MOTION IN NON-LINEAR THEORIES OF GRAVITY

Abstract

TIH' t.IH'sis dPals wit.h t.lw problem of Ulot.ion iu non-linear gravity theories which are const:nH't.<d using t.he gemnet.riwt.iou philosophy. lt. eoutains four chapters each has it.s conclusion and list of references. The thesis contains twelve comparison tables to enable the reader to arrive quickly to conclusions. Some of the results of chapters 2 and 3, jointly by the author and his supervisors, are published in four papers and the results of chapter 4 are in preparation for publication. Chapter 1: This chapter reviews briefly, in a unified way, two different philosophies used to tackle the problem of motion. The first is the geometrization scheme• and the second is quanti­ zation scheme. In the first, it is shown how different properties of the moving body, e.g. rotation, charge, are taken into account in the equations of motion. The same is consid- . ered in the second philosophy, but the properties of the moving particle are of quantum nature, especially spin. Two bridges between the two different treatments are given. The first bridge is the Path Integral Formalism which enables to get the quantum equation of motion starting from a classical (geometric) Lagrangian. The second bridge is WKB­ approximation using which one can get the classical (geometric) equation of motion starting with the corresponding quantum equation of motion. Discussion and criticism of the two treatments are given at the end of this chapter together with a list of references to the literature. Chapter 2:

In this chapter, two non-symmetric geometries, more wider than the Riemannian one, are examined for new path equations that can be used as trajectories of test particles. The first is the Absolute Parallelism geometry. The new path equations derived in this geometry possess some quantum properties ! The equations contain a torsion term which is naturally quantized, without applying any quantization scheme.