Gauge Theory of Gravitation

Diaa A Ahmed

e-mail: diahmed@yahoo.com

(Rotterdam November 1997)

Gravitation represent quantum topological phenomenon on a large scale. Introducing the action of gravitation into functional quantum space -through a phase angle- requires a change in our understanding of both gauge theory and general relativity. This display its unity with the rest of gauge interactions and demonstrate that the manifold is compact.

I. INTRODUCTION

The dimensionless coupling G (x) = k m / r , plays the role of phase angle of cosmological origin- coupling between dipole moments. We can derive its action in functional space by introducing it into the group structure, exp { i g Ta . wa (x)}. We may use the notation {ab} = gam gmb , and its contracted form { } , to represent this phase angle and to facilitate the calculations in terms of basis { wa (p)}, { eb (p)} , and phase angles < wa | eb >. The phase angles exist in functional space and its contractions equal in the geometric language to its projection on the metric. Action of the phase angle reconstructs the wave front and this determines the geometric structure of the manifold and the fields. We will now consider that these phase angles perform rotations that are subject to the same algebraic scheme as the fields W. This sort of rotations will mix up fields in order to bring in the transformations on these fields. Furthermore the transformations will not change the structure of physical law. This means that the phase wa (x) , that is involved is a general one and G (x) , is associated with the same algebraic scheme of Ta. This will permit these transformations to induce the appropriate transformations on the fields. Therefore we will assume,