From Local Regge Calculus towards Spin Foam Formalism?

Details From Local Regge Calculus towards Spin Foam Formalism? From Local Regge Calculus towards Spin Foam Formalism?

2006-03-28

arxiv.org/abs/gr-qc/0603107v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, 1 figures, proceeding of the Albert Einstein's International Conference 18-22 July 2005

Scientific paper

We introduce the basic elements of SO(n)-local theory of Regge Calculus. A first order formalism, in the sense of Palatini, is defined on the metric-dual Voronoi complex of a simplicial complex. The Quantum Measure exhibits an expansion, in four dimensions, in characters of irreducible representation of SO(4) which has close resemblance and differences as well with the Spin Foam Formalism. The coupling with fermionic matter is easily introduced which could have consequences for the Spin Foam Formalism and Loop Quantum Gravity.

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