Faddeev gravity action on the piecewise constant fundamental vector fields

Abstract

In the Faddeev formulation of gravity, the metric is regarded as composite field, bilinear of $d=10$ 4-vector fields. We derive the minisuperspace (discrete) Faddeev action by evaluating the Faddeev action on the spacetime composed of the (flat) 4-simplices with constant 4-vector fields. This is an analog of the Regge action obtained by evaluating the Hilbert-Einstein action on the spacetime composed of the flat 4-simplices. One of the new features of this formulation is that the simplices are not required to coincide on their common faces. Also an analog of the Barbero-Immirzi parameter $\gamma$ can be introduced in this formalism.

8 pages, reported on the conference "Quantum Field Theory and Gravity 2014" (July 28 - August 3 2014, Tomsk, Russia)

References in corpus (1)

• First order representation of the Faddeev formulation of gravity