Spin Foam Models with Finite Groups

@inproceedings{Bahr2011SpinFM,
  title={Spin Foam Models with Finite Groups},
  author={Benjamin Bahr and Bianca Dittrich and J. Patrick Ryan},
  year={2011}
}
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… 

Figures from this paper

Finite-group gauge theories on lattices as Hamiltonian systems with constraints

. In this work, we present a brief but insightful overview of the gauge theories, which are defined on n -dimensional lattices by using finite gauge groups, in order to show how they can be interpreted…

Holonomy Spin Foam Models: Definition and Coarse Graining

We propose a new holonomy formulation for spin foams, which naturally extends the theory space of lattice gauge theories. This allows current spin foam models to be defined on arbitrary 2-complexes…

Coarse graining methods for spin net and spin foam models

We undertake first steps in making a class of discrete models of quantum gravity, spin foams, accessible to a large-scale analysis by numerical and computational methods. In particular, we apply the…

Coarse Graining Spin Foam Quantum Gravityβ€”A Review

In quantum gravity, we envision renormalization as the key tool for bridging the gap between microscopic models and observable scales. For spin foam quantum gravity, which is defined on a…

Coarse graining of spin net models: dynamics of intertwiners

Spin foams are models of quantum gravity and therefore quantum space time. A key open issue is to determine the possible continuum phases of these models. Progress on this issue has been prohibited…

Towards a phase diagram for spin foams

One of the most pressing issues for loop quantum gravity and spin foams is the construction of the continuum limit. In this paper, we propose a systematic coarse-graining scheme for three-dimensional…

Lessons from toy-models for the dynamics of loop quantum gravity

We review some approaches to the Hamiltonian dynamics of (loop) quantum gravity, the main issues being the regularization of the Hamiltonian and the continuum limit. First, Thiemann's definition of…

Fusion basis for lattice gauge theory and loop quantum gravity

A bstractWe introduce a new basis for the gauge-invariant Hilbert space of lattice gauge theory and loop quantum gravity in (2 + 1) dimensions, the fusion basis. In doing so, we shift the focus from…

Topological lattice field theories from intertwiner dynamics

We introduce a class of 2D lattice models that describe the dynamics of intertwiners, or, in a condensed matter interpretation, the fusion and splitting of anyons. We identify different families and…

The Spin-Foam Approach to Quantum Gravity

  • A. Perez
  • Physics
    Living reviews in relativity
  • 2013
The present status of the spin-foam approach to the quantization of gravity is reviewed and the pedagogical presentation of the recently-introduced new models for four-dimensional quantum gravity is paid to.

References

SHOWING 1-10 OF 289 REFERENCES

The Group field theory approach to quantum gravity

We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local…

Wilson loops, geometric operators and fermions in 3d group field theory

Group field theories whose Feynman diagrams describe 3d gravity with a varying configuration of Wilson loop observables and 3d gravity with volume observables at each vertex are defined. The volume…

Geometric spin foams, Yang-Mills theory and background-independent models

We review the dual transformation from pure lattice gauge theory to spin foam models with an emphasis on a geometric viewpoint. This allows us to give a simple dual formulation of SU(N) Yang-Mills…

Group field theory formulation of 3D quantum gravity coupled to matter fields

We present a new group field theory describing 3D Riemannian quantum gravity coupled to matter fields for any choice of spin and mass. The perturbative expansion of the partition function produces…

A deformed PoincarΓ© invariance for group field theories

In the context of quantum gravity, group field theories are field theories that generate spinfoam amplitudes as Feynman diagrams. They can be understood as generalizations of the matrix models used…

Group field theory as the microscopic description of the quantum spacetime fluid: a new perspective on the continuum in quantum gravity

We introduce the group field theory (GFT) formalism for non-perturbative quantum gravity, and present it as a potential unifying framework for several other quantum gravity approaches, i.e. loop…

The dual of pure non-Abelian lattice gauge theory as a spin foam model

A new spin foam model for 4D gravity

Starting from Plebanski formulation of gravity as a constrained BF theory we propose a new spin foam model for 4D Riemannian quantum gravity that generalizes the well-known Barrett–Crane model and…

Introduction to loop quantum gravity and spin foams

These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection…

Spin-foam models and the physical scalar product

This paper aims at clarifying the link between Loop Quantum Gravity and Spin-Foam models in four dimensions. Starting from the canonical framework, we construct an operator P acting on the space of…
...