Quantum Regge Calculus of Einstein-Cartan theory
arXiv:0902.3407 · doi:10.1016/j.physletb.2009.10.082
Abstract
We study the Quantum Regge Calculus of Einstein-Cartan theory to describe quantum dynamics of Euclidean space-time discretized as a 4-simplices complex. Tetrad field e_μ(x) and spin-connection field ω_μ(x) are assigned to each 1-simplex. Applying the torsion-free Cartan structure equation to each 2-simplex, we discuss parallel transports and construct a diffeomorphism and {\it local} gauge-invariant Einstein-Cartan action. Invariant holonomies of tetrad and spin-connection fields along large loops are also given. Quantization is defined by a bounded partition function with the measure of SO(4)-group valued ω_μ(x) fields and Dirac-matrix valued e_μ(x) fields over 4-simplices complex.
The title, abstract and content of this article have been modified. The version to appear in Phys. Lett. B. 11 pages, 1 figure
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