Advertisement

Foundations of Physics

, Volume 28, Issue 9, pp 1465–1477 | Cite as

Quantum Gravity Induced from Unconstrained Membranes

  • Matej Pavšič
Article
  • 41 Downloads

Abstract

The theory of unconstrained membranes of arbitrary dimension is presented. Their relativistic dynamics is described by an action which is a generalization of the Stueckelberg point-particle action. In the quantum version of the theory, the evolution of a membrane's state is governed by the relativistic Schrödinger equation. Particular stationary solutions correspond to the conventional, constrained membranes. Contrary to the usual practice, our spacetime is identified, not with the embedding space (which brings the problem of compactification), but with a membrane of dimension 4 or higher. A 4-membrane is thus assumed to represent spacetime. The Einstein-Hilbert action emerges as an effective action after functionally integrating out the membrane's embedding functions.

Keywords

Stationary Solution Quantum Gravity Effective Action Arbitrary Dimension Usual Practice 
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.
    P. A. M. Dirac, Proc. R. Soc. London A 268, 57 (1962). J. Hughes, J. Liu, and J. Polchinski, Phys. Lett. B 180, 370 (1986). E. Bergshoeff, E. Sezgin, and P. K. Townsend, Phys. Lett. B 189, 75 (1987); 209, 451 (1988). E. Bergshoeff and E. Sezgin, Ann. Phys. 185, 330 (1988). M. P. Blencowe and M. J. Duff, Nucl. Phys. B 310, 387 (1988). U. Marquard and M. Scholl, Phys. Lett. B 209, 434 (1988). A. Karlhede and U. Lindström, Phys. Lett. B 209, 441 (1988). A. A. Bytsenko and S. Zerbini, Mod. Phys. Lett. A 8, 1573 (1993). A. Aurilia and E. Spallucci, Class. Quantum Gravit. 10, 1217 (1993).Google Scholar
  2. 2.
    M. Pavšič, Phys. Lett. B 197, 327 (1987); 205, 231 (1988); Class. Quantum Gravit. 5, 247 (1988). A. O. Barut and M. Pavšič, Lett. Math. Phys. 16, 333 (1988); Mod. Phys. Lett. A 7, 1381 (1992): Phys. Lett. B 306, 49 (1993); 331, 45 (1994).Google Scholar
  3. 3.
    A. D. Sakharov, Dokl. Akad. Nauk. SSSR 177, 70 (1967) [Sov. Phys. JETP 12, 1040 (1968) ]. L. S. Adler, Rev. Mod. Phys. 54, 729 (1982), and references therein.Google Scholar
  4. 4.
    V. Fock, Phys. Z. Sowj. 12, 404 (1937). E. C. G. Stueckelberg, Helv. Phys. Acta 14, 322 (1941). J. Schwinger, Phys. Rev. 82, 664 (1951); 14, 588 (1941); 15, 23 (1942). R. P. Feynman, Phys. Rev. 84, 108 (1951). L. P. Horwitz and C. Piron, Helv. Phys. Acta 46, 316 (1973). E. R. Collins and J. R. Fanchi, Nuovo Cimento A 48, 314 (1978). L. P. Horwitz, W. C. Schieve, and C. Piron, Ann. Phys. 137, 306 (1981). L. P. Horwitz, Found. Phys. 18, 1159 (1988); 22, 421 (1992). H. Enatsu, Progr. Theor. Phys. 30, 236 (1963); Nuovo Cimento A 95, 269 (1986). J. R. Fanchi, Phys. Rev. D 20, 3108 (1979). R. Kubo, Nuovo Cimento A 85, 293 (1985). N. Shnerb and L. P. Horwitz, Phys. Rev. A 48, 4068 (1993). J. R. Fanchi, Parametrized Relativistic Quantum Theory(Kluwer Academic, Dordrecht 1993).Google Scholar
  5. 5.
    M. Pavšič, Found. Phys. 21, 1005 (1991); Nuovo Cimento A 104, 1337 (1991); Doga Turk. J. Phys. 17, 768 (1993).Google Scholar
  6. 6.
    B. S. DeWitt, Rev. Mod. Phys. 29, 377 (1957); see also B. S. DeWitt, Phys. Rev. 85, 653 (1952).Google Scholar
  7. 7.
    T. Regge and C. Teitelboim, in Proceedings of the Marcel Grossman Meeting (Trieste, 1975). G. W. Gibbons and D. L. Wiltshire, Nucl. Phys. B 287, 717 (1987). V. Tapia, Class. Quantum Gravit. 6, L49 (1989). D. Maia, Class. Quantum Gravit. 6, 173 (1989). T. Hori, Phys. Lett. B 2, 188 (1989).Google Scholar
  8. 8.
    M. Pavšič, Class. Quantum Gravit. 2, 869 (1985); Phys. Lett. A 107, 66 (1985); Phys. Lett. A 116, 1 (1986). Nuovo Cimento 95, 297 (1986).Google Scholar
  9. 9.
    M. Pavšič, Found. Phys. 24, 1495 (1994).Google Scholar
  10. 10.
    M. Pavšič, Found. Phys. 25, 819 (1995); Nuovo Cimento A 108, 221 (1995).Google Scholar
  11. 11.
    M. Pavšič, Nuovo Cimento A 110, 369 (1997).Google Scholar
  12. 12.
    M. Pavšič, Found. Phys. 26, 159 (1996).Google Scholar
  13. 13.
    M. Pavšič, Class. Quantum Gravit. 9, L13 (1992).Google Scholar
  14. 14.
    B. S. DeWitt, Phys. Rep. 19, 295 (1975). S. M. Christensen, Phys. Rev. D 14, 2490 (1976). L. S. Brown, Phys. Rev. D 15, 1469 (1977). T. S. Bunch and L. Parker, Phys. Rev. D 20, 2499 (1979). H. Boschi-Filho and C. P. Natividade, Phys. Rev. D 46, 5458 (1992). A. Follacci, Phys. Rev. D 46, 2553 (1992).Google Scholar
  15. 15.
    M. Pavšič, Gravit. Cosmol. 2, 1 (1996).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • Matej Pavšič

There are no affiliations available

Personalised recommendations