Spin foam model for pure gauge theory coupled to quantum gravity

We analyse the classical and quantum geometry of the Barrett-Crane spin foam model for four dimensional quantum gravity, explaining why it has to be considering as a covariant realization of the projector operator onto physical quantum gravity states. We discuss how causality requirements can be consistently implemented in this framework, and construct causal transiton amplitudes between quantum gravity states, i.e. realising in the spin foam context the Feynman propagator between states. The resulting causal spin foam model can be seen as a path integral quantization of Lorentzian first order Regge calculus, and represents a link between several approaches to quantum gravity as canonical loop quantum gravity, sum-over-histories formulations, dynamical triangulations and causal sets. In particular, we show how the resulting model can be rephrased within the framework of quantum causal sets (or histories).2

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“…the 3-volume of the corresponding tetrahedron (more on the 4-volume operator in the Barrett-Crane model can be found in [43]). …”

Section: Geometric Meaning Of the Variables Of The Modelmentioning

confidence: 99%

Implementing causality in the spin foam quantum geometry

2003

Self Cite

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“…The spin labelling the faces are also SU (2) representations and are interpreted as quanta of area. this construction has been exemplified in 2+1 gravity [15] It was soon realized that spin foam models can naturally incorporate causality [16], Lorentzian signature [17] and coupling to gauge field theory [18]. The Barrett-Crane prescription was understood to be linked to the Plebanski formulation of gravity where the Einstein action is written as a BF theory subject to constraints [19].…”

Section: Introductionmentioning

confidence: 99%

Group Field Theory: An Overview

2005

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We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that this theory leads to a natural proposal for the physical scalar product of quantum gravity. We also show in which sense this theory provides a third quantization point of view on quantum gravity.

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“…On the other hand, our model is linked to gravity along the well known relationship between four dimensional BF theory and general relativity explicitly exhibit in the Plebansky formulation of gravity. In particular, it would be interesting to compare our model with the coupling to Yang-Mills theories proposed in [22].…”

Section: Discussionmentioning

confidence: 99%

Two-dimensional topological field theories coupled to four-dimensional BF theory

Montesinos

Pérez

2008

Phys. Rev. D

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Four dimensional BF theory admits a natural coupling to extended sources supported on two dimensional surfaces or string world-sheets. Solutions of the theory are in one to one correspondence with solutions of Einstein equations with distributional matter (cosmic strings). We study new (topological field) theories that can be constructed by adding extra degrees of freedom to the two dimensional world-sheet. We show how two dimensional Yang-Mills degrees of freedom can be added on the world-sheet, producing in this way, an interactive (topological) theory of Yang-Mills fields with BF fields in four dimensions. We also show how a world-sheet tetrad can be naturally added. As in the previous case the set of solutions of these theories are contained in the set of solutions of Einstein's equations if one allows distributional matter supported on two dimensional surfaces. These theories are argued to be exactly quantizable. In the context of quantum gravity, one important motivation to study these models is to explore the possibility of constructing a background independent quantum field theory where local degrees of freedom at low energies arise from global topological (world-sheet) degrees of freedom at the fundamental level.

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Spin foam model for pure gauge theory coupled to quantum gravity

Cited by 46 publications

References 33 publications

Implementing causality in the spin foam quantum geometry

Implementing causality in the spin foam quantum geometry

Group Field Theory: An Overview

Two-dimensional topological field theories coupled to four-dimensional BF theory

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