TL;DR
This paper introduces a first order formulation of Regge calculus inspired by Palatini's approach, using dihedral angles and triangle areas as independent variables to model spacetime discretization.
Contribution
It presents a novel first order Regge calculus framework with independent dihedral angles and triangle areas, exploring their role in parameterizing simplex geometries.
Findings
Defined a first order Regge calculus model
Analyzed the parameterization of simplices using areas
Discussed the relationship between dihedral angles and edge lengths
Abstract
A first order form of Regge calculus is defined in the spirit of Palatini's action for general relativity. The extra independent variables are the interior dihedral angles of a simplex, with conjugate variables the areas of the triangles. There is a discussion of the extent to which these areas can be used to parameterise the space of edge lengths of a simplex.
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