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Topological Quantum Field Theories
"... Abstract. Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of topological quantum field theories were constructed in my pa ..."
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Cited by 9 (1 self)
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Abstract. Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of topological quantum field theories were constructed in my
Topological Quantum Field Theory and
 Invariants of Graphs for Quantum Groups’, SFB 288preprint No
, 1993
"... Abstract: Starting from the quantum group Uq(sl(2, C)), we construct operator invariants of 3cobordisms with spin structure, satisfying the requirements of a topological quantum field theory and refining the Reshetikhin–Turaev and Turaev–Viro models. We establish the relationship between these two ..."
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Cited by 3 (0 self)
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Abstract: Starting from the quantum group Uq(sl(2, C)), we construct operator invariants of 3cobordisms with spin structure, satisfying the requirements of a topological quantum field theory and refining the Reshetikhin–Turaev and Turaev–Viro models. We establish the relationship between these two
Topological Quantum Field Theory and
, 1995
"... A topological quantum field theory is introduced which reproduces the SeibergWitten invariants of fourmanifolds. Dimensional reduction of this topological field theory leads to a new one in three dimensions. Its partition function yields a threemanifold invariant, which can be regarded as the Sei ..."
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A topological quantum field theory is introduced which reproduces the SeibergWitten invariants of fourmanifolds. Dimensional reduction of this topological field theory leads to a new one in three dimensions. Its partition function yields a threemanifold invariant, which can be regarded
Topological Quantum Field Theory
, 2000
"... I review some recent results on fourmanifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit results for the Donaldson invariants of nonsimply connected man ..."
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I review some recent results on fourmanifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit results for the Donaldson invariants of nonsimply connected
Lectures on topological quantum field theory
 Proceedings of the Meeting on Integrable Systems, Quantum Groups and Quantum Field Theory
, 1992
"... What follows are lecture notes about Topological Quantum Field Theory. While the lectures were aimed at physicists, the content is highly mathematical in its style and motivation. The subject of Topological Quantum Field Theory is young and developing rapidly in many directions. These lectures are n ..."
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Cited by 4 (0 self)
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What follows are lecture notes about Topological Quantum Field Theory. While the lectures were aimed at physicists, the content is highly mathematical in its style and motivation. The subject of Topological Quantum Field Theory is young and developing rapidly in many directions. These lectures
Gravitational Topological Quantum Field Theory
, 2003
"... Abstract: In a previous work, it was shown that the 8dimensional topological quantum field theory for a metric and a Kalb–Ramond 2form gauge field determines N = 1 D = 8 supergravity. It is shown here that, the combination of this TQFT with that of a 3form determines N = 2 D = 8 supergravity, tha ..."
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Abstract: In a previous work, it was shown that the 8dimensional topological quantum field theory for a metric and a Kalb–Ramond 2form gauge field determines N = 1 D = 8 supergravity. It is shown here that, the combination of this TQFT with that of a 3form determines N = 2 D = 8 supergravity
Quantum Gravity as topological quantum field theory.
, 1995
"... The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which spacetime is three dimensional. ..."
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Cited by 16 (3 self)
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The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which spacetime is three dimensional.
Morse Theory Interpretation of Topological Quantum Field Theories
 CERN preprint # CERNTH5240/88
, 1988
"... Topological quantum field theories are interpreted as a generalized form of Morse theory. This interpretation is applied to formulate the simplest topological quantum field theory: topological quantum mechanics. The only nontrivial topological invariant corresponding to this theory is computed and ..."
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Cited by 4 (0 self)
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Topological quantum field theories are interpreted as a generalized form of Morse theory. This interpretation is applied to formulate the simplest topological quantum field theory: topological quantum mechanics. The only nontrivial topological invariant corresponding to this theory is computed
On algebraic structures implicit in topological quantum field theories
 J. Knot Theory Ramifications
, 1999
"... In the course of the development of our understanding of topological quantum field theory (TQFT) [1,2], it has emerged that the structures of generators and relations for the construction of low dimensional TQFTs by various combinatorial methods are equivalent to the structures of various fundamenta ..."
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Cited by 52 (2 self)
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In the course of the development of our understanding of topological quantum field theory (TQFT) [1,2], it has emerged that the structures of generators and relations for the construction of low dimensional TQFTs by various combinatorial methods are equivalent to the structures of various
The Classification of Topological Quantum Field Theories in Two Dimensions
, 2014
"... The goal of this thesis is to introduce some of the major ideas behind extended topological quantum field theories with an emphasis on explicit examples and calculations. The statement of the Cobordism Hypothesis is explained and immediately used to classify framed and oriented extended 2 dimensiona ..."
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The goal of this thesis is to introduce some of the major ideas behind extended topological quantum field theories with an emphasis on explicit examples and calculations. The statement of the Cobordism Hypothesis is explained and immediately used to classify framed and oriented extended 2
Results 1  10
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