruz, Brazil. J. Phys. 26, 419 (1996)

    ADS  Google Scholar 

  27. S. Zeggari, T. Boudjedaa, L. Chetouani, Phys. Scripta 64, 285 (2001)

    Article  MATH  ADS  Google Scholar 

  28. J.D. Bjorken, S.D. Drell, Relativistic Quantum Fields (McGraw Hill, New York, 1965)

    MATH  Google Scholar 

  29. A.M. Polyakov, Gauge Fields and Strings (Harwood Academic, Chur, Switzerland, 1987)

    Google Scholar 

Download references

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Correspondence to L. Chetouani.

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PACS

04.30.-w; 03.65.Ca; 03.65.Db; 03.65.Pm

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Haouat, S., Chetouani, L. Worldline path integrals for a Dirac particle in a weak gravitational plane wave. Eur. Phys. J. C 53, 289–294 (2008). https://doi.org/10.1140/epjc/s10052-007-0448-7

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  • DOI: https://doi.org/10.1140/epjc/s10052-007-0448-7

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