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Geometrization of the Fundamental Interactions


The four fundamental interactions of Nature are described by theories of two distinct types, which share nevertheless a strong geometrical flavor. Gravitation, as described by Ggneral relativity, is a metric-mediated interaction. The strong, weak and electromagnetic interactions of the standard model have as mediating fields geometrical entities of another kind, connections. Curvatures turn up in the Lagrangians of both kinds of theory, but in different ways, and the ensuing dynamics are quite dissimilar. The Standard Model is ultimately a gauge theory, and general relativity is not. The geometrical bias, however, imparts to both sorts of theory many aspects in common. The central aim of the project is the study of the parallelisms and oppositions between general relativity and gauge theory, in view of amore comprehensive theory. All these theories have impressive experimental records, but they also face difficulties which justify the fact that the bulk of present day research activity in field theory concentrates in more comprehensive, enlarged theories. There is a fair consensus on the necessity of a more general framework. A first step would be to look for new ways of considering the theories as they are. In this vein falls the teleparallel approach to gravitation, as well as the conception of gauge theories as Lie algebra extensions of the translation group. Along this line, it is only natural to examine also schemes in which both merge into a larger structure, as the Kaluza-Klein formalism. Next comes the possibility of changing one of them, to make them closer. Hence the gauge models for gravitation. The de Sitter group is the only group related to space-time providing a coherent and renormalizable gauge theory. The recent rebirth of de Sitter models for cosmological reasons comforts this idea. The work already done, even in their present building-up stage, suggest generalizations. Adding torsion to curvature in gravitation, or deforming gauge theories to more general algebra extensions. With the above considerations in mind, the main lines of research will be: 1. to detail the Lie algebra extensions of the Weinberg-Salam theory: to examine how the mass spectrum, mixing angle, and other characteristics would come up in that scheme; to investigate which kind of gravitational model would result. 2. To pursue the study of de Sitter groups: by looking for effects favoring it as the classifying kinematic group of elementary particles; by analyzing the cosmological aspects, mainly the impact of a cosmological constant on usually accepted physics and its teleparallel interpretation. 3. To examine the Kaluza-Klein scheme by studying: its teleparallel version; its generalizations, e.g. via non-commutative geometry. 4. To deepen the teleparallel approach: by understanding it as a Lorentz group gauge theory; by looking at the definition of gravitational energy; by studying the possible sources of torsion and the coupling oftorsion to fields describing elementary particles; by analyzing its version of the equivalence principle. (AU)

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