Advertisement

Communications in Mathematical Physics

, Volume 24, Issue 4, pp 289–302 | Cite as

Einstein's equations and locality

  • L. Bracci
  • F. Strocchi
Article

Abstract

The problem of formulating a local quantum theory of Einstein equations is examined. It is proved that Einstein equations cannot hold as operator equations if written in terms of a potentialhµν(D) which is a weakly local field. This result is independent of the kind of metric chosen in the Hilbert space and it doesn't require covariance ofhµν.

As a consequence, the peculiar features of the radiation gauge method, i.e. non locality and non covariance, appear as necessary features of any solution not involving unphysical particles.

Keywords

Radiation Neural Network Covariance Statistical Physic Hilbert Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    For a review of the difficulties arising in the quantization of the Einstein's equations. See e.g. Kibble, T. W.: High energy physics and elementary particles (International Atomic Energy Agency, Wien 1965).Google Scholar
  2. 2.
    Strocchi, F.: Phys. Rev.,D 2, 2334 (1970).Google Scholar
  3. 3.
    Arnowitt, R., Deser, S., Misner, C. W.: Phys. Rev.113, 745 (1959);116, 1322 (1959);117, 1595 (1960).Google Scholar
  4. 3a.
    Weinberg, S.: Phys. Rev.134, B 882 (1964);138, B 988 (1965).Google Scholar
  5. 4.
    Landau, L., Lifchitz, E.: Théorie du champ. Editions Mir, Moscou 1966.Google Scholar
  6. 5.
    This point has been stressed by Weinberg, S.: Phys. Rev.134, B 882 (1964);138, B 988 (1965).Google Scholar
  7. 6.
    See Wightman, A. S.: Phys. Rev.101, 860 (1956). For a detailed discussion see: Streater, R., Wightman, A.S.: PCT, spin and statistics and all that. New York: W. A. Benjamin, Inc. 1964 and Wightman, A. S., Gärding, L.: Arch. Fysik28, 129 (1964).Google Scholar
  8. 7.
    For the time being it is not necessary to specify which kind of distributionsR µνρσ are supposed to be. The following results hold true for a large class of distributions including those introduced by A. M. Jaffe [8].Google Scholar
  9. 8.
    Jaffe, A. M.: Phys. Rev. Letters17, 661 (1966); Phys. Rev.158, 1454 (1967).Google Scholar
  10. 9.
    Dirac, P. A. M.: Proc. Roy. Soc. (London),180, 1 (1942).Google Scholar
  11. 9a.
    Pauli, W.: Rev. Mod. Phys.15, 176 (1943).Google Scholar
  12. 9b.
    Gupta, S. N.: Proc. Phys. Soc. (London)63, 681 (1950).Google Scholar
  13. 9c.
    Bleuler, K. T.: Helv. Phys. Acta23, 567 (1950).Google Scholar
  14. 10.
    Strocchi, F.: Phys. Rev.166, 1302 (1968).Google Scholar
  15. 11.
    Schwinger, J.: Phys. Rev.130, 1253 (1963).Google Scholar
  16. 11a.
    Arnowitt, R., Deser, S., Misner, C. W.: Phys. Rev.113, 745 (1959);116, 1322 (1959);117, 1595 (1960).Google Scholar
  17. 12.
    Ogievetsky, V. I., Polubarinov, I. V.: Ann. Phys. (N. Y.)35, 167, 1965. AppendixGoogle Scholar
  18. 13.
    Jost, R.: The general theory of quantized fields (Providence R. I., 1965); Streater, R., Wightman, A. S.: PCT spin and statistics and all that. New York: W. A. Benjamin, Inc. 1964.Google Scholar
  19. 14.
    For a discussion about the operator valued distributions for which WLC can be defined see Ref. [8].Google Scholar
  20. 15.
    Bracci, L.: Tesi di Perfezionamento, Scuola Normale Superiore, Pisa.Google Scholar
  21. 16.
    Kraus, K.: Commun. math. Phys.9, 339 (1968).Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • L. Bracci
    • 1
    • 2
  • F. Strocchi
    • 3
  1. 1.Istituto di Fisica dell'Università di PisaItaly
  2. 2.Scuola Normale SuperiorePisaItaly
  3. 3.Department of PhysicsUniversity of PrincetonPrincetonUSA

Personalised recommendations