Origin of Ashtekar's Variables in a Pure-Connection Theory of Gravity

Details Origin of Ashtekar's Variables in a Pure-Connection Theory of Gravity Origin of Ashtekar's Variables in a Pure-Connection Theory of Gravity

Sep 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phrvl..75.2074k&link_type=abstract

Physical Review Letters, Volume 75, Issue 11, September 11, 1995, pp.2074-2076

Mathematics

Logic

9

Scientific paper

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.

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