SU(2)-invariant reduction of the 3+1 dimensional Ashtekar's gravity
General Relativity and Quantum Cosmology
2009-10-30 v1
Abstract
We consider a space-time with spatial sections isomorphic to the group manifold of SU(2). Triad and connection fluctuations are assumed to be SU(2)-invariant. Thus, they form a finite dimensional phase space. We perform non-perturbative path integral quantization of the model. Contarary to previous claims the path integral measure appeared to be non-singular near configurations admitting additional Killing vectors. In this model we are able to calculate the generating functional of Green functions of the reduced phase space variables exactly.
Cite
@article{arxiv.gr-qc/9705080,
title = {SU(2)-invariant reduction of the 3+1 dimensional Ashtekar's gravity},
author = {Sergei Alexandrov and Ignati Grigentch and Dmitri Vassilevich},
journal= {arXiv preprint arXiv:gr-qc/9705080},
year = {2009}
}
Comments
12 pages