Twistorial phase space for complex Ashtekar variables

@article{Wieland2012TwistorialPS,
  title={Twistorial phase space for complex Ashtekar variables},
  author={Wolfgang M. Wieland},
  journal={Classical and Quantum Gravity},
  year={2012},
  volume={29},
  pages={045007}
}
  • Wolfgang M. Wieland
  • Published 2012
  • Physics
  • Classical and Quantum Gravity
  • We generalize the SU(2) spinor framework of twisted geometries developed by Dupuis, Freidel, Livine, Speziale and Tambornino to the Lorentzian case, that is the group . We show that the phase space for complex-valued Ashtekar variables on a spin-network graph can be decomposed in terms of twistorial variables. To every link there are two twistors—one to each boundary point—attached. The formalism provides a new derivation of the solution space of the simplicity constraints of loop quantum… CONTINUE READING
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