Preprint CQG-98/05-02 Parma U. UPRF-98-04 so(4) Plebanski Action and Relativistic Spin Foam Model

r - qc / 9 80 40 71 v 1 2 6 A pr 1 99 8 so ( 4 ) Plebanski Action and Relativistic Spin Foam Model

In this note we study the correspondence between the " relativistic spin foam " model introduced by Barrett, Crane and Baez and the so(4) Plebanski action. We argue that the so(4) Plebanski model is the continuum analog of the relativistic spin foam model. We prove that the Plebanski action possess four phases, one of which is gravity and outline the discrepancy between this model and the model...

Canonical “Loop” Quantum Gravity and Spin Foam Models

The canonical “loop” formulation of quantum gravity is a mathematically well defined, background independent, non perturbative standard quantization of Einstein’s theory of General Relativity. Some among the most meaningful results of the theory are: 1) the complete calculation of the spectrum of geometric quantities like the area and the volume and the consequent physical predictions about the...

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Spin foam model from canonical quantization

We suggest a modification of the Barrett-Crane spin foam model of 4-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop quantum gravity. Its kinematical Hilbert space is found as a space of the so-called projected spin networks. These spin networks are identified with the boundary states of a spin foam model and provide...

ar X iv : h ep - t h / 98 07 09 2 v 1 1 3 Ju l 1 99 8 CGPG - 98 / 4 - 5 Spin Foam Models and the Classical Action Principle

We propose a new systematic approach that allows one to derive the spin foam (state sum) model of a theory starting from the corresponding classical action functional. It can be applied to any theory whose action can be written as that of the BF theory plus a functional of the B field. Examples of such theories include BF theories with or without cosmological term, Yang-Mills theories and gravi...