Abstract
The mathematical structure, the field equations, and fundamentals of the kinematics of generalizations of general relativity based on semisimple invariance groups are presented. The structure is that of a generalized Kaluza-Klein theory with a subgroup as the gauge group. The group manifold with its Cartan-Killing metric forms the source-free solution. The gauge fields do not vanish even in this case and give rise to additional modes of free motion. The case of the de Sitter groups is presented as an example where the gauge field is tentatively assumed to mediate a spin interaction and give rise to spin motion. Generalization to the conformal group and a theory yielding features of Dirac's large-number hypothesis are discussed. The possibility of further generalizations to include fermions are pointed out. The Kaluza-Klein theory is formulated in terms of principal fibre bundles which need not to be trivial.
Similar content being viewed by others
References
Dirac, P. A. M. (1935).Annals of Mathematics,36(3), 657.
Dirac, P. A. M. (1936).Annals of Mathematics,37(2), 429.
Dirac, P. A. M. (1979).Proceedings of the Royal Society of London Series A,365, 19–30.
Ebner D. (1981). In Proceedings of the Symposium on Space-Time Physics Mexico City, June 1981, Keller, J., ed.
Eisenhart, L. P. (1933).Continuous Groups of Transformations. Princeton University Press, Princeton, New Jersey.
Halpern, L. (1977).General Relativity and Gravitation,8(8), 623.
Halpern, L. (1978). Proceed. Symp. on Group Theory and Physics, Austin, Texas.
Halpern, L. (1979).International Journal of Theoretical Physics,18(11), 845.
Halpern, L. (1980a).Annals of Israel Physical Society,3, 260.
Halpern, L. (1980b).Clausthal Summer Meeting on Differential Geometry and Physics, July 1980 (preprint).
Halpern, L. (1981).International Journal of Theoretical Physics,20(4), 297.
Jordan, P. (1948).Schwerkraft and Weltall, Y. Thiry, C. R. 226, p. 216.
Kerner, R. (1981).Annales de l'Institut Henri Poincaré,XXIV(4), 437.
Mecklenburg, W. (1979). Preprints IC/79/87 and IC/79/131.
Nomizu, K. (1956).Lie Groups and Differential Geometry, Vol. 2. Mathematical Society of Japan, Tokyo.
Steenrod, N. (1974).The Topology of Fibre Bundles, Section 7. Princeton University Press, Princeton, New Jersey.
Veblen, O. (1932).Projektive Relativitätstheorie. Vieweg.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Halpern, L. Generalizations of gravitational theory based on group covariance. Int J Theor Phys 21, 791–802 (1982). https://doi.org/10.1007/BF01856873
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01856873