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

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

Feb 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982phrvd..25..976i&link_type=abstract

Physical Review D (Particles and Fields), Volume 25, Issue 4, 15 February 1982, pp.976-987

Mathematics

Logic

28

Scientific paper

The gauge formulations of various gravitation theories are discussed. They are based on the approach in which we have the group Diff R4 acting on xμ and in which we attach to every xμ a tangent space with the group of action H. Group H does not act on xμ 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 R4. The full invariance group of the Lagrangian is then of the form Hloc⊗Diff R4. Here Hloc is a local gauge group obtained from H exactly as in the Yang-Mills theory. The approach has two characteristic features: (i) The group Hloc 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 R4 but differing in backgrounds. Thus if H is isomorphic to the Poincaré 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.

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