Kaluza-Klein Theories as a Tool to Find New Gauge Symmetries
Non-abelian Kaluza-Klein theories are studied with respect to using the invariances of multi-dimensional general relativity to investigate hidden symmetry, such as Kac-Moody Lie algebras, of the four-dimensional Yang-Mills theory. Several properties of the affine transformations on the self-dual set are identified and are used to motivate the Kaluza-Klein analysis. In this context, a system of differential equations is derived for new symmetry transformations which may be extendable to the full gauge theory.
KeywordsGauge Theory Gauge Symmetry Symmetry Transformation Hide Symmetry Affine Connection
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- Non-abelian KaluzaKlein theories, which are discussed in this talk, first appeared in B. DeWitt, in Lectures at 1963 Les Houches School, Relativity, Groups, and Topology, ed. B. DeWitt ( New York, Gordon and Breach, 1965 ) p. 725.Google Scholar
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