Related papers: Degenerate Plebanski Sector and Spin Foam Quantiza…
The goal of this work is two-fold. In the first part of this paper we regard classical Plebanski's action as a BF action supplemented by constraints. We introduce a spin foam model for Riemannian general relativity by systematically…
We introduce a three-dimensional Plebanski action for the gauge group SO(4). In this model, the $B$ field satisfies quadratic simplicity constraints similar to that of the four-dimensional Plebanski theory, but with the difference that the…
Starting from Plebanski formulation of gravity as a constrained BF theory we propose a new spin foam model for 4d Riemannian quantum gravity that generalises the well-known Barrett-Crane model and resolves the inherent to it ultra-locality…
This article reviews the present status of the spin foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently introduced new models for four dimensional quantum gravity. The…
Modern spin-foam models of four dimensional gravity are based on a discrete version of the $Spin(4)$ Plebanski formulation. Beyond what is already in the literature, we clarify the meaning of different Plebanski sectors in this classical…
We propose a new method of unifying gravity and the Standard Model by introducing a spin-foam model. We realize a unification between an SU(2) Yang-Mills interaction and 3D general relativity by considering a Spin(4) Plebanski action. The…
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…
We investigate a formulation of continuum 4d gravity in terms of a constrained BF theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum…
We provide the Barrett-Crane spin foam model for quantum gravity with a discrete action principle, consisting in the usual BF term with discretized simplicity constraints which in the continuum turn topological BF theory into gravity. The…
We investigate a formulation of continuum 4d gravity in terms of a constrained topological (BF) theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach…
Spin-foam models are hoped to provide a dynamics for loop quantum gravity. These start from the Plebanski formulation of gravity, in which gravity is obtained from a topological field theory, BF theory, through constraints, which, however,…
Spin foam models of quantum gravity are based on Plebanski's formulation of general relativity as a constrained BF theory. We give an alternative formulation of gravity as BF theory plus a certain potential term for the B-field. When the…
The most common spin foam models of gravity are widely believed to be discrete path integral quantizations of the Plebanski action. However, their derivation in present formulations is incomplete and lower dimensional simplex amplitudes are…
We introduce a vertex amplitude for 4d loop quantum gravity. We derive it from a conventional quantization of a Regge discretization of euclidean general relativity. This yields a spinfoam sum that corrects some difficulties of the…
We study a generalized action for gravity as a constrained BF theory, and its relationship with the Plebanski action. We analyse the discretization of the constraints and the spin foam quantization of the theory, showing that it leads…
Spin Foam Models are supposed to be discretised path integrals for quantum gravity constructed from the Plebanski-Holst action. The reason for there being several models currently under consideration is that no consensus has been reached…
We revise the classical continuum formulation behind the Spin Foam approach to the quantization of gravity. Based on the recent applications of the current EPRL-FK model beyond triangulations, we identify the tension with the implementation…
We define a four-dimensional spin-foam perturbation theory for the ${\rm BF}$-theory with a $B\wedge B$ potential term defined for a compact semi-simple Lie group $G$ on a compact orientable 4-manifold $M$. This is done by using the formal…
We derive the the Barrett-Crane spin foam model for Euclidean 4 dimensional quantum gravity from a discretized BF theory, imposing the constraints that reduce it to gravity at the quantum level. We obtain in this way a precise prescription…
In part I of [1] we have developed the tensor and spin representation of SO(4) in order to apply it to the simplicial decomposition of the Barrett-Crane model. We attach to each face of a triangle the spherical function constructed from the…