scholarly journals Coupling of spacetime atoms in 4D spin foam models from group field theory

2007 ◽  
Vol 2007 (02) ◽  
pp. 092-092 ◽  
Author(s):  
Etera R Livine ◽  
Daniele Oriti
Keyword(s):  
Field Theory ◽  
Spin Foam Models ◽  
Spin Foam ◽  
Group Field Theory

scholarly journals Spin Foam Models with Finite Groups

2013 ◽  
Vol 2013 ◽  
pp. 1-28 ◽  
Author(s):  
Benjamin Bahr ◽  
Bianca Dittrich ◽  
James P. Ryan
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Finite Groups ◽  
Loop Quantum Gravity ◽  
Theory Approach ◽  
Test Bed ◽  
Spin Foam Models ◽  
Spin Foam ◽  
Group Field Theory ◽  
The Many

Spin foam models, loop quantum gravity, and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity-inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community, we provide an introduction to some essential concepts in the loop quantum gravity, spin foam, and group field theory approach and point out the many connections to the lattice field theory and the condensed-matter systems.

scholarly journals Quantum Field Theory of Open Spin Networks and New Spin Foam Models

2003 ◽  
Vol 18 (supp02) ◽  
pp. 83-96 ◽  
Author(s):  
A. Miković
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vector Bundles ◽  
Tensor Category ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Spin Networks ◽  
Spin Foam Models ◽  
Topological Quantum ◽  
Spin Foam

We describe how a spin-foam state sum model can be reformulated as a quantum field theory of spin networks, such that the Feynman diagrams of that field theory are the spin-foam amplitudes. In the case of open spin networks, we obtain a new type of state-sum models, which we call the matter spin foam models. In this type of state-sum models, one labels both the faces and the edges of the dual two-complex for a manifold triangulation with the simple objects from a tensor category. In the case of Lie groups, such a model corresponds to a quantization of a theory whose fields are the principal bundle connection and the sections of the associated vector bundles. We briefly discuss the relevance of the matter spin foam models for quantum gravity and for topological quantum field theories.

scholarly journals MEASUREMENTS AND INFORMATION IN SPIN FOAM MODELS

2012 ◽  
Vol 27 (28) ◽  
pp. 1250164
Author(s):  
J. MANUEL GARCÍA-ISLAS
Keyword(s):  
Information Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Shannon Entropy ◽  
Three Dimensional ◽  
Spin Network ◽  
Spin Foam Models ◽  
Foam Model ◽  
Spin Foam Model ◽  
Spin Foam

In the three-dimensional spin foam model of quantum gravity with a cosmological constant, there exists a set of observables associated with spin network graphs. A set of probabilities is calculated from these observables, and hence the associated Shannon entropy can be defined. We present the Shannon entropy associated with these observables and find some interesting bounded inequalities. The problem relates measurements, entropy and information theory in a simple way which we explain.

scholarly journals Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime

2018 ◽  
Vol 98 (10) ◽  
Author(s):  
Benjamin Bahr ◽  
Giovanni Rabuffo ◽  
Sebastian Steinhaus
Keyword(s):  
Asymptotic Regime ◽  
Spin Foam Models ◽  
Spin Foam

scholarly journals Renormalization of a SU(2) Tensorial Group Field Theory in Three Dimensions

2014 ◽  
Vol 330 (2) ◽  
pp. 581-637 ◽  
Author(s):  
Sylvain Carrozza ◽  
Daniele Oriti ◽  
Vincent Rivasseau
Keyword(s):  
Field Theory ◽  
Three Dimensions ◽  
Group Field Theory

scholarly journals Coarse graining in spin foam models

2003 ◽  
Vol 20 (5) ◽  
pp. 777-799 ◽  
Author(s):  
Fotini Markopoulou
Keyword(s):  
Coarse Graining ◽  
Spin Foam Models ◽  
Spin Foam

Quantum gravity, group field theory (GFT), and combinatorics

2021 ◽  
pp. 121-165
Author(s):  
Adrian Tanasa
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Specific Model ◽  
Algebraic Combinatorics ◽  
Saddle Point Method ◽  
Feynman Integrals ◽  
Causal Dynamical Triangulations ◽  
Group Field Theory ◽  
Definition Of

This chapter is the first chapter of the book dedicated to the study of the combinatorics of various quantum gravity approaches. After a brief introductory section to quantum gravity, we shortly mention the main candidates for a quantum theory of gravity: string theory, loop quantum gravity, and group field theory (GFT), causal dynamical triangulations, matrix models. The next sections introduce some GFT models such as the Boulatov model, the colourable and the multi-orientable model. The saddle point method for some specific GFT Feynman integrals is presented in the fifth section. Finally, some algebraic combinatorics results are presented: definition of an appropriate Conne–Kreimer Hopf algebra describing the combinatorics of the renormalization of a certain tensor GFT model (the so-called Ben Geloun–Rivasseau model) and the use of its Hochschild cohomology for the study of the combinatorial Dyson–Schwinger equation of this specific model.

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