Gauge formulation of gravitation theories. I. The Poincare, de Sitter, and conformal cases

Journal Article · Mon Feb 15 00:00:00 EST 1982 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.25.976· OSTI ID:5727028

Ivanov, E A; Niederle, J

The gauge formulations of various gravitation theories are discussed. They are based on the approach in which we have the group Diff R/sup 4/ acting on x/sup ..mu../ and in which we attach to every x/sup ..mu../ a tangent space with the group of action H. Group H does not act on x/sup ..mu../ and plays the role of an internal (global) symmetry group in the standard Yang-Mills theory. The matter fields in the theory transform according to representations of H and are assumed to be scalars of Diff R/sup 4/. The full invariance group of the Lagrangian is then of the form H/sup loc/xDiff R/sup 4/. Here H/sup loc/ is a local gauge group obtained from H exactly as in the Yang-Mills theory. The approach has two characteristic features: (i) The group H/sup loc/ must be spontaneously broken in order to exclude redundant gauge fields (the Lorentz connections) from the theory in a way covariant with respect to the gauge transformations. (ii) To different H there correspond different gravitational theories, all invariant under Diff R/sup 4/ but differing in backgrounds. Thus if H is isomorphic to the Poincare group the corresponding gauge theory turns out to be equivalent to the usual Einstein or Einstein-Cartan theory of gravity in the Minkowski space as a background. The other choices for H considered in the paper are the de Sitter groups and the conformal group. They yield the Einstein theory with a negative (or positive) cosmological term in the corresponding de Sitter space and the Weyl or Cartan-Weyl theory (depending on realization of the conformal group), respectively.

• Research Organization: Institute of Physics, Czechoslovak Academy of Sciences, Na Slovance 2, CS-180 40 Prague 8, Czechoslovakia
• OSTI ID: 5727028
• Journal Information: Phys. Rev. D; (United States), Vol. 25:4
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
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