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Canonical formalism on a null surface: The scalar and the electromagnetic fields

R. Nagarajan

J. N. Goldberg

  • Syracuse University, Syracuse, New York, 13210

  • Syracuse University, Syracuse, New York 13210 and Institut Henri Poincaré, Laboratoire de Physique Théorique, ERA 533, 11 rue Pierre et Marie Curie, Paris 5e

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Phys. Rev. D 31, 1354 – Published 15 March, 1985

DOI: https://doi.org/10.1103/PhysRevD.31.1354

Abstract

The Hamiltonian for the scalar and electromagnetic fields are set up on an outgoing null cone plus that portion of scrI+ which extends back to space-like infinity. The latter portion is just the energy radiated so that the Hamiltonian is the total energy, a constant of the motion. Because the formalism is set on a characteristic surface, the momenta must satisfy certain constraints in addition to the gauge constraints. These null-surface constraints form a second-class system in the nomenclature of Dirac. Therefore, they are eliminated from the theory by the construction of Dirac brackets. With the Dirac brackets, the Hamiltonian gives the once-integrated field equations for the dynamical field variables. The usual commutation relations for the field strengths restricted to the domain of integration for H are i times the Dirac brackets.

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References (30)

  1. P. A. M. Dirac, Can. J. Math. 2, 129 (1950).
  2. P. A. M. Dirac, Can. J. Math. 3, 1 (1951).
  3. P. G. Bergmann, Phys. Rev. 75, 680 (1949).
  4. F. A. E. Pirani and A. Schild, Phys. Rev. 79, 986 (1950).
  5. B. S. DeWitt, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962).
  6. R. Arnowitt, S. Deser, and C. Misner (Ref. 5).
  7. Quantum Gravity 2, edited by C. Isham, R. Penrose, and D. Sciama (Clarendon, Oxford, 1981).
  8. H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, Proc. R. Soc. London A 269, 21 (1962).
  9. R. K. Sachs, Proc. R. Soc. London A 270, 103 (1962).
  10. E. T. Newman and R. Penrose, J. Math. Phys. 3, 566 (1962).
  11. R. A. d'Inverno and J. Stachel, J. Math. Phys. 19, 2447 (1978).
  12. R. A. d'Inverno and J. Smallwood, Phys. Rev. D 22, 1233 (1980).
  13. J. Smallwood, J. Math. Phys. 24, 599 (1983).
  14. A. Ashtekar, J. Math. Phys. 22, 2885 (1981).
  15. R. Geroch, in Asymptotic Structure of Space-Time, edited by F. P. Esposito and L. Witten (Plenum, New York, 1977).
  16. R. Penrose, Proc. R. Soc. London A 284, 159 (1965).
  17. F. Rohrlich, Acta Phys. Austriaca 32, 87 (1970).
  18. F. Rohrlich, Acta Phys. Austriaca, Suppl. VIII, 277 (1971).
  19. J. B. Kogut and D. E. Soper, Phys. Rev. D 1, 2901 (1970).
  20. J. D. Bjorken, J. B. Kogut and D. E. Soper, Phys. Rev. D 3, 1382 (1971).
  21. P. J. Steinhardt, Ann. Phys. (N.Y.) 128, 425 (1980).
  22. A. J. Hanson, T. Regge, and C. Teitelboim, Constrained Hamiltonian Systems (Academia Nazionale dei Lincei, Rome, 1976).
  23. T. Regge and C. Teitelboim, Ann. Phys. (N.Y.) 88, 286 (1974).
  24. P. A. M. Dirac, Proc. R. Soc. London A 246, 333 (1958).
  25. P. A. M. Dirac, Phys. Rev. 114, 924 (1959).
  26. P. G. Bergmann and A. Komar, Phys. Rev. Lett. 4, 432 (1960).
  27. C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).
  28. J. N. Goldberg, Report No. ARL 70-0003, 1970 (unpublished).
  29. R. Motill, Ph.D. thesis, Syracuse University, 1974.
  30. L. Eimers, Ph.D. thesis, Syracuse University, 1970.

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Phys. Rev. D 31, 1354– Published 15 March, 1985
  • Received 31 May 1984

© 1985 American Physical Society

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