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Gauge-covariant canonical formalism revisited with application to the proton spin decomposition

Cédric Lorcé

  • IPNO, Université Paris-Sud, CNRS/IN2P3, 91406 Orsay, France and LPT, Université Paris-Sud, CNRS, 91405 Orsay, France

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Phys. Rev. D 88, 044037 – Published 21 August, 2013

DOI: https://doi.org/10.1103/PhysRevD.88.044037

Abstract

We revisit the gauge-covariant canonical formalism by separating explicitly physical and gauge degrees of freedom. We show in particular that the gauge-invariant linear and angular momentum operators proposed by Chen et al. can consistently be derived from the standard procedure based on Noether’s theorem. Finally, we demonstrate that this approach is essentially equivalent to the gauge-invariant canonical formalism based on the concept of Dirac variables. Because of many similarities with the background field method, the formalism developed here should also be relevant to general relativity and any metric theories.

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References (81)

  1. P. A. M. Dirac, Can. J. Phys. 33, 650 (1955).
  2. B. S. DeWitt, Phys. Rev. 125, 2189 (1962).
  3. S. Mandelstam, Ann. Phys. (N.Y.) 19, 1 (1962).
  4. I. Bialynicki-Birula, Bull. Acad. Pol. Sci., Sér. sci. tech. 11, 135 (1963).
  5. S. Mandelstam, Phys. Rev. 175, 1580 (1968).
  6. S. Mandelstam, Phys. Rev. 175, 1604 (1968).
  7. O. Steinmann, Ann. Phys. (N.Y.) 157, 232 (1984).
  8. O. Steinmann, Helv. Phys. Acta 58, 995 (1985).
  9. N. B. Skachkov, I. L. Solovtsov, and O. Y. Shevchenko, Z. Phys. C 29, 631 (1985).
  10. P. E. Haagensen and K. Johnson, arXiv:hep-th/9702204.
  11. R. Horan, M. Lavelle, and D. McMullan, Pramana 51, 317 (1998).
  12. T. Masson and J.-C. Wallet, arXiv:1001.1176.
  13. C. Fournel, J. Francois, S. Lazzarini, and T. Masson, arXiv:1212.6702.
  14. X.-S. Chen, arXiv:1203.1288.
  15. V. Pervushin, Fiz. Elem. Chastits At. Yadra 34, 679 (2003) [Phys. Part. Nucl. 34, 348 (2003)].
  16. L. Lantsman, Fiz. B 18, 99 (2009).
  17. J. Schwinger, Phys. Rev. 125, 1043 (1962).
  18. J. S. Schwinger, Phys. Rev. 130, 402 (1963).
  19. R. L. Arnowitt and S. I. Fickler, Phys. Rev. 127, 1821 (1962).
  20. T. Goto, Prog. Theor. Phys. 36, 1283 (1966).
  21. R. P. Treat, J. Math. Phys. (N.Y.) 13, 1704 (1972); 14, 1296(E) (1973).
  22. R. P. Treat, Phys. Rev. D 12, 3145 (1975).
  23. Y. S. Duan and M. L. Ge, Sci. Sin., Ser. A, Math. phys. astron. tech. sci. 11, 1072 (1979).
  24. Y. Duan and S.-C. Zhao, Commun. Theor. Phys. 2, 1553 (1983).
  25. Y.-S. Duan and X.-G. Li, Commun. Theor. Phys. 29, 237 (1998).
  26. Y.-S. Duan and P.-M. Zhang, Mod. Phys. Lett. A 17, 2283 (2002).
  27. R. O. Fulp and L. K. Norris, J. Math. Phys. (N.Y.) 24, 1871 (1983).
  28. T. Kashiwa and N. Tanimura, Fortschr. Phys. 45, 381 (1997).
  29. T. Kashiwa and N. Tanimura, Phys. Rev. D 56, 2281 (1997).
  30. X.-S. Chen, X.-F. Lu, W.-M. Sun, F. Wang, and T. Goldman, Phys. Rev. Lett. 100, 232002 (2008).
  31. X.-S. Chen, W.-M. Sun, F. Wang, and T. Goldman, Phys. Rev. D 83, 071901 (2011).
  32. M. Wakamatsu, Phys. Rev. D 81, 114010 (2010).
  33. M. Wakamatsu, Phys. Rev. D 83, 014012 (2011).
  34. C. Lorcé, Phys. Rev. D 87, 034031 (2013).
  35. B. S. DeWitt, Phys. Rev. 162, 1195 (1967).
  36. B. S. DeWitt, Phys. Rev. 162, 1239 (1967).
  37. B. S. DeWitt, in A Gauge-Invariant Effective Action,in Quantum Gravity 2, A Second Oxford Symposium, edited by C. J. Isham, R. Penrose, and D. W. Sciama (Clarendon Press, Oxford, 1981), pp. 449–487; [California University Santa Barbara, Report No. NSF-ITP-80-031].
  38. G. ’t Hooft, in Proceedings of Acta Universitatis Wratislaviensis, Karpacz, 1975, No. 368, Vol. 1 (Publisher, Wroclaw, 1976), pp. 345–369.
  39. M. T. Grisaru, P. van Nieuwenhuizen, and C. C. Wu, Phys. Rev. D 12, 3203 (1975).
  40. D. G. Boulware, Phys. Rev. D 23, 389 (1981).
  41. L. F. Abbott, Nucl. Phys. B185, 189 (1981).
  42. G. ’t Hooft, Nucl. Phys. B62, 444 (1973).
  43. G. ’t Hooft and M. J. G. Veltman, Ann. Inst. Henri Poincaré, A 20, 69 (1974).
  44. S. Deser, J. H. Kay, and K. S. Stelle, Phys. Rev. Lett. 38, 527 (1977).
  45. L. F. Abbott and S. Deser, Nucl. Phys. B195, 76 (1982).
  46. A. N. Petrov, arXiv:0705.0019.
  47. A. N. Petrov and R. R. Lompay, Gen. Relativ. Gravit. 45, 545 (2013).
  48. R. F. Dashen and D. J. Gross, Phys. Rev. D 23, 2340 (1981).
  49. L. F. Abbott and S. Deser, Phys. Lett. 116B, 259 (1982).
  50. M. Luscher and P. Weisz, Nucl. Phys. B452, 213 (1995).
  51. F. Freire, D. F. Litim, and J. M. Pawlowski, Phys. Lett. B 495, 256 (2000).
  52. D. Binosi and J. Papavassiliou, Phys. Rep. 479, 1 (2009).
  53. D. Binosi and A. Quadri, Phys. Rev. D 85, 121702 (2012).
  54. L. F. Abbott, Acta Phys. Pol. B 13, 33 (1982).
  55. L. H. Ryder, Quantum Field Theory (Cambridge University Press, Cambridge, England, 1985).
  56. E. Noether, Gott. Nachr. 1918, 235 (1918) [Transp. Theory Stat. Phys. 1, 186 (1971)].
  57. J. R. Ray, Nuovo Cimento A 56, 189 (1968).
  58. R. Jackiw, Phys. Rev. Lett. 41, 1635 (1978).
  59. B. A. Levitsky and Y. A. Yappa, Teor. Mat. Fiz. 48, 227 (1981) [Theor. Math. Phys. 48, 715 (1981)].
  60. B. A. Levitsky and Y. A. Yappa, Teor. Mat. Fiz. 53, 250 (1982) [Theor. Math. Phys. 53, 1107 (1982)].
  61. S. Hamamoto, Z. Phys. C 19, 353 (1983).
  62. G. Barnich, F. Brandt, and M. Henneaux, Phys. Lett. B 346, 81 (1995).
  63. C. L. Lewis, Am. J. Phys. 77, 839 (2009).
  64. B. S. DeWitt, Int. ser. monogr. phys. 114, 1 (2003).
  65. T. Frankel, The Geometry of Physics: An Introduction (Cambridge University Press, Cambridge, England, 1997).
  66. F. de Felice and C. J. S. Clarke, Relativity on Curved Manifolds (Cambridge University Press, Cambridge, England, 1990).
  67. A. Unzicker and T. Case, arXiv:physics/0503046.
  68. Z.-Q. Guo and I. Schmidt, Phys. Rev. D 87, 114016 (2013).
  69. Z.-Q. Guo and I. Schmidt, Phys. Rev. D 87, 114017 (2013).
  70. H.-M. Chan and S. T. Tsou, Phys. Rev. D 57, 2507 (1998).
  71. H.-M. Chan and S. T. Tsou, Int. J. Mod. Phys. A 27, 1230002 (2012).
  72. M. J. Baker, J. Bordes, H. M. Chan, and S. T. Tsou, Int. J. Mod. Phys. A 27, 1250087 (2012).
  73. H. A. Al-Kuwari and M. O. Taha, Am. J. Phys. 59, 363 (1991).
  74. C. Lorcé, arXiv:1306.0456.
  75. C. Lorcé, Phys. Lett. B 719, 185 (2013).
  76. Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959).
  77. J. Collins, Foundations of Perturbative QCD, Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology Vol. 32 (Cambridge University Press, Cambridge, England, 2011).
  78. V. N. Gribov, Nucl. Phys. B139, 1 (1978).
  79. A. Bassetto, I. Lazzizzera, and R. Soldati, Phys. Lett. 131B, 177 (1983).
  80. S. V. Ivanov, G. P. Korchemsky, and A. V. Radyushkin, Yad. Fiz. 44, 230 (1986) [Sov. J. Nucl. Phys. 44, 145 (1986)].
  81. A. Burnel, Lect. Notes Phys. 761, 1 (2009).

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Phys. Rev. D 88, 044037– Published 21 August, 2013
  • Received 21 June 2013

© 2013 American Physical Society

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