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Relativistic Two-Boson System in Presence of Electromagnetic Plane Wave

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Abstract

The relativistic two-body problem is considered for spinless particles subject to an external electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided the mutual interaction between particles is known), it is possible to write down explicitly a pair of coupled wave equations (corresponding to a pair of mass-shell constraints) which takes into account also the field contribution. These equations are manifestly covariant; constants of the motion are exhibited, so one ends up with a reduced problem involving five degrees of freedom.

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Notes

  1. But some situations of physical interest are not included in this case: for instance when the external field is a single monochromatic plane wave, it turns out that the wave vector is a direction of strong translation invariance; but it is a null vector, so in this case E L admits no orthonormal frame.

  2. In contrast eq. (8) of that reference holds only if P L is timelike, which is not the case eventually considered in the present paper.

  3. In contrast G fails to be invariant by rotation in \(\mathcal {E}_{12}\), as can be seen by a direct computation.

  4. Space ⊕ three-dimensional hyperbolic, not to be confused with the usual time ⊕ space decomposition.

  5. The eigenvalue of −N appears denoted as b 2 in the work of Todorov [18–21]; divided by the reduced mass it is proportional to the leading term in the development of the mass defect M−(m 1 + m 2), insofar as an isolated system is concerned.

References

  1. Marzlin, K-P., Audretsch, J.: Phys. Rev. A 53, 1004 (1996)

    Article  ADS  Google Scholar 

  2. Bordé, Ch. J. In: Arecchi, F.T., Strumia, F., Walther, H (eds.) Advances in Laser Spectroscopy. Plenum Publishing Corp (1983)

  3. Ishikawa, J., Riehle, F., Helmcke, J., Bordé, Ch J.: Phys. Rev. A 49, 4794–4825 (1994)

    Article  ADS  Google Scholar 

  4. Ruf, M., Mocken, G., Mueller, C., Hatsagortsyan, K., Keitel, Ch.: Phys. Rev. Lett. 102, 080402 (2009)

    Article  ADS  Google Scholar 

  5. Heinzl, Th., Ilderton, A., Marklund, M.: Phys. Lett. B 692, 250–256 (2010)

    Article  ADS  Google Scholar 

  6. An introductive (non-exhaustive) account of modern relativistic dynamics is available in Relativistic Action-at-a-distance, Classical and quantum aspects, Lecture Notes in Phys. 162, J. Llosa Editor, Springer Verlag (1982) and references therein

  7. Droz-Vincent, Ph.: Reports Math. Phys 8, 79 (1975)

    Article  ADS  MathSciNet  Google Scholar 

  8. Droz-Vincent, Ph.: Phys. Rev. D 19, 702 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  9. Bel, L. In: Cahen, M., Flato, M. (eds.) Differential Geometry and Relativity, p 197. Reidel, Dordrecht (1976)

  10. Bel, L.: Phys. Rev. D 28, 1308 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  11. Leutwyler, H., Stern, J.: Ann. of Phys. (N-Y) 112, 94 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  12. Leutwyler, H., Stern, J. Phys. Lett. B 73, 75 (1978)

    Article  ADS  Google Scholar 

  13. Crater, H.W., Van Alstine, P.: Phys. Lett. B 100, 166 (1981)

    Article  ADS  Google Scholar 

  14. Todorov, I.T.: JINR Report E2-10125. unpublished (1976)

  15. Molotkov, V.V., Todorov, I.T.: Commun. Math. Phys 79, 111 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  16. Todorov, I.T.: Contribution to reference [6]

  17. Popov, V.S.: Phys. Lett. A 298, 83 (2002)

    Article  ADS  Google Scholar 

  18. Todorov, I.T.: Phys. Rev. D 3, 2351 (1971)

    Article  ADS  Google Scholar 

  19. Todorov, I.T. In: Zichichi, A. (ed.) Properties of Fundamental Interactions, vol. 9, part C, p 951. editrice Compositori, Bologna (1973)

  20. Rizov, V. A., Todorov, I.T.: Sov. J. Part. Nucl 6, 269 (1975)

    MathSciNet  Google Scholar 

  21. Rizov, V. A., Todorov, I.T., Aneva, B. L.: Nucl. Phys. B 98, 447 (1975)

    Article  ADS  Google Scholar 

  22. Sazdjian, H.: Phys. Lett. B 156, 381 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  23. Sazdjian, H.: J. Math. Phys 28, 2618 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  24. Crater, H.W., Becker, R.L., Wong, C.Y., Van Alstine, P.: Phys. Rev. D 46, 5117–5153 (1992)

    Article  ADS  Google Scholar 

  25. Jallouli, Sazdjian, H.: Ann. Phys. (N-Y) 253, 376–426 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  26. Bijtebier, J.: J. Broekaert Nuovo Cim A 105, 351 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  27. Sokolov, S.N.: Theor. Math. Phys 36, 193 (1978)

    Article  Google Scholar 

  28. Sokolov, S.N.: Theor. Math. Phys. 37, 1029 (1979)

    Article  Google Scholar 

  29. Droz-Vincent, Ph.: Int. J. Theor. Phys 48, 2177–2189 (2009)

    Article  MathSciNet  Google Scholar 

  30. Bijtebier, J.: Nuovo Cim. A 102, 1285 (1989)

    Article  Google Scholar 

  31. Droz-Vincent, Ph.: Nuovo Cimento A 105, 1103–1126 (1992). There are several misprints in this paper: in p.1107 one should read condition (2.15) instead of condition (3.15). In Appendices B and C: Z was skipped from the r.h.s. of formula B.5. One should read \( K = \overline {H} +G\) and \(\overline {H}_{1} + \overline {H}_{2} = {P^{2} \over 4} + y^{2}\)

    Article  ADS  Google Scholar 

  32. Droz-Vincent, Ph.: Few-Body Syst. 14, 97–115 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  33. Droz-Vincent, Ph.: Two-body relativistic system in external field. In: Colomo, F., Lusanna, L., Marmo, G. (eds.) Constraint Theory and Quantization Methods. World Scientific, Montepulciano (1994)

  34. Currie, D.G.: J. Math. Phys. 4, 1470 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  35. Currie, D.G: Phys. Rev. 142, 817 (1966)

    Article  ADS  MathSciNet  Google Scholar 

  36. Currie, D.G., Jordan, T.F., Sudarshan, E.C.G.: Rev. Mod. Phys. 35, 350 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  37. Droz-Vincent, Ph.: Int. J. Theor. Phys 39, 389–403 (2000)

    Article  Google Scholar 

  38. Volkov, D.M.: Zeits. Phys 94, 250 (1935)

    Article  ADS  Google Scholar 

  39. Brown, L S, Kibble, T W B: Phys. Rev 133A, 705 (1964)

    Article  ADS  Google Scholar 

  40. Bergou, J., Varró, S.: J. Phys. A: Math. Gen 13, 2823–2837 (1980)

    Article  ADS  Google Scholar 

  41. Droz-Vincent, Ph.: Phys. Rev. A 52, 1837–1844 (1995)

    Article  ADS  Google Scholar 

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  1. Observatoire de Paris-Meudon, Université Paris-Diderot, 5 place Jules Janssen, 92195, Meudon, France

    Ph. Droz-Vincent

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Droz-Vincent, P. Relativistic Two-Boson System in Presence of Electromagnetic Plane Wave. Int J Theor Phys 55, 4124–4141 (2016). https://doi.org/10.1007/s10773-016-3040-9

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