Advertisement

General Relativity and Gravitation

, Volume 21, Issue 5, pp 457–466 | Cite as

Holonomy and gravity

  • J. W. Barrett
Research Articles

Abstract

It is proposed that the gravitational field can be described in an invariant way by its “holonomy set” involving paths in Minkowski space and points in the Lorentz group. The differentiable manifold of gravity does not enter as a basic object but is constructed in a manner depending on the field configuration. Thus there is no diffeomorphism symmetry in this description of gravity, nor is the topology of space-time fixed at the outset. It is therefore proposed that the “holonomy description” of gravity provides a much better starting point for the analysis of quantum gravity. Striking similarities with Yang-Mills gauge theories emerge which shed light on the problem of whether gravity is or is not a gauge theory.

Keywords

Manifold Gauge Theory Quantum Gravity Differential Geometry Gravitational Field 
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.
    Einstein, A. (1922).The Meaning of Relativity, 6th ed. (Chapman and Hall, London).Google Scholar
  2. 2.
    Isham, C. J. (1981). InQuantum Gravity 2, a Second Oxford Symposium, Isham, C. J. Penrose, and Sciama, eds. (Clarendon Press, Oxford).Google Scholar
  3. 3.
    Isham, C. J. (1984).Topological and Global Aspects of Quantum Theory, 1983 Les Houches Summer School Lectures “Relativity, Groups and Topology. (North-Holland, Amsterdam).Google Scholar
  4. 4.
    Feynman, R. P. (1950).Phys. Rev.,80, 440 (Appendix A).Google Scholar
  5. 5.
    Lashof, R. (1956).Ann. Math.,64, 436.Google Scholar
  6. 6.
    Teleman, C. (1969).Indagation. Math.,31, 89, 104.Google Scholar
  7. 7.
    Anandan, J. (1980).Int. J. Theor. Phys.,19, 537; see alsoHolonomy Groups in Gravity and Gauge Fields, Proc. Conf. Different. Geomet. Methods Theor. Phys., Trieste 1981, Denardo, G., and Doebner, H. D., eds. (World Scientific, Cleveland).Google Scholar
  8. 8.
    Barrett, J. W. (1985). Ph.D. thesis (University of London, London).Google Scholar
  9. 9.
    Kobayashi, S., and Nomizu, K. (1963).Foundations of Differential Geometry, Vol. 1, ed. 1 (Interscience, New York, London).Google Scholar
  10. 10.
    Sklar, L. (1974).Space, Time and Space-Time (University of California Press, Berkeley).Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • J. W. Barrett
    • 1
  1. 1.Department of PhysicsThe UniversityNewcastle upon TyneEngland

Personalised recommendations