Research Articles

General Relativity and Gravitation

, Volume 19, Issue 10, pp 983-1002

First online:

A unified approach to the gauging of space-time and internal symmetries

  • Eric A. LordAffiliated withDepartment of Applied Mathematics, Indian Institute of Science

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The properties of the manifold of a Lie groupG, fibered by the cosets of a sub-groupH, are exploited to obtain a geometrical description of gauge theories in space-timeG/H. Gauge potentials and matter fields are pullbacks of equivariant fields onG. Our concept of a connection is more restricted than that in the similar scheme of Ne'eman and Regge, so that its degrees of freedom are just those of a set of gauge potentials forG, onG/H, with no redundant components. The “translational” gauge potentials give rise in a natural way to a nonsingular tetrad onG/H. The underlying groupG to be gauged is the groupG of left translations on the manifoldG and is associated with a “trivial” connection, namely the Maurer-Cartan form. Gauge transformations are all those diffeomorphisms onG that preserve the fiber-bundle structure.