Gravity as a gauge theory with Cartan connection

Journal Article · Fri Jul 01 04:00:00 EDT 1988 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.528197· OSTI ID:5182821

Zardecki, A

A gauge formulation of gravity, based on the notion of the connection of Cartan, is given. The Cartan connection involves two principal fiber bundles P and P' with groups G and G', respectively; G' is a subgroup of G and can be regarded as a symmetry group to which G is broken. When the differential form defining the connection in P gives absolute parallelism in P', one speaks about the Cartan connection. General geometric framework is specialized to the case in which G is the de Sitter group SO(4,1) and G' is the Lorentz group SO(3,1). The action of the Yang--Mills type is similar to, but not identical with, the action derived earlier by Townsend. The field equations in P are translated into a system of coupled equations for curvature and torsion in P'. Under contraction of SO(4,1) to the Poincare group ISO(3,1), and for vanishing torsion, the equations become Yang's equation and Einstein's equation in vacuum. The BRS invariance of the theory, supplemented by Faddeev--Popov and gauge fixing terms, is analyzed in some detail.

• Research Organization: Theoretical Division, MS K723, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
• OSTI ID: 5182821
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 29:7; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL GEOMETRY
EINSTEIN FIELD EQUATIONS
EQUATIONS
FIELD EQUATIONS
GAUGE INVARIANCE
GEOMETRY
GRAVITATION
INVARIANCE PRINCIPLES
MATHEMATICS
SYMMETRY GROUPS
TOPOLOGY