First order minisuperspace model for the Faddeev formulation of gravity

TL;DR

This paper develops a discrete minisuperspace model for Faddeev's formulation of gravity, representing it in a connection-type form similar to the continuum Hilbert-Einstein action, and explores its relation to general relativity.

Contribution

It introduces a novel discrete representation of Faddeev gravity using a Cartan-Weyl connection-like form, extending previous minisuperspace models.

Findings

Discrete model formulated on polytopes like 4-simplices or cuboids

Representation analogous to connection form in continuum GR

Potential for new insights into quantum gravity approaches

Abstract

Faddeev formulation of general relativity (GR) is considered where the metric is composed of ten vector fields or a ten-dimensional tetrad. Upon partial use of the field equations, this theory results in the usual GR. Earlier we have proposed some minisuperspace model for the Faddeev formulation where the tetrad fields are piecewise constant on the polytopes like 4-simplices or, say, cuboids into which ${\rm I \hspace{-3pt} R}^4$ can be decomposed. Now we study some representation of this (discrete) theory, an analogue of the Cartan-Weyl connection-type form of the Hilbert-Einstein action in the usual continuum GR.