English

New Variables for Classical and Quantum Gravity in all Dimensions III. Quantum Theory

General Relativity and Quantum Cosmology 2013-02-13 v2 High Energy Physics - Theory Mathematical Physics math.MP

Abstract

We quantise the new connection formulation of D+1 dimensional General Relativity developed in our companion papers by Loop Quantum Gravity (LQG) methods. It turns out that all the tools prepared for LQG straightforwardly generalise to the new connection formulation in higher dimensions. The only new challenge is the simplicity constraint. While its "diagonal" components acting at edges of spin network functions are easily solved, its "off-diagonal" components acting at vertices are non trivial and require a more elaborate treatment.

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Cite

@article{arxiv.1105.3705,
  title  = {New Variables for Classical and Quantum Gravity in all Dimensions III. Quantum Theory},
  author = {Norbert Bodendorfer and Thomas Thiemann and Andreas Thurn},
  journal= {arXiv preprint arXiv:1105.3705},
  year   = {2013}
}

Comments

36 pages. v2: Journal version. Discussion on simplicity constraints extended. Conclusion and outlook extended. Minor clarifications

R2 v1 2026-06-21T18:09:17.095Z