A new Hamiltonian for the topological BF phase with spinor networks

DOI10.1063/1.4731771zbMath1279.83017arXiv1110.3272OpenAlexW1990821890WikidataQ64007772 ScholiaQ64007772MaRDI QIDQ2865531

Etera R. Livine, Valentin Bonzom

Publication date: 29 November 2013

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.3272

zbMATH Keywords

latticequantizationnew scalar Hamiltoniantopological BF phasetopological ground stateWigner 6j-symbol

Mathematics Subject Classification ID

Topological characterizations of particular spaces (54F65) Relativistic cosmology (83F05) Yang-Mills and other gauge theories in quantum field theory (81T13) Quantization of the gravitational field (83C45) Quantum field theory on lattices (81T25) Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory (83C27) Topological field theories in quantum mechanics (81T45) Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism (83C60)

Related Items (12)

Self-duality of the \(6j\)-symbol and Fisher zeros for the tetrahedron ⋮ Duality between spin networks and the 2D Ising model ⋮ Non-perturbative 3D quantum gravity: quantum boundary states and exact partition function ⋮ The Fock space of loopy spin networks for quantum gravity ⋮ Quasi-local holographic dualities in non-perturbative 3d quantum gravity. I: Convergence of multiple approaches and examples of Ponzano-Regge statistical duals ⋮ q-deformed 3D loop gravity on the torus ⋮ On the exact evaluation of spin networks ⋮ Deformations of polyhedra and polygons by the unitary group ⋮ The quantum gravity disk: Discrete current algebra ⋮ The Ponzano–Regge cylinder and propagator for 3d quantum gravity ⋮ Deformed spinor networks for loop gravity: towards hyperbolic twisted geometries ⋮ Probing the shape of quantum surfaces: the quadrupole moment operator

Cites Work

• Topological \(BF\) field theory description of topological insulators
• Bubble divergences from twisted cohomology
• Superconductors with topological order
• Towards the graviton from spinfoams: the complete perturbative expansion of the 3d toy model
• Holomorphic factorization for a quantum tetrahedron
• On quantum gauge theories in two dimensions
• Classical \(6j\)-symbols and the tetrahedron
• Four-dimensional Yang-Mills theory as a deformation of topological \(BF\) theory
• Canonical BF-type topological field theory and fractional statistics of strings.
• Geometry and quantum physics. Proceedings of the 38th internationale Universitätswochen für Kern- und Teilchenphysik, Schladming, Austria, January 9--16, 1999
• Exactly soluble diffeomorphism invariant theories
• Fault-tolerant quantum computation by anyons
• Superconductors are topologically ordered
• Spin networks in gauge theory
• Spin foam models and the classical action principle
• Exotic statistics for strings in 4d BF theory
• Spinor representation for loop quantum gravity
• The Hamiltonian constraint in 3d Riemannian loop quantum gravity
• Asymptotics of Wigner 3nj-symbols with small and large angular momenta: an elementary method
• The Ponzano–Regge model
• Asymptotic analysis of the Ponzano–Regge model for handlebodies
• Recurrence relations for spin foam vertices
• The 6j-symbol: recursion, correlations and asymptotics
• Quantum geometry from phase space reduction
• Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity
• (Broken) Gauge symmetries and constraints in Regge calculus
• PERTURBATION THEORY FOR ANTISYMMETRIC TENSOR FIELDS IN FOUR DIMENSIONS
• Ponzano–Regge model revisited: I. Gauge fixing, observables and interacting spinning particles
• Three-dimensional loop quantum gravity: physical scalar product and spin-foam models
• so (4) Plebanski action and relativistic spin-foam model
• Background independent quantum gravity: a status report
• Topological quantum memory
• Topological BF theories in 3 and 4 dimensions
• The fine structure of SU(2) intertwiners from U(N) representations
• U(N) coherent states for loop quantum gravity
• U( N ) tools for loop quantum gravity: the return of the spinor
• Phase space descriptions for simplicial 4D geometries
• Structure of the Wigner 9j Coefficients in the Bargmann Approach
• Partition functions and topology-changing amplitudes in the three-dimensional lattice gravity of Ponzano and Regge

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