• DOI:10.1103/PhysRevD.84.044047
• Corpus ID: 118494757

Unimodular loop quantum gravity and the problems of time

@article{Smolin2010UnimodularLQ,
  title={Unimodular loop quantum gravity and the problems of time},
  author={Lee Smolin},
  journal={Physical Review D},
  year={2010},
  volume={84},
  pages={044047}
}

• L. Smolin
• Published 10 August 2010
• Physics
• Physical Review D

We develop the quantization of unimodular gravity in the Plebanski and Ashtekar formulations and show that the quantum effective action defined by a formal path integral is unimodular. This means that the effective quantum geometry does not couple to terms in the expectation value of energy proportional to the metric tensor. The path integral takes the same form as is used to define spin foam models, with the additional constraint that the determinant of the four metric is constrained to be a constant by a gauge fixing term. This extends the results of [10] to the Hilbert space and path integral of loop quantum gravity. We review the proposal of Unruh, Wald and Sorkin- that the hamiltonian quantization yields quantum evolution in a physical time variable equal to elapsed four volume-and discuss how this may be carried out in loop quantum gravity.