Reality conditions and Ashtekar variables: A different perspective

@article{Barbero1995RealityCA,
  title={Reality conditions and Ashtekar variables: A different perspective},
  author={J. Fernando G. Barbero},
  journal={Physical Review D},
  year={1995},
  volume={51},
  pages={5498-5506}
}
  • 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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