Real Ashtekar variables for Lorentzian signature space-times.

@article{Barbero1995RealAV,
  title={Real Ashtekar variables for Lorentzian signature space-times.},
  author={J. Fernando G. Barbero},
  journal={Physical Review D},
  year={1995},
  volume={51},
  pages={5507-5510}
}
I suggest in this letter a new strategy to attack the problem of the reality conditions in the Ashtekar approach to classical and quantum general relativity. By writing a modified Hamiltonian constraint in the usual $SO(3)$ Yang-Mills phase space I show that it is possible to describe space-times with Lorentzian signature without the introduction of complex variables. All the features of the Ashtekar formalism related to the geometrical nature of the new variables are retained; in particular… 
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