PIRSA:07110034 Scientific Series Quantum Gravity

DOI10.48660/07110034

Series: Quantum Gravity

Bahr, B. (2007). Automorphisms in Loop Quantum Gravity. Perimeter Institute. https://pirsa.org/07110034

Bahr, Benjamin. Automorphisms in Loop Quantum Gravity. Perimeter Institute, Nov. 15, 2007, https://pirsa.org/07110034 

@misc{ pirsa_PIRSA:07110034,
  doi = {10.48660/07110034},
  url = {https://pirsa.org/07110034},
  author = {Bahr, Benjamin},
  keywords = {Quantum Gravity},
  language = {en},
  title = {Automorphisms in Loop Quantum Gravity},
  publisher = {Perimeter Institute},
  year = {2007},
  month = {nov},
  note = {PIRSA:07110034 see, \url{https://pirsa.org}}
}

Abstract

There is a deep relation between Loop Quantum Gravity and notions from category theory, which have been pointed out by many researchers, such as Baez or Velhinho. Concepts like holonomies, connections and gauge transformations can be naturally formulated in that language. In this formulation, the (spatial) diffeomorphisms appear as the path grouopid automorphisms. We investigate the effect of extending the diffeomorphisms to all such automorphisms, which can be viewed as \"distributional diffeomorphisms\". We also give a notion of \"categorial holonomy-flux-algebra\", and present the construction of the automorphism-invariant Hilbert space for abelian gauge groups, which will be entirely combinatorial.

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