scholarly journals Topological quantum field theory of three-dimensional bosonic Abelian-symmetry-protected topological phases

2016 ◽  
Vol 93 (20) ◽  
Author(s):  
Peng Ye ◽  
Zheng-Cheng Gu
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Three Dimensional ◽  
Topological Quantum Field Theory ◽  
Topological Phases ◽  
Quantum Field ◽  
Topological Quantum ◽  
Symmetry Protected

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.

Sign in / Sign up

Export Citation Format

Share Document