Recently two of us generalized the topological massive gauge model of gravity of Deser, Jackiw, and Templeton (DJT) by liberating its translational gauge degrees of freedom. Consequently, the newR3◯SO(1,2) gauge model «lives» in a 3-dimensional Riemann-Cartan space-time with torsion. The extended Lagrangian consists, of the familiar Einstein-Cartan term, the Chern-Simons 3-form for the curvature, and, in addition, of a new translational Chern-Simons term. In this article we uncover a «dynamical symmetry» of the new theory by inquiring how the two Noether identities, the two Bianchi identities, and the two field equations are interrelated to each other. This includes two important subcases in which the first Bianchi identity is mapped into the second one and the first (energy-momentum) Noether into the second (angular-momentum) Noether identity. As a furtherexact result, the topological gauge field equations imply a covariant Proca-type field equation, for the translational gauge potential,i.e. the coframe. Thus the theory encompasses massive gravitons, as in the DJT model.
Unified field theories and other theories of gravitation
Quantum theory of gravitation
Models for gravitational interaction
This is a preview of subscription content, log in to check access.
S. Deser, R. Jackiw andS. Templeton:Phys. Rev. Lett.,48, 975 (1982);Ann. Phys. (N.Y.),140, 372 (1982).ADSCrossRefGoogle Scholar
S. Deser:Phys. Rev. Lett.,64, 611 (1990);S. Deser: inSupermembranes and Physics in 2+1Dimensions, Proceedings of the Trieste Conference, July 17–21, 1989, edited byM. J. Duff, C. N. Pope andE. Sezgin (World Scientific, Singapore, 1990), p. 239.MathSciNetADSCrossRefGoogle Scholar
R. Tresguerres:Topological gravity in a 3-dimensional metric-affine spacitime, inJ. Math. Phys. (to be published).Google Scholar
F. W. Hehl:Four lectures on Poincaré gauge theory, inProceedings of the 6th Course of the School of Cosmology and Gravitation on Spin, Torsion, Rotation, and Supergravity, Erice, Italy, May 1979, edited byP. G. Bergmann andV. de Sabbata (Plenum, New York, N.Y., 1980), p. 5.Google Scholar
E. W. Mielke:Geometrodynamics of Gauge Fields—On the Geometry of Yang-Mills and Gravitational Gauge Theories (Akademie-Verlag, Berlin, 1987).Google Scholar
A. Trautman:Symposia Mathematica, Vol.12 (Academic Press, London, 1973), p. 139.Google Scholar
A. Trautman: inProceedings of the 6th Course of the School of Cosmology and Gravitation on Spin, Torsion, Rotation, and Supergravity, Erice, Italy, May 1979 edited byP. G. Bergmann andV. de Sabbata (Plenum, New York, N. Y. 1980), p. 493.Google Scholar
W. Kopczyński:Ann. Phys. (N.Y.),203, 308 (1990); cf.F. W. Hehl andG. D. Kerlick:Gen. Relativ. Gravit.,9, 691 (1978).ADSCrossRefGoogle Scholar