PIRSA:13040104 Scientific Series Quantum Gravity

DOI10.48660/13040104

Series: Quantum Gravity

Tomlin, C. (2013). Loop quantization of a weak-coupling limit of Euclidean gravity. Perimeter Institute. https://pirsa.org/13040104

Tomlin, Casey. Loop quantization of a weak-coupling limit of Euclidean gravity. Perimeter Institute, Apr. 25, 2013, https://pirsa.org/13040104 

@misc{ pirsa_PIRSA:13040104,
  doi = {10.48660/13040104},
  url = {https://pirsa.org/13040104},
  author = {Tomlin, Casey},
  keywords = {Quantum Gravity},
  language = {en},
  title = {Loop quantization of a weak-coupling limit of Euclidean gravity},
  publisher = {Perimeter Institute},
  year = {2013},
  month = {apr},
  note = {PIRSA:13040104 see, \url{https://pirsa.org}}
}

Abstract

I will describe recent work in collaboration with Adam Henderson, Alok Laddha, and Madhavan Varadarajan on the loop quantization of a certain $G_{\mathrm{N}}\rightarrow 0$ limit of Euclidean gravity, introduced by Smolin. The model allows one to test various quantization choices one is faced with in loop quantum gravity, but in a simplified setting.  The main results are the construction of finite-triangulation Hamiltonian and diffeomorphism constraint operators whose continuum limits can be evaluated in a precise sense, such that the quantum Dirac algebra of constraints closes nontrivially and free of anomalies.  The construction relies heavily on techniques of Thiemann's QSD treatment, and lessons learned applying such techniques to the loop quantization of parameterized scalar field theory and the diffeomorphism constraint in loop quantum gravity.  I will also briefly discuss the status of the quantum constraint algebra in full LQG, and how some of the lessons learned from the present model may guide us in that setting.

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