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	Topological quantum field theory - Wikipedia, the free encyclopedia
		A topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants.
		Topological field theories are not very interesting on the flat Minkowski spacetime used in particle physics.
		Most of the known topological field theories are defined on spacetimes of dimension less than five.
	en.wikipedia.org /wiki/Topological_quantum_field_theory (935 words)

	PlanetMath: local field
		A local field is a topological field which is Hausdorff and locally compact as a topological space.
		In fact, this list is complete--every local field is isomorphic as a topological field to one of the above fields.
		This is version 4 of local field, born on 2002-06-18, modified 2005-04-03.
	planetmath.org /encyclopedia/LocalField.html (155 words)

	Topological ring -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		Every topological ring is a (additional info and facts about topological group) topological group (with respect to addition) and hence a (additional info and facts about uniform space) uniform space in a natural manner.
		One can thus ask whether a given topological ring R is (additional info and facts about complete) complete.
		To have a topological field we should also specify that (Turning upside down; setting on end) inversion is continuous, when restricted to F\.
	www.absoluteastronomy.com /encyclopedia/t/to/topological_ring.htm (276 words)

	RMK articles : Chirality and Helicity vs Topological Spin and Topological Torsion (Site not responding. Last check: 2007-10-21)
		From a topological viewpoint, Maxwell's electrodynamics indicates that the concept of Chirality is to be associated with a third rank tensor density of Topological Spin induced by the interaction of the 4 vector potentials {A, phi } and the field excitations (D, H).
		The distinct concept of Helicity is to be associated with the third rank tensor field of Topological Torsion induced by the interaction of the 4 vector potentials and field intensities (E, B).
		The topological analysis indicates that Optical Activity is related to the D field (and possible translational accelerations), while Faraday rotation is related to B field (and possible rotational accelerations).
	www22.pair.com /csdc/pd2/pd2fre52.htm (462 words)

	2) Yang-Mills theories, topological field theories and colour confinement
		The BF theory is called topological, because it doesn't contain any local excitation (no particles), but describes global observables related to the topological invariants of the manifold on which it is defined and of its sub-manifolds.
		The hope of this approach is that the topological theory contained in the YM theory could describe the long range features of its ``mother'', being sensitive to the global structure of the manifold on which it is defined and to the non-perturbative sectors of the theory like, e.g., the instantons.
		In [9] and [8] the first order YM theory, named BFYM theory, is correctly quantized in 3 and 4 dimensions and shown to be equivalent also at the quantum level in perturbation theory to the original second order version.
	www.tphys.uni-heidelberg.de /~accardi/research/node2.html (393 words)

	[No title]
		I present an algorithm that extracts local topological structure of arbitrary regions in a 2D vector field.
		It is based on a mathematical analysis of the topological vector field structure in these regions.
		It is based on a mathem= atical analysis of the topological vector field structure in these regions.
	mambo.ucsc.edu /psl/cis_seminars/200007/20000714.html (338 words)

	[No title]
		The first step in a topological model is an identification of photospheric sources by grouping concentrations in a magnetogram.
		A model of the coronal magnetic field is constructed by first replacing each photopsheric source by a point magnetic charge with equivalent flux, located on a plane tangent to the phtosphere.
		In this example the current density is assumed to be proportion to the magnetic field with a constant of proportionality of +0.012 Mm (not an atypical value for an active region).
	solar.physics.montana.edu /muri/nuggets/jun2002/flare.html (759 words)

	[No title]
		A rudimentary theory of topological 4D gravity Jack Morava Department of Mathematicss The Johns Hopkins University Baltimore 21218 Md. jack@math.jhu.edu Abstract A theory of topological gravity is a homotopy-theoretic represen- tation of the Segal-Tillmann topologification of a two-category with cobordisms as morphisms.
		A topological quantum field theory in the sense of Atiyah [12 x1.7] is thus a (continous) monoidal functor from a topological gravity category to the (topological) category of modules over a discrete topological ring.
		A (projective) Hilbert-space representation of a topological gravity category, along the lines considered by Segal in his definition of a conformal field theory, is thus very close to a quantum theory of gravity.
	hopf.math.purdue.edu /Morava/PGGravityfinal.txt (3741 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Topological field theory deals with field theories (TFT's) that do not depend on small deformations of the theory.
		This is a consequence of the topological property of the integral: $I_f$ does not depend on local changes, and therefore also not on the scale.
		In topological field theory, so for topological path integrals, the moduli space usually is a union of finite dimensional subspaces of the infinite dimensional field space.
	www.weizmann.ac.il /home/hofman/tft.tex (4396 words)

	Application of Spin Field
		The spin field is described rigorously by R. Kiehn: [1] [2] [3] From a topological viewpoint, Maxwell's electrodynamics indicates that the concept of chirality is to be associated with a third rank tensor density of Topological Spin induced by the interaction of the 4 vector potentials {A, phi } and the field excitations (D, H).
		For the spin field created by the spin field generator, as designed by A. Shpilman in 1995, [5] the longitudinal momentum of the spin field impulse is equal to the impulse of a proton, with an energy of 300 electron-volts in air, and 3 electron-volts in ferrite.
		We arranged the spin field generator on the vertical axis centered above both containers as in the diagram below, with the generator at G, the alcohol at R, the water at W, where the spin field is denoted by the light blue cone, A. We irradiated the stack of containers for the recommended 10 minutes.
	www.rialian.com /rnboyd/spinfield-effects.htm (3744 words)

	Learn more about Rational number in the online encyclopedia. (Site not responding. Last check: 2007-10-21)
		In mathematics, the term "rational XXX" means that the underlying field considered is the field of rational numbers.
		The rationals are the smallest field with characteristic 0: every other field of characteristic 0 contains a copy of Q.
		In addition to the absolute value metric mentioned above, there are other metrics which turn Q into a topological field: let p be a prime number and for any non-zero integer a let
	www.onlineencyclopedia.org /r/ra/rational_number.html (810 words)

	3) Yang-Mills theories, topological field theories and colour confinement
		21], where it is shown that, in 4 dimensions, by a suitable redefinition of the fields it is possible to divide the
		Correspondingly, the original BFYM Lagrangian is split into two parts: the Topological Yang-Mills (TYM) Lagrangian, which describes the dynamics of the non-perturbative fields, and a deformation Lagrangian which describes the dynamics of the gluons over such a non-perturbative background.
		Contact with confinement is made by observing that the TYM theory is a twisted version of the N=2 supersymmetric YM theory (SYM), whose low-energy behaviour has been exactly computed by Seiberg and Witten.
	nt3.phys.columbia.edu /people/aaccardi/Research/node7.html (391 words)

	Topological Quantum Field Theory (291) graduate course, Fall 2004 (Site not responding. Last check: 2007-10-21)
		This discovery proved to be the tip of the iceberg: several other knot related knot polynomials (HOMFLY, Kauffman,...) were quickly discovered, and in 1989 Witten explained how this family of invariants should extend naturally to give lots of invariants for three-manifolds.
		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.
		It is still impossible to treat his approach as rigorous, but fortunately the invariants can be studied (in particular, shown to exist!) by many other methods.
	math.ucsd.edu /~justin/TQFT.html (402 words)

	Holocaust - Uncyclopedia
		Some political fields have a tragic characteristic, which is the smallest negative element n of the tragic numbers such that when acting upon the political field, 0 is attained.
		Political fields of finite tragic characteristic include the Schiavo field, the Chandra-Levy field, the Elysian field, and the Phillip-Bustert field.
		In 1905, Bertrand Russell proved the existence of a universal political field of tragic infinite characteristic.
	uncyclopedia.org /uncyclopedia/index.php?title=Holocaust (636 words)

	IngentaConnect Topological Field Theories Associated with Three-Dimensional Seib... (Site not responding. Last check: 2007-10-21)
		Three-dimensional topological field theories associated with the three-dimensional version of Abelian and non-Abelian Seiberg–Witten monopoles are presented.
		As the local gauge symmetries with topological shifts are found to be first-stage-reducible, the Batalin–Vilkovisky algorithm is suitable for quantization.
		Nontrivial observables associated with Chern classes are obtained from the geometric sector and are found to correspond to those of the topological field theory of Bogomol'nyi monopoles.
	www.ingentaconnect.com /content/klu/ijtp/1998/00000037/00000003/00296628 (176 words)

	[No title]
		That topological gravity and quantum cohomology are closely related is clear from [37], but I suspect that the simplicity of the underlying geometry is not * *widely understood.
		T* he domain of this generalized topological* field theory is the monoidal category (S* table Curves) with finite ordered sets as objects; morphisms are finite unions of mar *ked curves.
		* In the language of physics, the elements zi are the `primary fields' of a topological* * field theory defined by the quantum cohomology of V, while ckzi is the kth `topologi *cal descendant' of zi.
	hopf.math.purdue.edu /Morava/Luminy6-final.txt (5111 words)

	ORDINAL REAL NUMBERS 2
		In this topology, as it is known, the field F is a topological field.
		As in the case of fields that are classes, we may permit topological spaces that are classes and the open sets is a class of subclasses closed to union and finite intersection.
		In other words the fields of ordinal real numbers are Archemidean complete fields (although they may be non-Archemidean).But this is a characteristic property of the fields of transfinite real numbersb of Glayzal.
	softlab.ntua.gr /~kyritsis/PapersInMaths/InfinityandStochastics/OR2.htm (2766 words)

	Michael H. Freedman
		The work for which he is best known is the solution of the long-standing Poincare conjecture in four dimensions, for which he received the Fields Medal, the highest honor in mathematics.
		An extended Hubbard model with ring exchange: a route to a non-abelian topological phase.
		Fields Medal, Int'l Congress of Mathematicians, Berkeley, CA National Medal of Science (White House, June 1987)
	research.microsoft.com /research/theory/freedman (431 words)

	Topological Quantum Field Theory
		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.
		These are called topological quantum field theories, or `TQFTs'.
		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!
	math.ucr.edu /home/baez/planck/node3.html (1399 words)

	Frobenius algebras and 2D topological quantum field theories (Site not responding. Last check: 2007-10-21)
		The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics.
		Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations.
		The picture on the cover is the topological expression of the main axiom for a Frobenius algebra.
	www.cirget.uqam.ca /%7Ekock/TQFT.html (284 words)

	Seminar Topological String Theory (Site not responding. Last check: 2007-10-21)
		Antony Wassermann (Luminy): Operator algebraic analysis of solvable lattice models and boundary conformal field theory.
		Workshop ``Conformal field theory and supersymmetry'', MSRI April 15-26 2002.
		Symposium ``Topology, Geometry and Quantum Field Theory", Oxford June 24-29 2002.
	guests.mpim-bonn.mpg.de /rosellen/seminar.html (379 words)

	Topological Field Theory and Interactions between Mathematics and Physics (Site not responding. Last check: 2007-10-21)
		Topological Field Theory and Interactions between Mathematics and Physics, July 17 - 22, 1995
		The Green-Hurst Institute for Theoretical Physics in Adelaide, South Australia, is hosting a regional meeting in Topological Field Theory and, more generally, Interactions between Mathematics and Physics, to be held during the third week of July, beginnining on July 17th 1995.
		In his 1992 paper `Two dimensional gauge theories revisited' Witten reexamined two dimensional topological Yang-Mills theory by introducing his `nonabelian localization principle' (a nonabelian version of the Duistermaat-Heckman integration formula) and using it to obtain general expressions for intersection pairings on moduli spaces of flat connections on a two dimensional manifold.
	www.physics.adelaide.edu.au /itp/workshops/TFT.html (938 words)

	From String Backgrounds to Topological Field Theories (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		The concept of a string background has been extended to the notion of W -strings, where the BRST symmetry is still largely conjectural.
		More recently, the BRST formalism has entered the construction of two dimensional topological conformal quantum field theories, such as those that arise from...
		2 Operadic formulation of topological vertex algebras and Gers..
	citeseer.ist.psu.edu /lian95from.html (738 words)

	Degenerate Solutions of General Relativity from Topological Field Theory - Baez (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		In these solutions the cotetrad field e (and thus the metric) vanishes outside a neighborhood of \Sigma, while inside this neighborhood the connection A and the field E = ee satisfy the equations of 4-dimensional BF theory.
		Baez, Degenerate solutions of general relativity from topological field theory, to appear in Commun.
		4 Four-dimensional BF theory as a topological quantum field th..
	citeseer.ist.psu.edu /baez97degenerate.html (534 words)

	IngentaConnect Topological field theory and physics (Site not responding. Last check: 2007-10-21)
		Topological Yang - Mills theory with the Belavin - Polyakov - Schwarz - Tyupkin SU(2) instanton is solved completely, revealing an underlying multi-link intersection theory.
		The physical relevance of topological field theory and its invariants is discussed.
		By embedding topological Yang - Mills theory into pure Yang - Mills theory, it is shown that the topological version TQFT of a quantum field theory QFT allows us to formulate consistently the perturbative expansion of QFT in the topologically nontrivial sectors.
	api.ingentaconnect.com /content/iop/cqg/1997/00000014/00000001/art00005 (200 words)

	PlanetMath: topological vector space
		is a vector space over a topological field
		Cross-references: independent, open, subset, isomorphic, topology, finite dimensional, product topologies, continuous, operations, Hausdorff topology, topological field, vector space
		This is version 7 of topological vector space, born on 2002-02-03, modified 2005-02-09.
	planetmath.org /encyclopedia/TopologicalVectorSpace.html (76 words)

	Topological Field Theory, Primitive Forms and Related Topics (Site not responding. Last check: 2007-10-21)
		This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as a mathematical notion to define a "good period mapping" for a family of analytic structures.
		The invited papers in this volume are expository in nature by participants of the Taniguchi Symposium on "Topological Field Theory, Primitive Forms and Related Topics" and the RIMS Symposium bearing the same title, both held in Kyoto.
		The papers reflect the broad research of some of the world's leading mathematical physicists, and should serve as an excellent resource for researchers as well as graduate students of both disciplines.
	isbn.nu /0817639756 (435 words)

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