General Relativity and Gravitation

, Volume 22, Issue 11, pp 1283–1307 | Cite as

The localization of energy in gauge field theories and in linear gravitation

  • Jacek Jezierski
  • Jerzy Kijowski
Research Articles


It is shown how the energy-positivity criterion enables us to localize the energy in various field theories. For this purpose the role of surface integrals in a canonical formalism is investigated. The same techniques are applied to linearized gravity, where the mixed Cauchy-boundary value problem in a finite volume is analyzed. Unconstrained degrees of freedom and boundary data which have to be controlled are found. This paper is part of a program to analyze the possibility of localization of gravitational energy in complete General Relativity.


Field Theory General Relativity Differential Geometry Finite Volume Canonical Formalism 
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  1. 1.
    Einstein, A. (1916).Ann. Phys.,49, 769; von Freud, Ph. (1939).Ann. Math.,40, 417; Arnowitt, R. Deser, S., Misner, C. (1962). InGravitation, An Introduction to Current Research, L. Witten, ed. (Wiley and Sons, New York; Dubois-Violette, M., Madore, J. (1987).Comm. Math. Phys.,108, 213.Google Scholar
  2. 2.
    Denisov, V. L., Logunov, A. A., Mestvereshvili, M. A. (1981).Probl. Fiz. ECAJ, 12, 5; Denisov, V. I., and Logunov, A. A. (1980).Teoret. Mat. Fiz.,43, 187.Google Scholar
  3. 3.
    Penrose, R. (1982).Proc. Roy. Soc. Lond.,A381, 53;id. (1983). InAsymptotic Behaviour of Mass and Spacetime Geometry, (Lecture Notes in Physics, vol. 202, Springer-Verlag, Berlin); Shaw, W. T. (1983).Proc. Roy. Soc. Lond.,A390, 191; Tod, K. P. (1983).Proc. Roy. Soc. Lond.,A388, 457.Google Scholar
  4. 4.
    Kijowski, J. (1984). InGravitation, Geometry and Relativistic Physics, (Lecture Notes in Physics, vol. 212, Springer-Verlag, Berlin);id. (1986). InProceedings of the IV Marcel Grossmann meeting on General Relativity, Rome, R. Ruffini, ed. (Elsevier, Amsterdam).Google Scholar
  5. 5.
    Jezierski, J., and Kijowski, J. (1987).Phys. Rev. D,36, 1041.Google Scholar
  6. 6.
    Kijowski, J. (1985). InProceedings of Journées Relativistes 1983, Turin, S. Benenti, M. Ferraris, M. Francaviglias, eds. (Pitagora Editrice, Bologna).Google Scholar
  7. 7.
    Tulczyjew, W. M. (1974).Symposia Math.,14, 247; Kijowski, J. and Tulczyjew, W. M. (1979).A Symplectic Framework for Field Theories, (Lecture Notes in Physics, vol. 107, Springer-Verlag, Berlin); Benenti, S., and Tulczyjew, W. M. (1980).Ann. Mat. Pura Appl.,74, 139.Google Scholar
  8. 8.
    Chernoff, P. R., Marsden, J. E. (1974).Properties of Infinite Dimensional Hamitonian Systems, (Lecture Notes in Mathematics, vol. 425, Springer-Verlag, Berlin).Google Scholar
  9. 9.
    Korn, A. (1914). InMathem. Abhandlungen H. A. Schwarz, reprinted 1974 inMathematische Abhandlungen, O. Bolza et al. (Chelsea Publishing Company, London). Lichtenstein, L. (1916).Bull. Int. Acad. Sci. Cracovie, ser.A, 192.Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • Jacek Jezierski
    • 1
  • Jerzy Kijowski
    • 2
  1. 1.Institute for Mathematical Methods in PhysicsWarsaw UniversityWarsawPoland
  2. 2.Max-Planck-Institute fur AstrophysikGarching b. MünchenFederal Republic of Germany

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