New variables for classical and quantum gravity in all dimensions: III. Quantum theory
Abstract
We quantize 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 generalize to the new connection formulation in higher dimensions. The only new challenge is the simplicity constraint. While its ‘diagonal’ components acting at edges of spinnetwork functions are easily solved, its ‘offdiagonal’ components acting at vertices are nontrivial and require a more elaborate treatment.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 February 2013
 DOI:
 10.1088/02649381/30/4/045003
 arXiv:
 arXiv:1105.3705
 Bibcode:
 2013CQGra..30d5003B
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 36 pages. v2: Journal version. Discussion on simplicity constraints extended. Conclusion and outlook extended. Minor clarifications