Il Nuovo Cimento B (1971-1996)

, Volume 107, Issue 1, pp 91–110 | Cite as

Dynamical symmetries in topological 3D gravity with torsion

  • P. Baekler
  • E. W. Mielke
  • F. W. Hehl


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.

PACS 04.50

Unified field theories and other theories of gravitation 

PACS 04.60

Quantum theory of gravitation 

PACS 12.25

Models for gravitational interaction 


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Copyright information

© Società Italiana di Fisica 1992

Authors and Affiliations

  • P. Baekler
    • 1
  • E. W. Mielke
    • 1
  • F. W. Hehl
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of CologneKöln 41Germany

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