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PonzanoRegge model revisited. III: Feynman diagrams and effective field theory
"... We study the no gravity limit GN → 0 of the PonzanoRegge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with Hadamard propagator) expressed as an abelian spin foam model. We show how the GN expansion of the PonzanoRegge amplitudes can be resummed ..."
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Cited by 52 (4 self)
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We study the no gravity limit GN → 0 of the PonzanoRegge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with Hadamard propagator) expressed as an abelian spin foam model. We show how the GN expansion of the PonzanoRegge amplitudes can be resummed. This leads to the conclusion that the effective dynamics of quantum particles coupled to quantum 3d gravity can be expressed in terms of an effective new non commutative field theory which respects the principles of doubly special relativity. We discuss the construction of Lorentzian spin foam models including Feynman propagators.
so(4) Plebański Action and Relativistic Spin Foam Model
, 1999
"... 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 fo ..."
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Cited by 46 (3 self)
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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 of Euclidean gravity. We also show that the Plebanski model possess another natural dicretisation and can be associate with another, new, spin foam model that appear to be the so(4) counterpart of the spin foam model describing the self dual formulation of gravity. Typeset using REVTEX 1 I.
Cosmological deformation of Lorentzian Spin Foam Models
 arXiv: grqc/0211109
, 2003
"... We study the quantum deformation of the BarrettCrane Lorentzian spin foam model which is conjectured to be the discretization of Lorentzian Plebanski model with positive cosmological constant and includes therefore as a particular sector quantum gravity in deSitter space. This spin foam model is c ..."
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Cited by 22 (1 self)
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We study the quantum deformation of the BarrettCrane Lorentzian spin foam model which is conjectured to be the discretization of Lorentzian Plebanski model with positive cosmological constant and includes therefore as a particular sector quantum gravity in deSitter space. This spin foam model is constructed using harmonic analysis on the quantum Lorentz group. The evaluation of simple spin networks are shown to be non commutative integrals over the quantum hyperboloid defined as a pile of fuzzy spheres. We show that the introduction of the cosmological constant, removes all the infrared divergences: for any fixed triangulation, the integration over the area variables is finite for a large class of normalization of the amplitude of the edges and of the faces. I.
CGPG98/45 Spin Foam Models and the Classical Action Principle
, 1998
"... 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 s ..."
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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, YangMills theories and gravity in various spacetime dimensions. Our main idea is twofold. First, we propose to take into account in the path integral certain distributional configurations of the B field in which it is concentrated along lower dimensional hypersurfaces in spacetime. Second, using the notion of generating functional we develop perturbation expansion techniques, with the role of the free theory played by the BF theory. We test our approach on various theories for which the corresponding spin foam (state sum) models are known. We find that it exactly reproduces the known models for BF and 2D YangMills theories. For the BF theory with cosmological term in 3 and 4 dimensions we calculate the terms of the transition amplitude that are of the first order in the cosmological constant, and find an agreement with the corresponding first order terms of the known state sum models. We discuss implications of our results for existing quantum gravity models.
Spin Foam Models and the Classical Action Principle
, 1999
"... 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 s ..."
Abstract
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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, YangMills theories and gravity in various spacetime dimensions. Our main idea is twofold. First, we propose to take into account in the path integral certain distributional configurations of the B field in which it is concentrated along lower dimensional hypersurfaces in spacetime. Second, using the notion of generating functional we develop perturbation expansion techniques, with the role of the free theory played by the BF theory. We test our approach on various theories for which the corresponding spin foam (state sum) models are known. We find that it exactly reproduces the known models for BF and 2D YangMills theories. For the BF theory with cosmological term in 3 and 4 dimensions we calculate the terms of the transition amplitude that are of the first order in the cosmological constant, and find an agreement with the corresponding first order terms of the known state sum models. We discuss implications of our results for existing quantum gravity models.
CGPG99/11 BF Description of HigherDimensional Gravity Theories
, 1999
"... It is well known that, in the firstorder formalism, pure threedimensional gravity is just the BF theory. Similarly, fourdimensional general relativity can be formulated as BF theory with an additional constraint term added to the Lagrangian. In this paper we show that the same is true for all hig ..."
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It is well known that, in the firstorder formalism, pure threedimensional gravity is just the BF theory. Similarly, fourdimensional general relativity can be formulated as BF theory with an additional constraint term added to the Lagrangian. In this paper we show that the same is true for all higherdimensional gravity theories: in any dimension gravity can be described as a constrained BF theory. We describe in details the structure of these constraints. Then we discuss the “spin foam ” quantization of these theories, which proves to be quite similar to the spin foam quantization of general relativity in three and four dimensions. In particular, in any dimension, we solve the quantum constraints and find the socalled simple representations and intertwiners. These exhibit a simple and beautiful structure that is common to all dimensions.