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	Spin foam - Wikipedia, the free encyclopedia
		In physics, a spin foam is a four-dimensional graph made out of two-dimensional faces that represents one of the configurations that must be summed to obtain Feynman's path integral (functional integration) describing the alternative formulation of quantum gravity known as loop gravity or loop quantum gravity.
		Spin network is defined as a diagram (like Feynman diagram) which make a basis of connections between the elements of a differentiable manifold for the Hilbert spaces defined over them.
		Spacetime is considered as a quantic superposition of spin foams, which is a generalized Feynman diagram where instead of a graph we use a higher-dimensional complecies.
	en.wikipedia.org /wiki/Spin_foam (279 words)

	Spin network - Wikipedia, the free encyclopedia
		A spin network is a (directed) graph whose edges are associated with irreducible representations of a compact Lie group, G and vertices are associated with intertwiners of the edge reps adjacent to it.
		Spin networks were applied to the physics problem of quantum gravity by Carlo Rovelli, Lee Smolin, Fotini Markopoulou-Kalamara, and others to reformulate loop quantum gravity in the canonical approach.
		One of the key results of loop quantum gravity is quantization of areas: according to several related derivations based on loop quantum gravity, the operator of the area A of a two-dimensional surface Σ should have a discrete spectrum.
	en.wikipedia.org /wiki/Spin_network (493 words)

	Foam Sleeper (Site not responding. Last check: 2007-10-08)
		Foam is a problem because it alters the liquid flow and blocks oxygen transfer from air (therefore preventing microbial respiration in fermentation processes).
		The ''quantum'' in ''quantum foam'' comes from quantum mechanics, and the ''foam'' comes from the idea that at extremely small distances (of the order of the Planck length), the energy of spacetime itself ceases to be smooth, and resembles instead a kind of rapidly changing foam.
		Spacetime is considred as a quantic superposition of spin foams, which is a generalized Feynman diagram where instead of a graph we use a higher-dimensional complecies.
	www.blownspeakers.com /pages3/34/foam-sleeper.html (1492 words)

	Historical Notes: Quantum gravity
		Spin networks were introduced in 1964 by Roger Penrose as a way to set up an intrinsically quantum mechanical model of spacetime.
		In attempting extensions to 4D, spin foams have been introduced - and variously interpreted in terms of simplified Feynman diagrams, constructs in multidimensional category theory, and possible evolutions of spin networks.
		In all cases, however, spin networks and spin foams seem to be viewed just as calculational constructs that must be evaluated and added together to get quantum amplitudes - quite different from my idea of associating an explicit evolution history for the universe with the evolution of a network.
	www.wolframscience.com /reference/notes/1054a (1043 words)

	Spin foam -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		Any evolution of (Click link for more info and facts about spin network) spin network provides a spin foam over a (A pipe that has several lateral outlets to or from other pipes) manifold of one dimensional higher than the dimensions of the corresponding spin network.
		A spin foam may be viewed as a (Click link for more info and facts about quantum history) quantum history.
		Spacetime is considred as a quantic superposition of spin foams, which is a generalized (Click link for more info and facts about Feynman diagram) Feynman diagram where instead of a graph we use a higher-dimensional complecies.
	www.absoluteastronomy.com /encyclopedia/s/sp/spin_foam.htm (341 words)

	Loop quantum gravity
		Being closely related to topological quantum field theory and group representation theory, LQG is mostly established at the level of rigour of mathematical physics, as opposed to string theory, which is established at the level of rigour of physics.
		After the spin network basis was described, progress was made on the analysis of the spectra of various operators resulting in a predicted spectrum for area and volume (see below).
		Spin foams are new framework intended to tackle the problem of dynamics and the continuum limit simultaneously.
	www.sciencedaily.com /encyclopedia/loop_quantum_gravity (6191 words)

	Re: Spin foams and gauge theories
		In particular, regardless of whether we consider the spin foams as embedded in a spacetime manifold or as "abstract", they are certainly not embedded in a manifold with a fixed background metric.
		Or, perhaps better, sum over spin foams weighted in such a way that this sum (a kind of superposition) can be said to mimic a classical spacetime geometry shaped like a slab 1 minute in thickness.
		If we sum over spin foams embedded in a manifold, there is a concept of surface in that manifold, but no way to tell (even given a particular spin foam embedded in a particular way) whether a given point of that surface is "spacelike" - there's no metric.
	www.lns.cornell.edu /spr/2000-10/msg0028632.html (1144 words)

	[No title]
		A spin foam is a 2-dimensional analogue of a Feynman diagram.
		Similarly, a spin foam is a 2-dimensional cell complex with polygonal faces labelled by representations and edges labelled by intertwining operators.
		The spin foam faces are all labelled by `balanced' representations of Spin (4) = SU (2) x SU (2), that is, those of the form j j.
	jdc.math.uwo.ca /papers/foam4.txt (9236 words)

	Spin networks, spin foams and loop quantum gravity
		A covariant (path integral) formulation of the theory is expected to be in the form of a spin foam model, such as the Barrett-Crane model.
		A spin network is supposed to be a model of space, while a spin foam is suppose to model the evolution of space from one time to another, and so be like spacetime.
		An Introduction to Spin Foam Models of BF Theory and Quantum Gravity, 1999.
	jdc.math.uwo.ca /spin-foams (2348 words)

	week113
		More generally, a spin foam is a 2-dimensional complex with faces labelled by irreducible representations of some group and edges labelled by intertwining operators.
		This seems to be a particularly interesting sort of spin foam for quantum gravity in 4 dimensions: a spin foam dual to a triangulation of spacetime.
		Similarly, a spin foam is a 2-dimensional complex with faces labelled by representations and edges labelled by intertwiners.
	math.ucr.edu /home/baez/week113.html (2737 words)

	Citebase - Spin Foam Models for Quantum Gravity (Site not responding. Last check: 2007-10-08)
		Relativistic quantum spins are related to the geometry of the 2-dimensional faces of a 4-simplex.
		This is an introduction to spin foam models for non-perturbative quantum gravity, an approach that lies at the point of convergence of many different research areas, including loop quantum gravity, topological quantum field theories, path integral quantum gravity, lattice field theory, matrix mode...
		The concept of `spin foam' is intended to serve as a similar picture for the quantum geometry of spacetime.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/0301113 (1891 words)

	angusfire - Foam Testing Service (Site not responding. Last check: 2007-10-08)
		If you are reviewing your foam stocks why not also consider the latest technology fluoroprotein based foam concentrates which have exceptional fire performance and minimal environmental impact.
		In addition to our modern foam research laboratory, live fire foam testing facilities using realistic scenarios are available to determine the most appropriate foam for use on any specific hazardous material that you, as a foam user, may utilise in your facility.
		Stocks of the main foam types are held at our factory for immediate despatch in the event of a fire emergency anywhere in the world.
	www.angusfire.co.uk /wnpres63.shtml (1297 words)

	Re: Spin foams and gauge theories
		And the answer is: spin foam faces are dual to triangles in a triangulation of our 4-manifold (spacetime).
		Spin foam faces in the 4-manifold give spin network edges in the 3-manifold.
		This recipe generalizes to a recipe for calculating transition amplitudes between spin network states when we have a 4-manifold that's a cobordism from one 3-manifold to another, and spin networks sitting in the 3-manifolds.
	www.lns.cornell.edu /spr/2000-10/msg0029140.html (1676 words)

	Homepage of Robert Oeckl (Site not responding. Last check: 2007-10-08)
		Surprisingly many approaches have converged on spin foam models, for example the canonical quantization known as loop quantum gravity as well as covariant path integral quantizations.
		Spin foams can be thought of as encoding quantum space-time.
		Applications dicsussed in the book include spin foam models of quantum gravity and quantum supergravity, non-abelian duality, spin models, generating field theory (generalized matrix models) and renormalization.
	www.matmor.unam.mx /~robert (1024 words)

	Luboš Motl's reference frame: Troubled loop gravity (Site not responding. Last check: 2007-10-08)
		It allows a direct construction of spin foam models, by imposing the quadratic constraints in the measure of the path integral for BF theory.
		The second physical question is to classify the universality classes of the spin foam models and, having done this, learn which classes of theories have a good low energy behaivor that reproduces classical GR and QFT.
		But no one should mind if the most successful spin foam model, in terms of both matheamtical elegance and physical results, was not the quantization of a classical theory, but only reproduced the classical theory in the low energy limit.
	motls.blogspot.com /2005/01/troubled-loop-gravity.html (9333 words)

	Mining Technology - Minova International - Resin and Cement Capsules, Cementitious Foams and Grouts, Resin and Cement ...
		Recent developments, such as the Lokset Spin to Stall cartridge in South Africa, have helped eliminate the effects of operational variables, such as ambient temperature and spin speed, so that the installation becomes self-timing and self-checking.
		These grouts and foams are formulated to use a high water content, which leads to reduced material usage and reduced transport costs.
		Wilflex is a two component phenolic foam which when pumped through a suitable application pump forms a rapidly reacting foam.
	www.mining-technology.com /contractors/roofing/minova (698 words)

	Minnowbrook: Baez (Site not responding. Last check: 2007-10-08)
		A spin network is a graph with edges labeled by representations of some group and vertices labeled by intertwining operators.
		Thanks in part to the introduction of spin network techniques, we now have a mathematically rigorous and intuitively compelling picture of the kinematical aspects of loop quantum gravity.
		A spin foam is a 2-dimensional cell complex with faces labeled by representations and edges labeled by intertwining operators; generically, any slice of a spin foam gives a spin network.
	www.phy.syr.edu /research/hetheory/minnowbrook/baez.html (148 words)

	Solid State Dynamics, Polymers, and Imaging
		NMR data might be used for a further understanding of the mechanical properties of the foams which are used in the manufacturing of car seats etc. The uptake of water in poly(sodium acrylate) material has also been studied.
		F 25 kHz spin echo and TOSS spectra were acquired to differentiate residual sidebands from isotropic peaks and the latter allowed peak assignments to be carried out in a straightforward manner.
		The understanding of spin relaxation is crucial to the experimental interpretation and methodology development in magnetic resonance.
	www.enc-conference.org /1998Abstracts/dpi_posters.html (4874 words)

	Spin Foam Models Of Riemannian Quantum Gravity - Baez, Christensen (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		In the version with modi ed face and edge amplitudes due to Perez and Rovelli, we show the partition function converges so rapidly that the sum is dominated by spin foams...
		However, in both versions the spin foam vertex amplitudes are given by the Riemannian 10j symbols, and the key fact we need to show is...
		6 An introduction to spin foam models of quantum gravity and B..
	citeseer.ist.psu.edu /622241.html (825 words)

	Spin Networks (Technical Notes) (Site not responding. Last check: 2007-10-08)
		In the language of group theory, the map C is described as an intertwiner between the two representations of SU(2) that apply to the incoming and outgoing states.
		References: “Spin Networks in Nonperturbative Quantum Gravity” and “An Introduction to Spin Foam Models of Quantum Gravity and BF Theory” by John C. Baez; “The Future of Spin Networks” by Lee Smolin.
		Dan Christensen has a page of links to a number of other articles and web pages that deal with spin foams and spin networks, including many links to John Baez's site.
	gregegan.customer.netspace.net.au /SCHILD/Spin/SpinNotes.html (407 words)

	Citebase - Implementing causality in the spin foam quantum geometry (Site not responding. Last check: 2007-10-08)
		We analyse the classical and quantum geometry of the Barrett-Crane spin foam model for four dimensional quantum gravity, explaining why it has to be considering as a covariant realization of the projector operator onto physical quantum gravity states.
		The resulting causal spin foam model can be seen as a path integral quantization of Lorentzian first order Regge calculus, and represents a link between several approaches to quantum gravity as canonical loop quantum gravity, sum-over-histories formulations, dynamical triangulations and causal sets.
		In general, a spin network is a graph with edges labelled...
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/0210064 (2127 words)

	Abstracts of papers (Site not responding. Last check: 2007-10-08)
		We investigate both the Reisenberger and the Barrett-Crane spin foam model in view of their amenability to a renormalization treatment.
		In particular, we are able to formulate LGT as well as spin foam models of BF-type with quantum gauge group (in dimension <=4) and with supersymmetric gauge group (in any dimension).
		This transformation is available for the partition function, for the expectation value of observables (spin networks), and for the correlator of centre monopoles which is a ratio of partition functions in the original model and an ordinary expectation value in the dual formulation.
	www.matmor.unam.mx /~robert/abstracts/papers.html (3302 words)

	Paola Zizzi Abstract.
		Then, spin networks were re-discovered by Rovelli and Smolin in the context of loop quantum gravity.
		Basically, spin networks are graphs embedded in 3-space, with edges labeled by spins and vertices labeled by intertwining operators.
		We interprete spin networks as qubits when their edges are labeled by the spin-1/2 representation of SU(2).
	www.mindspring.com /~cerebroscopic/Zizzi.html (709 words)

	[No title]
		As I'm sure you know [this is the hint for you to ask a question], it decomposes as the direct sum of all irreps of the form j tensor j, where j ranges over all irreps of SU(2).
		And the answer is: spin network edges are dual to triangles in a triangulation of our 4-manifold (spacetime).
		To add to my confusion, the recipe you described computed a number for a closed spin foam, going from the empty spin network to itself, so no spin network edges were labelled at all.
	jdc.math.uwo.ca /spin-foams/s.p.r (12899 words)

	[No title]
		In spin foam models, spacetime is not a continuum, so the term "continuum limit" can lead to confusion about what we're trying to do.
		In my paper "Spin Foam Perturbation Theory", I proved that perturbation about TQFTs gives a class of spin foam models where everything can be computed as a convergent power series in the coupling constant that governs the perturbation.
		I don't know any spin foam models which we understand, but can only be understood without use of perturbation theory.
	www.math.niu.edu /~rusin/known-math/00_incoming/foam (2744 words)

	It's equal but it's different: This week in the arXivs... (Site not responding. Last check: 2007-10-08)
		31Jan05 and#8212; 04Feb05: New Spin Foam Models of Quantum Gravity Conformal invariance and the conformal-traceless decomposition of the gravitational field Quantum gravity in terms of topological observables Higher-Spin Gauge Fields and Duality Algebraic Geometry of Discrete Dynamics.
		The first paper above starts from the Barret-Crane spin foam model for Quantum Gravity and then moves on to describing two different and new spin foam models that don’t have some of the drawbacks that the Barret-Crane has.
		Namely these models are: spin foam invariants for the embedded spin networks in loop quantum gravity and the spin foam model based on the integration of the tetrads in the path integral for the Palatini action.
	blog.olympus.het.brown.edu /science/archives/000200.php (2160 words)

	Not Even Wrong » Blog Archive » Loop Quantum Gravity Debate (Site not responding. Last check: 2007-10-08)
		So they began exploring other paths, like spin foams with their connection to BF theory and related areas, which have turned out to be interesting and are still being pursued.
		In general, a spin network is a graph with edges labelled by representations and vertices labelled by intertwining operators.
		Similarly, a spin foam is a 2-dimensional complex with faces labelled by representations and edges labelled by intertwining operators.
	www.math.columbia.edu /~woit/blog/archives/000145.html (7812 words)

	Loop quantum gravity
		One of the key results of loop quantum gravity is quantization of areas: according to several related derivations based on loop quantum gravity, the operator of the area of a two-dimensional surface should have discrete spectrum.
		where the sum goes over all intersections of with the spin network.
		In this formula, is the gravitational constant, is the Immirzi parameter and is the spin associated with the link of the spin network.
	www.brainyencyclopedia.com /encyclopedia/l/lo/loop_quantum_gravity.html (6262 words)

	Re: Supersymmetric spin foams
		He has written papers about QFT, quantum groups and geometry, susy and also a spin foams paper [1] which is based on your spin foams paper.
		I don't know why he started to study susy spin foams but maybe it was because I asked him a question about Yi Ling's susy spin networks paper or because he had already been thinking about susy and spin foams.
		I might not be able to understand these drafts anyway, but perhaps they would be happy to have a spin foams expert such as yourself as a potential reviewer.
	www.lns.cornell.edu /spr/2001-09/msg0035645.html (325 words)

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