Reality conditions and Ashtekar variables: A different perspective

  title={Reality conditions and Ashtekar variables: A different perspective},
  author={J. Fernando G. Barbero},
  journal={Physical Review D},
  • J. F. Barbero
  • Published 11 October 1994
  • Mathematics
  • Physical Review D
We give in this paper a modified self-dual action that leads to the $SO(3)$-ADM formalism without having to face the difficult second class constraints present in other approaches (for example if one starts from the Hilbert-Palatini action). We use the new action principle to gain some new insights into the problem of the reality conditions that must be imposed in order to get real formulations from complex general relativity. We derive also a real formulation for Lorentzian general relativity… 
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Bibliography of Publications related to Classical and Quantum Gravity in terms of the Ashtekar Variables
This bibliography attempts to give a comprehensive overview of all the literature related to the Ashtekar variables. The original version was compiled by Peter H\"ubner in 1989, and it has been
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
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