q-Deformed spin foam models of quantum gravity

Abstract

We numerically study Barrett-Crane models of Riemannian quantum gravity. We have extended the existing numerical techniques to handle q-deformed models and arbitrary space-time triangulations. We present and interpret expectation values of a few selected observables for each model, including a spin-spin correlation function which gives insight into the behaviour of the models. We find the surprising result that, as the deformation parameter q goes to 1 through roots of unity, the limit is discontinuous.

21 pages, 6 figures, amsrefs

References in corpus (16)

• Spin Foam Models for Quantum Gravity
• Relativistic spin networks and quantum gravity
• Spin Foam Models
• Group Field Theory: An overview
• A Lorentzian Signature Model for Quantum General Relativity
• Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
• Linking Topological Quantum Field Theory and Nonperturbative Quantum Gravity
• A spin foam model without bubble divergences
• Asymptotics of 10j symbols
• 4-Dimensional BF Theory as a Topological Quantum Field Theory
• Cosmological Deformation of Lorentzian Spin Foam Models
• On relativistic spin network vertices
• Spin Foam Models of Riemannian Quantum Gravity
• An efficient algorithm for the Riemannian 10j symbols
• Positivity of Spin Foam Amplitudes
• Positivity in Lorentzian Barrett-Crane Models of Quantum Gravity

Cited by in corpus (14)

• The complete LQG propagator: II. Asymptotic behavior of the vertex
• Hypercuboidal renormalization in spin foam quantum gravity
• Coarse graining flow of spin foam intertwiners
• Coarse graining of spin net models: dynamics of intertwiners
• Quantum group spin nets: refinement limit and relation to spin foams
• Dual Computations of Non-abelian Yang-Mills on the Lattice
• Calculating statistical distributions from operator relations: the statistical distributions of various intermediate statistics
• Spin-Foam Models and the Physical Scalar Product
• Numerical indications on the semiclassical limit of the flipped vertex
• Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
• Evaluation of new spin foam vertex amplitudes
• Recurrence relation for the 6j-symbol of su_q(2) as a symmetric eigenvalue problem
• Exact Lorentz-violating $q$-deformed O($N$) universality class
• Influence of exact Lorentz-violating mechanism on the critical exponents for massive $q$-deformed $\lambda {\varphi }^4$ scalar field theory