General Relativity as a (constrained) Yang-Mills's Theory and a Novel Gravity with Torsion

Details General Relativity as a (constrained) Yang-Mills's Theory and a Novel Gravity with Torsion General Relativity as a (constrained) Yang-Mills's Theory and a Novel Gravity with Torsion

2000-10-21

arxiv.org/abs/gr-qc/0010080v3

Gen.Rel.Grav. 34 (2002) 1781-1792

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages. This replaced version has slightly modified title, some additional information that render our results clearer and a

Scientific paper

We show that General Relativity (GR) with cosmological constant may be formulated as a rather simple constrained SO(D-1,2) (or SO(D,1))-Yang-Mills (YM) theory. Furthermore, the spin connections of the Cartan-Einstein formulation for GR appear as solutions of a genuine SO(D-1,1)-YM. We also present a theory of gravity with torsion as the most natural extension of this result. The theory comes out to be strictly an YM-theory upon relaxation of a suitable constraint. This work sets out to enforce the close connection between YM theories and GR by means of a new construction.

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