Quantum Regge Calculus of Einstein-Cartan theory

Details Quantum Regge Calculus of Einstein-Cartan theory Quantum Regge Calculus of Einstein-Cartan theory

2009-02-19

arxiv.org/abs/0902.3407v4

Phys. Lett. B682 (2009) 300

Physics

High Energy Physics

High Energy Physics - Theory

The title, abstract and content of this article have been modified. The version to appear in Phys. Lett. B. 11 pages, 1 figure

Scientific paper

10.1016/j.physletb.2009.10.082

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_\mu(x) and spin-connection field \omega_\mu(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 \omega_\mu(x) fields and Dirac-matrix valued e_\mu(x) fields over 4-simplices complex.

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