Studies in Kaluza - Klein approach to unification

Abstract

The revival of Kaluza-Klein theory, with added features essentially occupies a major part in supergravity, and superstring theories, which are higher dimensional theories. The technique of Kaluza-Klein spontaneous compactification could be useful, for dimensional reduction of higher dimensional theories. The incorporation of fermions and possible realization of chiral fermions provide deep insight into the geometrical structure of the theory. The four important structures viz., i) Quantum effects in Kaluza-Klein theory with spontaneous compactification induced by non-linear sigma model; ii) Asymmetric expansion of space in a model in which the extra space has a non-linear sigma model; iii) Spontaneous compactification of M^4 * CP^2 induced by instantons in CP^2 and fermions; and iv) Generalized spin structure on CP^2, are studied in this thesis. This research work is presented in 5 chapters. There are appendices at the end of the Chapter 2, 4 and 5 containing some mathematical details used in various places.