Spin network
In physics, a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics.[1] Spin networks have since been applied to the theory of quantum gravity by Carlo Rovelli, Lee Smolin, Jorge Pullin, Rodolfo Gambini and others.A unit with spin number n is called an n-unit and has angular momentum nħ/2, where ħ is the reduced Planck constant.Over a manifold however, assumptions like diffeomorphism invariance are needed to make the duality exact (smearing Wilson loops is tricky).Michael A. Levin and Xiao-Gang Wen have also defined string-nets using tensor categories that are objects very similar to spin networks.In mathematics, spin networks have been used to study skein modules and character varieties, which correspond to spaces of connections.
physicsstatesparticlesfieldsquantum mechanicsmathematicalmultilinear functionsrepresentationsmatrix groupsRoger Penrosequantum gravityCarlo RovelliLee SmolinJorge PullinRodolfo Gambinifunctionalconnectionsgauge transformationsworld lineelementary particlespin numberangular momentumPlanck constantbosonsphotonsgluonsfermionselectronsquarksprobabilitiesTriangle inequalityirreduciblecompactLie groupverticesholonomiesloop quantum gravitygravitational fieldhypersurfaces-knotsdiffeomorphismscountableHilbert spacequantizationspectrumeigenstatePlanck lengthImmirzi parameterconnection formdualitymanifolddiffeomorphism invarianceWilson loopsquantum groupsTannaka–Krein dualityXiao-Gang Wenstring-netstensor categoriesString-net condensationtopologically orderedskein modulescharacter varietiesSpin connectionSpin structureCharacter varietyPenrose graphical notationSpin foamString-netTrace diagramTensor networkJohn C. BaezI. RobinsonBibcodeAdvances in MathematicsPredrag CvitanovićThe Emperor's New MindShadows of the MindThe Road to RealityCycles of TimeFashion, Faith, and Fantasy in the New Physics of the UniverseThe Nature of Space and TimeStephen HawkingThe Large, the Small and the Human MindAbner ShimonyNancy CartwrightBrian W. AldissTwistor theoryAbstract index notationBlack hole bombGeometry of spacetimeCosmic censorshipWeyl curvature hypothesisPenrose interpretation of quantum mechanicsMoore–Penrose inverseNewman–Penrose formalismPenrose diagramPenrose–Hawking singularity theoremsRiemannian Penrose inequalityPenrose processPenrose tilingPenrose trianglePenrose stairsPenrose transformPenrose–Terrell effectOrchestrated objective reductionPenrose–Lucas argumentFELIX experimentTrapped surfaceAndromeda paradoxConformal cyclic cosmologyLionel PenroseOliver PenroseJonathan PenroseShirley HodgsonJohn Beresford LeathesIllumination problemQuantum mind