Phys. Rev. Lett. 75, 2074–2076 (1995)Origin of Ashtekar's Variables in a Pure-Connection Theory of GravityReceived 19 June 1995; published in the issue dated 11 September 1995 A pure-connection formulation of general relativity is presented in which the only dynamical variable present in the action is a connection one-form with values in the Lie algebra of the pseudounitary group SU(2,2). The action is quadratic in the curvature and is independent of any space-time metric. Although manifestly SU(2,2) gauge invariant, the symmetry group of the action can be broken down to that of the Lorentz group SL(2, C) yielding Jacobson and Smolin's covariant self-dual version (modulo a topological and cosmological term) of the Ashtekar formulation of general relativity. © 1995 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.75.2074
DOI:
10.1103/PhysRevLett.75.2074
PACS:
04.50.+h, 04.60.Ds
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