Complex Ashtekar Variables and Reality Conditions for Holst’s Action

@article{Wieland2012ComplexAV,
  title={Complex Ashtekar Variables and Reality Conditions for Holst’s Action},
  author={Wolfgang M. Wieland},
  journal={Annales Henri Poincar{\'e}},
  year={2012},
  volume={13},
  pages={425-448}
}
  • Wolfgang M. Wieland
  • Published 2012
  • Mathematics, Physics
  • Annales Henri Poincaré
  • From the Holst action in terms of complex valued Ashtekar variables, additional reality conditions mimicking the linear simplicity constraints of spin-foam gravity are found. In quantum theory with the results of Ding and Rovelli, we are able to implement these constraints weakly, that is in the sense of Gupta and Bleuler. The resulting kinematical Hilbert space matches the original one of loop quantum gravity, that is for real valued Ashtekar connection. Our results perfectly fit with recent… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 39 REFERENCES
    Reality conditions for Ashtekar gravity from Lorentz-covariant formulation
    21
    Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action.
    • Holst
    • Physics, Medicine
    • 1996
    407
    Four-dimensional Lorentzian Holst action with topological terms
    35
    The physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
    47
    New variables for classical and quantum gravity.
    993
    Action Integrals and Partition Functions in Quantum Gravity
    1945
    Flipped spinfoam vertex and loop gravity
    236