PIRSA:14030088 Scientific Series Quantum Gravity

DOI10.48660/14030088

Series: Quantum Gravity

Wieland, W. (2014). A one-dimensional action for simplicial gravity in three dimensions. Perimeter Institute. https://pirsa.org/14030088

Wieland, Wolfgang. A one-dimensional action for simplicial gravity in three dimensions. Perimeter Institute, Mar. 06, 2014, https://pirsa.org/14030088 

@misc{ pirsa_PIRSA:14030088,
  doi = {10.48660/14030088},
  url = {https://pirsa.org/14030088},
  author = {Wieland, Wolfgang},
  keywords = {Quantum Gravity},
  language = {en},
  title = {A one-dimensional action for simplicial gravity in three dimensions},
  publisher = {Perimeter Institute},
  year = {2014},
  month = {mar},
  note = {PIRSA:14030088 see, \url{https://pirsa.org}}
}

Abstract

Loop quantum gravity has a spinorial representation. Spinors simplify the symplectic structure of the theory, but can they also teach us something about the dynamics? We study this question in three dimensions, and derive the Ponzano–-Regge model from a spinorial action. Our construction starts from the first-order Palatini formalism, and gives the discretised action in the spinorial representation. A one-dimensional refinement limit brings us back to a continuum theory. The three-dimensional action turns into a line integral over the edges of the discretisation. We compute the gauge-fixed path integral for a generic simplicial discretisation. The resulting amplitudes reproduce the Ponzano–-Regge model.

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