Detailed discussions and calculations of quantum Regge calculus of Einstein-Cartan theory

Abstract

This article presents detailed discussions and calculations of the recent paper "Quantum Regge calculus of Einstein-Cartan theory" in Phys. Lett. B682 (2009) 300. The Euclidean space-time is discretized by a four-dimensional simplicial complex. We adopt basic tetrad and spin-connection fields to describe the simplicial complex. By introducing diffeomorphism and local Lorentz invariant holonomy fields, we construct a regularized Einstein-Cartan theory for studying the quantum dynamics of the simplicial complex and fermion fields. This regularized Einstein-Cartan action is shown to properly approach to its continuum counterpart in the continuum limit. Based on the local Lorentz invariance, we derive the dynamical equations satisfied by invariant holonomy fields. In the mean-field approximation, we show that the averaged size of 4-simplex, the element of the simplicial complex, is larger than the Planck length. This formulation provides a theoretical framework for analytical calculations and numerical simulations to study the quantum Einstein-Cartan theory.

the final version to appear in PRD, 52 pages and 6 figures, title has been changed

References in corpus (9)

• Gravitational Wilson Loop and Large Scale Curvature
• A locally finite model for gravity
• The phase structure of Einstein-Cartan theory
• Quantum Regge Calculus of Einstein-Cartan theory
• Gravitational Wilson Loop in Discrete Quantum Gravity
• Defining integrals over connections in the discretized gravitational functional integral
• Integration over connections in the discretized gravitational functional integrals
• Gauge invariant discretization of Poincare quantum gravity
• On the possibility of finite quantum Regge calculus

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