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 spin-network functions are easily solved, its ‘off-diagonal’ components acting at vertices are non-trivial and require a more elaborate treatment.
Classical and Quantum Gravity
- Pub Date:
- February 2013
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory;
- Mathematical Physics
- 36 pages. v2: Journal version. Discussion on simplicity constraints extended. Conclusion and outlook extended. Minor clarifications