PIRSA:12020096 Scientific Series Quantum Gravity

DOI10.48660/12020096

Series: Quantum Gravity

Ziprick, J. (2012). Continuous Formulation of the Loop Quantum Gravity Phase Space. Perimeter Institute. https://pirsa.org/12020096

Ziprick, Jonathan. Continuous Formulation of the Loop Quantum Gravity Phase Space. Perimeter Institute, Feb. 01, 2012, https://pirsa.org/12020096 

@misc{ pirsa_PIRSA:12020096,
  doi = {10.48660/12020096},
  url = {https://pirsa.org/12020096},
  author = {Ziprick, Jonathan},
  keywords = {Quantum Gravity},
  language = {en},
  title = {Continuous Formulation of the Loop Quantum Gravity Phase Space},
  publisher = {Perimeter Institute},
  year = {2012},
  month = {feb},
  note = {PIRSA:12020096 see, \url{https://pirsa.org}}
}

Abstract

We relate the discrete classical phase space of loop gravity to the continuous phase space of general relativity. Our construction shows that the flux variables do not label a unique geometry, but rather a class of gauge-equivalent geometries. We resolve the tension between the loop gravity geometrical interpretation in terms of singular geometry, and the spin foam interpretation in terms of piecewise-flat geometry, showing that both geometries belong to the same equivalence class. We also establish a clear relationship between Regge geometries and the piecewise-flat spin foam geometries. All of this is based on arXiv:1110.4833.

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