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The European Physical Journal A

, Volume 37, Issue 1, pp 33–54 | Cite as

Form factors in RQM approaches: Constraints from space-time translations

  • B. DesplanquesEmail author
  • Y. B. DongEmail author
Regular Article — Theoretical Physics

Abstract

Different relativistic quantum-mechanic approaches have recently been used to calculate properties of various systems, form factors in particular. It is known that predictions, which most often rely on a single-particle current approximation, can lead to predictions with a very large range. It was shown that accounting for constraints related to space-time translations could considerably reduce this range. It is shown here that predictions can be made identical for a large range of cases. These ones include the following approaches: instant form, front form, and “point form” in arbitrary momentum configurations and a dispersion-relation approach which can be considered as the approach which the other ones should converge to. This important result supposes both an implementation of the above constraints and an appropriate single-particle-like current. The change of variables that allows one to establish the equivalence of the approaches is given. Some points are illustrated with numerical results for the ground state of a system consisting of scalar particles.

PACS

13.40.Gp Electromagnetic form factors 21.45.-v Few-body systems 11.10.St Bound and unstable states; Bethe-Salpeter equations 11.30.Cp Lorentz and Poincaré invariance 

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References

  1. 1.
    P.A.M. Dirac, Rev. Mod. Phys. 21, 392 (1949).zbMATHCrossRefADSMathSciNetGoogle Scholar
  2. 2.
    B. Keister, W. Polyzou, Adv. Nucl. Phys. 20, 225 (1991).Google Scholar
  3. 3.
    A. Amghar, B. Desplanques, L. Theußl, Nucl. Phys. A 714, 213 (2003).CrossRefADSGoogle Scholar
  4. 4.
    Jun He, B. Julia-Diaz, Yu-bing Dong, Phys. Lett. B 602, 212 (2004).CrossRefADSGoogle Scholar
  5. 5.
    B. Julia-Diaz, D.O. Riska, F. Coester, Phys. Rev. C 69, 035212 (2004); 75, 069902 (2007)(E).CrossRefADSGoogle Scholar
  6. 6.
    W. Plessas, in Proceedings of the Workshop of the Physics of Excited Nucleons, Grenoble (France), March 24–27, 2004 (NSTAR 2004), edited by J.P. Bocquet et al. (World Scientific, 2004).Google Scholar
  7. 7.
    T.W. Allen, W.H. Klink, W.N. Polyzou, Phys. Rev. C 63, 034002 (2001).CrossRefADSGoogle Scholar
  8. 8.
    P.L. Chung et al., Phys. Rev. C 37, 2000 (1988).CrossRefADSGoogle Scholar
  9. 9.
    J.W. Van Orden, N. Devine, F. Gross, Phys. Rev. Lett. 75, 4369 (1995).CrossRefADSGoogle Scholar
  10. 10.
    B. Desplanques, nucl-th/0407074.Google Scholar
  11. 11.
    V.V. Anisovich et al., Nucl. Phys. A 544, 747 (1992).CrossRefADSGoogle Scholar
  12. 12.
    A.F. Krutov, V.E. Troitsky, Phys. Rev. C 65, 045501 (2002).CrossRefADSGoogle Scholar
  13. 13.
    D. Melikhov, hep-ph/0110087, Eur. Phys. J. C direct 4, 4 (2002).Google Scholar
  14. 14.
    G.C. Wick, Phys. Rev. 96, 1124 (1954).zbMATHCrossRefADSMathSciNetGoogle Scholar
  15. 15.
    R.E. Cutkosky, Phys. Rev. 96, 1135 (1954).zbMATHCrossRefADSMathSciNetGoogle Scholar
  16. 16.
    F.M. Lev, Riv. Nuovo Cimento 16, 1 (1993).MathSciNetGoogle Scholar
  17. 17.
    B. Bakamjian, L.H. Thomas, Phys. Rev. 92, 1300 (1953).zbMATHCrossRefADSMathSciNetGoogle Scholar
  18. 18.
    B. Bakamjian, Phys. Rev. 121, 1849 (1961).zbMATHCrossRefADSMathSciNetGoogle Scholar
  19. 19.
    S.N. Sokolov, Theor. Math. Phys. 62, 140 (1985).CrossRefGoogle Scholar
  20. 20.
    B. Desplanques, L. Theußl, Eur. Phys. J. A 21, 93 (2004).CrossRefADSGoogle Scholar
  21. 21.
    F. Coester, Few-Body Suppl. 15, 219 (2002).Google Scholar
  22. 22.
    B. Desplanques, Nucl. Phys. A 748, 139 (2005).CrossRefADSGoogle Scholar
  23. 23.
    R.F. Wagenbrunn et al., Phys. Lett. B 511, 33 (2001).CrossRefADSGoogle Scholar
  24. 24.
    S.N. Sokolov, A.N. Shatnii, Theor. Math. Phys. 37, 1029 (1978).CrossRefMathSciNetGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  1. 1.LPSC, Université Joseph Fourier Grenoble 1, CNRS/IN2P3, INPGGrenoble CedexFrance
  2. 2.Institute of High Energy PhysicsChinese Academy of ScienceBeijingPRC

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