Geometry of Kaluza-Klein theory. II. Field equations

Details Geometry of Kaluza-Klein theory. II. Field equations Geometry of Kaluza-Klein theory. II. Field equations

Jan 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985phrvd..31..268m&link_type=abstract

Physical Review D (Particles and Fields), Volume 31, Issue 2, 15 January 1985, pp.268-272

Physics

3

Gravity In More Than Four Dimensions, Kaluza-Klein Theory, Unified Field Theories, Alternative Theories Of Gravity

Scientific paper

In the preceding paper a geometric formulation of Kaluza-Klein theory was presented with the basic assumption that the space-time is locally and isometrically embedded in the high-dimensional space which emerged at the big bang. In the present note the Gauss-Codazzi-Ricci equations which are the integrability equations for the embedding are interpreted as the dynamical equations for a low-energy observer. The second quadratic form which results from the embedding is interpreted as a fundamental spin-two massless field. The dynamics for an observer with high-energy probes is described as usual by the Einstein-Hilbert action defined in the high-dimensional space and dimensionally reduced by integration over the internal space. The behavior of fermion masses under different gravitational field strengths is implemented by use of the mass operator defined with the second-order Casimir operator of the embedding symmetry group.

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