Physics
Scientific paper
Dec 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978aipc...48..140h&link_type=abstract
AIP Conference Proceedings, Volume 48, pp. 140-152 (1978).
Physics
Fundamental Problems And General Formalism, Gravity In More Than Four Dimensions, Kaluza-Klein Theory, Unified Field Theories, Alternative Theories Of Gravity
Scientific paper
Two different methods are presented by which gravitational theories can be developed from intransitive groups of transformations. A minimal invariant variety of the group forms the unperturbed universe. A Lie derivative of spinors is defined in this space-time. A condition is derived for the coincidence of individual group trajectories and geodesics. A speculation on the physical meaning also of nongeodesic group trajectories is put forward. The gravitational fields of localized masses break the homogenous character of the space. This can be achieved either by introducing a metric with suitable homogenuity conditions into the higer dimensional space which is transformed by the group, or alternatively by applying a gauge formalism to the field of basis vectors of the group. The relation of the second method with the metric is shown. It results in field equations of the Maxwell-Yang Mills type corresponding to and generalizing the metric Lagrangian. √gRμνδφRμνδφ
It is shown that a theory which fulfills the requirement of Dirac's Large Number Hypothesis can not be based on an invariance group with Killing vectors with time components. Some aspects of an approach to such a theory are discussed.
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