COMBINATORIC MASSEY–MILNOR LINKING THEORY

2011 ◽  
Vol 20 (06) ◽  
pp. 927-938 ◽  
Author(s):  
CHUN-CHUNG HSIEH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Configuration Space ◽  
Invariant Theory ◽  
Knot Theory ◽  
Quantum Field ◽  
Perturbative Quantum ◽  
Knot Diagrams ◽  
Chern Simons ◽  
Milnor Invariant

In this paper following the scheme of Massey–Milnor invariant theory [C. C. Hsieh, Combinatoric and diagrammatic studies in knot theory J. Knot Theory Ramifications16 (2007) 1235–1253; C. C. Hsieh, Massey-Milnor linking = Chern-Simons-Witten graphs, J. Knot Theory Ramifications17 (2008) 877–903; C. C. Hsieh and S. W. Yang, Chern-Simons-Witten configuration space integrals in knot theory, J. Knot Theory Ramifications14 (2005) 689–711], we studied the first non-vanishing linkings of knot theory in ℝ3 and also derived the combinatorial formulae from which we could read out the invariants directly from the knot diagrams. Though the theme is calculus, the idea comes from perturbative quantum field theory.

CHERN–SIMONS–WITTEN CONFIGURATION SPACE INTEGRALS IN KNOT THEORY

2005 ◽  
Vol 14 (06) ◽  
pp. 689-711 ◽  
Author(s):  
CHUN-CHUNG HSIEH ◽  
SU-WIN YANG
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Configuration Space ◽  
Knot Theory ◽  
Quantum Field ◽  
Perturbative Quantum ◽  
Perturbative Quantum Field Theory ◽  
Chern Simons ◽  
Configuration Space Integrals

In the context of perturbative quantum field theory, we express the first non-vanishing Massey–Milnor linkings in terms of Chern–Simons–Witten configuration space integrals in knot theory.

MASSEY–MILNOR LINKING = CHERN–SIMONS–WITTEN GRAPHS

2008 ◽  
Vol 17 (07) ◽  
pp. 877-903 ◽  
Author(s):  
CHUN-CHUNG HSIEH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Configuration Space ◽  
Quantum Field ◽  
Perturbative Quantum ◽  
Perturbative Quantum Field Theory ◽  
Chern Simons ◽  
Configuration Space Integrals

We express the first non-vanishing Massey–Milnor linkings in terms of Chern–Simons–Witten configuration space integrals in perturbative quantum field theory.

FIRST NON-VANISHING SELF-LINKING OF KNOTS (I) COMBINATORIC AND DIAGRAMMATIC STUDY

2011 ◽  
Vol 20 (12) ◽  
pp. 1637-1648 ◽  
Author(s):  
CHUN-CHUNG HSIEH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Knot Theory ◽  
Feynman Diagrams ◽  
Quantum Field ◽  
Borromean Rings ◽  
Diagrammatic Representation ◽  
Perturbative Quantum ◽  
Perturbative Quantum Field Theory ◽  
Chern Simons

In this paper, following the scheme of [Borromean rings and linkings, J. Geom. Phys.60 (2010) 823–831; Combinatoric and diagrammatic study in knot theory, J. Knot Theory Ramifications16 (2007) 1235–1253; Massey–Milnor linking = Chern–Simons–Witten graphs, J. Knot Theory Ramifications17 (2008) 877–903], we study the first non-vanishing self-linkings of knots, aiming at the study of combinatorial formulae and diagrammatic representation. The upshot of perturbative quantum field theory is to compute the Feynman diagrams explicitly, though it is impossible in general. Along this line in this paper we could not only compute some Feynman diagrams, but also give the explicit and combinatorial formulae.

LINKING IN KNOT THEORY

2006 ◽  
Vol 15 (08) ◽  
pp. 957-962 ◽  
Author(s):  
CHUN-CHUNG HSIEH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Knot Theory ◽  
Quantum Field ◽  
Perturbative Quantum ◽  
Perturbative Quantum Field Theory ◽  
Chern Simons

In this talk, we will give an explicit/combinatorial formulae for Massey–Milnor first non-vanishing linking, and also express this linking in terms of Chern–Simons–Witten perturbative quantum field theory.

COMBINATORIC AND DIAGRAMMATIC STUDY IN KNOT THEORY

2007 ◽  
Vol 16 (09) ◽  
pp. 1235-1253 ◽  
Author(s):  
CHUN-CHUNG HSIEH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Knot Theory ◽  
Quantum Field ◽  
Perturbative Quantum ◽  
Perturbative Quantum Field Theory

Motivated by Massey–Milnor linking and Chern–Simon–Witten perturbative quantum field theory, we developed some combinatorial and diagrammatic study in this paper, aiming at knot theory in the combinatoric aspect.

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.

scholarly journals The relation between quantum and classical field theory with a classical source

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200656
Author(s):  
S. A. Fulling ◽  
A. G. S. Landulfo ◽  
G. E. A. Matsas
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Classical Field Theory ◽  
Classical Field ◽  
Quantum Field ◽  
Schwarzschild Solution ◽  
Classical Source ◽  
Time Quantum ◽  
Perturbative Quantum ◽  
Classical Picture

Classical field theory is about fields and how they behave in space–time. Quantum field theory, in practice, usually seems to be about particles and how they scatter. Nevertheless, classical fields must emerge from quantum field theory in appropriate limits, and Michael Duff showed how this happens for the Schwarzschild solution in perturbative quantum gravity. In a series of papers, we and others have shown how classical radiation from an accelerated charge emerges from quantum field theory when the Unruh thermal effect is taken into account. Here, we sharpen those conclusions by showing that, even at finite times, the quantum picture is meaningful and is in close agreement with the classical picture.

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