scholarly journals Three-dimensional topological quantum field theory of Witten type

1998 ◽  
Author(s):  
Małgorzata Bakalarska ◽  
Bogusław Broda
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Three Dimensional ◽  
Topological Quantum Field Theory ◽  
Quantum Field ◽  
Topological Quantum

TOPOLOGICAL QUANTUM FIELD THEORY AND INVARIANTS OF SPATIAL GRAPHS

1992 ◽  
Vol 06 (11n12) ◽  
pp. 1825-1846
Author(s):  
KENNETH C. MILLETT
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Three Dimensional ◽  
Topological Quantum Field Theory ◽  
Dimensional Sphere ◽  
Quantum Field ◽  
Topological Quantum ◽  
Spatial Graphs ◽  
Jones Polynomials ◽  
Knots And Links

According to Sir Michael Atiyah [At], the study of topological quantum field theory is equivalent to the study of invariant quantities associated to three-dimensional manifolds. Although one has long considered the classical homology and cohomology structures and their extremely successful generalizations, the real subject of the Atiyah assertion is the new invariants proposed by Witten associated to the Jones polynomials of classical knots and links in the three-dimensional sphere. There have been many manifestations described by Reshetikhin & Turaev [Re1&2], Turaev & Viro [TV], Lickorish [Li 11– 15]. Kirby & Melvin [KM1&2], and Blanchet, Habegger, Mausbaum & Vogel [BHMV]. In these notes I describe some of the fundamental aspects of this theory, discuss the interest in these invariants and their extensions to the class of spatial graphs by Jonish & Millett [JonM], Kauffman & Vogel [KauV], Yamada [Ya2], Millett [Mi1&2], Kuperberg [Ku1&2], and Jaeger, Vertigan and Welsh [JaVW].

scholarly journals TQFT VERSUS RCFT: 3-D TOPOLOGICAL INVARIANTS

1995 ◽  
Vol 10 (04) ◽  
pp. 331-336
Author(s):  
BOGUSŁAW BRODA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Three Dimensional ◽  
Topological Quantum Field Theory ◽  
Topological Invariants ◽  
Quantum Field ◽  
Conformal Field ◽  
Topological Quantum

A straightforward relationship between the two approaches to three-dimensional topological invariants, one of them put forward by Witten in the framework of topological quantum field theory, and the second one proposed by Kohno in terms of rational conformal field theory, is established.

QFT and unification of knot theories

2014 ◽  
Vol 29 (24) ◽  
pp. 1430025
Author(s):  
Alexey Sleptsov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Knot Theory ◽  
Topological Quantum Field Theory ◽  
Quantum Field ◽  
Knot Invariants ◽  
Topological Quantum

We discuss relation between knot theory and topological quantum field theory. Also it is considered a theory of superpolynomial invariants of knots which generalizes all other known theories of knot invariants. We discuss a possible generalization of topological quantum field theory with the help of superpolynomial invariants.

TOWARDS A QUANTUM ALGORITHM FOR THE PERMANENT

2007 ◽  
Vol 05 (01n02) ◽  
pp. 223-228 ◽  
Author(s):  
ANNALISA MARZUOLI ◽  
MARIO RASETTI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Computation ◽  
Quantum Computer ◽  
Quantum Algorithm ◽  
Topological Quantum Field Theory ◽  
Quantum Field ◽  
Topological Quantum

We resort to considerations based on topological quantum field theory to outline the development of a possible quantum algorithm for the evaluation of the permanent of a 0 - 1 matrix. Such an algorithm might represent a breakthrough for quantum computation, since computing the permanent is considered a "universal problem", namely, one among the hardest problems that a quantum computer can efficiently handle.

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