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Topic: Topological quantum field theory

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	Loop quantum gravity - Wikipedia, the free encyclopedia
		Loop quantum gravity (LQG), also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the seemingly incompatible theories of quantum mechanics and general relativity.
		Being closely related to topological quantum field theory and group representation theory, LQG is mostly established at the level of rigour of mathematical physics.
		LQG is a quantization of a classical Lagrangian field theory which is equivalent to the usual Einstein-Cartan theory in that it leads to the same equations of motion describing general relativity with torsion.
	en.wikipedia.org /wiki/Loop_quantum_gravity (1971 words)

	Topological quantum field theory - Wikipedia, the free encyclopedia
		Although TQFTs were invented by physicists (notably Witten), they are primarily of mathematical interest, being related to, among other things, knot theory and the theory of four-manifolds in algebraic topology, and to the theory of moduli spaces in algebraic geometry.
		In Schwarz-type TQFTs, the correlation functions computed by the path integral are topological invariants because the path integral measure and the quantum field observables are explicitly independent of the metric.
		Atiyah suggested a set of axioms for topological quantum field theory which was inspired by Segal's proposed axioms for conformal field theory.
	en.wikipedia.org /wiki/Topological_quantum_field_theory (934 words)

	Topological orders (Site not responding. Last check: 2007-10-22)
		New Results in Topological Field Theory and Abelian Gauge Theory These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June.
		Geometry of 2D Topological Field Theory These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories.
		Quantum Topology Project The objective of the Project are to use topological quantum field theories to explore low-dimensional topological objects.
	www.serebella.com /encyclopedia/article-Topological_orders.html (378 words)

	Encyclopedia: Topological quantum field theory (Site not responding. Last check: 2007-10-22)
		In the mathematical field of topology a topological property or topological invariant is a property of a topological space which is invariant under homeomorphisms.
		Quantum Topology Project - The objective of the Project are to use topological quantum field theories to explore low-dimensional topological objects.
		Topological Quantum Field Theory, a Progress Report - A brief introduction to Topological Quantum Field Theory as well as a description of recent progress made in the field is presented.
	www.nationmaster.com /encyclopedia/Topological-quantum-field-theory (305 words)

	Directory - Science: Physics: Quantum Mechanics: Quantum Field Theory: Topological
		Quantum Topology Project · cached · The objective of the Project are to use topological quantum field theories to explore low-dimensional topological objects.
		The field theories to be used are combinatorially and algebraically defined, and the emphasis is on numerical computation and detection of counterexamples rather than general structure.
		Topological Quantum Field Theory, a Progress Report · A brief introduction to Topological Quantum Field Theory as well as a description of recent progress made in the field is presented.
	www.incywincy.com /default?p=210316 (465 words)

	Topological quantum field theory - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-22)
		Topological quantum field theory in theoretical physics provides an example of background-independent quantum theory, but with no local degrees of freedom, and only finitely many degrees of freedom globally.
		This is inadequate to describe gravity in four dimensions, which even in vacuum has local degrees of freedom according to general relativity.
		Advances in Topological Quantum Field Theory : Proceedings of the NATO Adavanced Research Workshop on New Techniques in Topological Quantum Field Theory,...
	encyclopedia.worldsearch.com /topological_quantum_field_theory.htm (182 words)

	Topological dimension (Site not responding. Last check: 2007-10-22)
		topological topological space dimension fourth dimension hardwood dimension hyper dimension hyper dimension download
		Research Group on Topological Quantum Field Theory and Knots Research Group on Topological Quantum Field Theories in any dimension and their relation to topological invariants.
		Topological Defects This is an introductory set of lecture notes on topological defects, given to an audience with interests ranging from astronomy to particle physics.
	www.serebella.com /encyclopedia/article-Topological_dimension.html (423 words)

	Lessons from Topological Quantum Field Theory
		In quantum field theory on curved spacetime, space and spacetime are not just manifolds: they come with fixed `background metrics' that allow us to measure distances and times.
		The big difference is that in topological quantum field theory we cannot measure time in seconds, because there is no background metric available to let us count the passage of time.
		Thus, we hasten to reassure the reader that this peculiarity of topological quantum field theory is not crucial to our overall point, which is the analogy between categories describing space and spacetime and those describing quantum states and processes.
	math.ucr.edu /home/baez/quantum/node2.html (1456 words)

	Knotty Calculations: Science News Online, Feb. 22, 2003 (Site not responding. Last check: 2007-10-22)
		A quantum computer, if it is ever built, will have the power to crack the cryptographic schemes that safeguard Internet transactions and to create incredibly detailed simulations of the behavior of the universe at the tiniest scale.
		"Topological quantum computation is far away from realization now, but it has such appealing features that it wouldn't take me by surprise if it turned into the dominant paradigm," he says.
		For building a topological quantum computer, one system that Freedman and Kitaev are considering is an exotic form of matter called a fractional quantum Hall fluid.
	www.sciencenews.org /20030222/bob11.asp (2611 words)

	Topological Quantum Field Theory (291) graduate course, Fall 2004 (Site not responding. Last check: 2007-10-22)
		This will be a topics course explaining the theory of "Quantum invariants of three-manifolds" and its relationship with other parts of low-dimensional topology.
		The guiding principle is Topological Quantum Field Theory: an axiomatic characterisation of the class of invariants resembling the Eilenberg-Steenrod homology axioms but of an essentially multiplicative rather than additive character.
		These span quite a large area of mathematics: chiefly algebra (quantum groups, tensor categories) and differential topology (the rigorous approach to perturbation theory), but there are also elementary combinatorial approaches and a whole lot of interesting diagrammatic methods available.
	math.ucsd.edu /~justin/TQFT.html (402 words)

	Quantum Field Theory (Site not responding. Last check: 2007-10-22)
		DC MetaData for: From Euclidean Field Theory to Quantum Field Theory...
		5.1 Quantum field theory on a differentiable manifold...
		Quantum field theory on curved spacetime at the Erwin Schrödinger Institute...
	www.scienceoxygen.com /phys/247.html (227 words)

	Citebase - Topological Quantum Field Theory and Seiberg-Witten Monopoles
		the Abelian topological field theory corresponding to the Seiberg--Witten monopole equations.
		In the first part we consider duality in topological quantum field theories, concentrating on the Donaldson and Seiberg-Witten theories as (dual) approaches to the study of four-manifolds.
		A brief introduction to Topological Quantum Field Theory as well as a description of recent progress made in the field is presented.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:hep-th/9504005 (1062 words)

	4-Dimensional BF Theory as a Topological Quantum Field Theory (ResearchIndex)
		57 Quantum field theory and the Jones polynomial (context) - Witten - 1989
		21 State-sum invariants of 3-manifolds and quantum 6jsymbols (context) - Turaev, Viro - 1992
		11 Topological quantum field theories derived from the Kauffman..
	citeseer.ist.psu.edu /138789.html (520 words)

	Citations: Higher-dimensional algebra and topological quantum field theory - Baez, Dolan (ResearchIndex)
		Citations: Higher-dimensional algebra and topological quantum field theory - Baez, Dolan (ResearchIndex)
		Baez and J. Dolan, Higher-dimensional algebra and topological quantum eld theory, Jour.
		Baez and J. Dolan, Higher-dimensional algebra and topological quantum field theory, Jour.
	citeseer.ist.psu.edu /context/119973/45311 (3387 words)

	Citebase - Lectures in Topological Quantum Field Theory
		Generalizations of Donaldson-Witten theory are reviewed, and the structure of the vacuum expectation values of their observables is analyzed in the context of duality for the simplest case.
		We focus on the structure of the contact terms in the twisted topological theory, and on the connection between Whitham hierarchies and the u-plane integrals for...
		Topological field theory is discussed from the point of view of infinite-dimensional differential geometry.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:hep-th/9709192 (1713 words)

	this week's finds (Site not responding. Last check: 2007-10-22)
		Invariants of 3-manifolds and conformal field theories, by Micheal Polyak, preprint.
		On the constraints of quantum gravity in the loop representation, Bernd Bruegmann and Jorge Pullin, Nucl.
		Quantum field theory and the Jones polynomial, by Edward Witten, Comm.
	math.ucr.edu /home/baez/twf.html (12501 words)

	Topological Quantum Field Theory (Site not responding. Last check: 2007-10-22)
		Besides general relativity and quantum field theory as usually practiced, a third sort of idealization of the physical world has attracted a great deal of attention in the last decade.
		Loosely speaking, they all say that a TQFT maps structures in differential topology -- by which I mean the study of manifolds -- to corresponding structures in quantum theory.
		Quantum topology is very technical, as anything involving mathematical physicists inevitably becomes.
	math.ucr.edu /home/baez/planck/node3.html (1399 words)

	Citebase - The Bekenstein Bound, Topological Quantum Field Theory and Pluralistic Quantum Field Theory
		A quantum state of the universe is an assignment of a statistical state into each of these Hilbert spaces, subject to certain conditions of consistency which come from an analysis of the measurement problem.
		A proposal for a concrete realization of these postulates is described, which is based on certain results in the loop representation and topological quantum field theory, and in particular on the fact that spin networks and punctured surfaces appear in both contexts.
		Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/9508064 (2401 words)

	V’}‘Ä“à (Site not responding. Last check: 2007-10-22)
		Noncommutative geometry and representation theory in mathematical physics : satellite conference to the Fourth European Congress of Mathematics, July 5-10, 2004, Karlstad University, Karlstad, Sweden / Jurgen Fuchs...
		Discrete gauge theory from lattices to tqft / Robert Oeckl.
		Quantum algebras and poisson geometry in mathematical physics / M.V. Karasev, editor ; translated by Maria Shishkova.
	opac.dl.itc.u-tokyo.ac.jp /newbook/800/new.html (3185 words)

	Amazon.com: Quantum Field Theory (International Series in Pure and Applied Physics): Books: Claude Itzykson (Site not responding. Last check: 2007-10-22)
		The discussion on charged scalar fields, and why they are needed to formulate a (scalar) theory of particles and antiparticles.
		The existence of a bound state in quantum field theory has yet to be proven using these equations, but they supposedly hold the answer to this existence.
		This is a must read for anyone wishing to study field theory beyond the basics and obtain a mastery of the subject.
	www.amazon.com /exec/obidos/tg/detail/-/0070320713?v=glance (1441 words)

	Gravitational topological quantum field theory versus N = 2 D = 8 supergravity and its lift to N = 1 D = 11 supergravity
		Gravitational topological quantum field theory versus N = 2 D = 8 supergravity and its lift to N = 1 D = 11 supergravity
		In a previous work, it was shown that the 8-dimensional topological quantum field theory for a metric and a Kalb-Ramond 2-form gauge field determines N = 1 D = 8 supergravity, at least in the fermion quadratic aproximation.
		It is shown here that, the combination of this TQFT with that of a 3-form determines N = 2 D = 8 supergravity, that is, an untruncated dimensional reduction of N = 1 D = 11 supergravity.
	stacks.iop.org /1126-6708/2004/i=04/a=044 (393 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations (Site not responding. Last check: 2007-10-22)
		We give a construction of the Abelian Chern{endash}Simons gauge theory from the point of view of a 2+1-dimensional topological quantum field theory.
		The definition of the quantum theory relies on geometric quantization ideas that have been previously explored in connection to the non-Abelian Chern{endash}Simons theory[J. Diff.
		We formulate the topological quantum field theory in terms of the category of extended 2- and 3-manifolds introduced in a preprint by Walker in 1991 and prove that it satisfies the axioms of unitary topological quantum field theories formulated by Atiyah[Publ.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=565706 (193 words)

	Citations: Lectures on axiomatic topological quantum field theory - Quinn (ResearchIndex)
		Higher-Dimensional Algebra and Topological Quantum Field Theory - Baez, Dolan (1995)
		It is, in fact, the theory of extended TQFTs that provides the best information about the relationship between higher dimensional algebra and TQFTs.
		Quinn, Lectures on axiomatic topological quantum field theory, Virginia Polytechnic Institute and State U. preprint, to appear in the proceedings of the Park City Geometry Institute.
	citeseer.ist.psu.edu /context/353450/0 (449 words)

	Strings, Quantum Field Theory and Statistical Mechanics (Site not responding. Last check: 2007-10-22)
		Topological quantum field theory: perturbative topological quantum field theory and deformation quantization, topological quantum field theory and invariants of manifolds.
		Matrix models and matrix integrals (random matrices): matrix models in string theory and quantum field theory, random matrices and growth models.
		Quantum field theory: integrable non-conformal perturbations of conformal field theory, boundary perturbations.
	www.physics.berkeley.edu /events/mm/Workshop.htm (90 words)

	quantum field theory, quantum topodynamics, quantum topology
		Quantum Topodynamics, Topological Quantum Field Theory, M Theory, Quantum Supergravity
		The manifold and quantum dynamics are connected in a mathematical manner
		topology of the quantum state being computed from the functional integral of quantum topodynamics.
	www.homestead.com /qft (756 words)

	GT Monographs 2 (1999) Paper 4 (Abstract) (Site not responding. Last check: 2007-10-22)
		The goal of this paper is to give a new proof of a theorem of Meng and Taubes that identifies the Seiberg-Witten invariants of 3-manifolds with Milnor torsion.
		The point of view here will be that of topological quantum field theory.
		In particular, we relate the Seiberg-Witten equations on a 3-manifold with the Abelian vortex equations on a Riemann surface.
	www.maths.warwick.ac.uk /gt/GTMon2/paper4.abs.html (133 words)

	The Rasetti--Regge Lagrangian, topological quantum field theory and vortices in quantum fluids
		The Rasetti--Regge Lagrangian, topological quantum field theory and vortices in quantum fluids
		A topological string: the Rasetti–Regge Lagrangian, topological quantum field theory and vortices in quantum fluids
		for vortex lines is studied and its relevance to string theory is established.
	stacks.iop.org /0305-4470/35/8859 (292 words)

	Research Group on Topological Quantum Field Theory and Knots
		To study topological field theories in any dimension and their relation to topological invariants.
		Topological invariants include 3-manifold invariants and invariants of ordinary links and knots and, at the higher dimensional level, the homology and cohomology of the spaces of imbedded and immersed loops and spheres.
		Topological Field Theory Interpretation of String Topology [abs] [ps]
	wwwteor.mi.infn.it /users/cotta/tqft.html (265 words)

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