EXPLICIT FORMULATION OF A THIRD ORDER FINITE KNOT INVARIANT DERIVED FROM CHERN-SIMONS THEORY

1996 ◽  
Vol 05 (06) ◽  
pp. 805-847 ◽  
Author(s):  
ALLEN C. HIRSHFELD ◽  
UWE SASSENBERG
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Simons Theory ◽  
Third Order ◽  
Torus Knots ◽  
Explicit Formulation ◽  
Vassiliev Invariants ◽  
Knot Invariant ◽  
Chern Simons ◽  
Chern Simons Theory

An explicit formulation of a third order finite knot invariant is derived from the perturbative expression of the Wilson loop integral along a knotted line in Chern-Simons theory. This is achieved by an appropriate deformation of the knot line in three dimensional space. It is demonstrated that this formulation fulfils the axioms of the Vassiliev invariants. We use our formula in order to calculate the invariant for knots with up to nine crossings and for some torus knots.

A Combinatorial Link Invariant of Finite Type Derived from Chern-Simons Theory

1997 ◽  
Vol 06 (02) ◽  
pp. 243-280 ◽  
Author(s):  
Allen C. Hirshfeld ◽  
Uwe Sassenberg ◽  
Thomas Klöker
Keyword(s):  
Wilson Loop ◽  
Perturbation Expansion ◽  
Simons Theory ◽  
Link Invariant ◽  
Third Order ◽  
Expectation Value ◽  
Knot Invariant ◽  
Chern Simons ◽  
Combinatorial Expression ◽  
Chern Simons Theory

We derive from the perturbation expansion of the Wilson loop expectation value in the Chern-Simons theory an explicit combinatorial expression for a third-order finite link invariant, thereby generalising the knot invariant considered in a previous article.

scholarly journals DERIVATION OF THE TOTAL TWIST FROM CHERN-SIMONS THEORY

1996 ◽  
Vol 05 (04) ◽  
pp. 489-515 ◽  
Author(s):  
ALLEN C. HIRSHFELD ◽  
UWE SASSENBERG
Keyword(s):  
Three Dimensional ◽  
Simons Theory ◽  
Conway Polynomial ◽  
Knot Invariant ◽  
Euclidian Space ◽  
Original Definition ◽  
Definition Of ◽  
Knot Diagrams ◽  
Chern Simons ◽  
Chern Simons Theory

The total twist number, which represents on one hand the second coefficient of the Alexander-Conway polynomial and on the other hand the first non-trivial Vassiliev knot invariant, is derived from the second order expression of the Wilson loop expectation value in the Chern-Simons theory. Using the well-known fact that the analytical expression is an invariant, a combinatorial expression for the total twist based on the evaluation of knot diagrams is constructed by an appropriate deformation of the knot line in the three-dimensional Euclidian space. The relation to the original definition of the total twist is elucidated.

scholarly journals Chern–Simons theory, Vassiliev invariants, loop quantum gravity and functional integration without integration

2015 ◽  
Vol 30 (35) ◽  
pp. 1530067
Author(s):  
Louis H. Kauffman
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Measure Theory ◽  
Dimensional Space ◽  
Functional Integration ◽  
Three Dimensional ◽  
Functional Integral ◽  
Simons Theory ◽  
Vassiliev Invariants ◽  
Chern Simons

This paper is an exposition of the relationship between Witten’s Chern–Simons functional integral and the theory of Vassiliev invariants of knots and links in three-dimensional space. We conceptualize the functional integral in terms of equivalence classes of functionals of gauge fields and we do not use measure theory. This approach makes it possible to discuss the mathematics intrinsic to the functional integral rigorously and without functional integration. Applications to loop quantum gravity are discussed.

INDUCED PARITY VIOLATION ANOMALY FOR THE PROCA FIELD IN A THREE-DIMENSIONAL SPACE–TIME

1999 ◽  
Vol 14 (02) ◽  
pp. 271-280
Author(s):  
E. R. BEZERRA DE MELLO ◽  
V. M. MOSTEPANENKO
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Nonrelativistic Limit ◽  
Space Time ◽  
Simons Theory ◽  
Proca Field ◽  
Dimensional Space Time ◽  
Chern Simons ◽  
Three Dimensional Space ◽  
Chern Simons Theory

In this paper we develop diagrammatic computations of spontaneous parity-violating anomalies for a complex massive vector field (Proca field) induced by its interaction with an electromagnetic field in a three-dimensional space–time. We also calculate the effective potential energy between two charged particles in Maxwell–Chern–Simons theory in a nonrelativistic limit.

scholarly journals $$ T\overline{T} $$-deformation of q-Yang-Mills theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Leonardo Santilli ◽  
Richard J. Szabo ◽  
Miguel Tierz
Keyword(s):  
Phase Transition ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Line Bundles ◽  
Boltzmann Entropy ◽  
Third Order ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We derive the $$ T\overline{T} $$ T T ¯ -perturbed version of two-dimensional q-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the $$ T\overline{T} $$ T T ¯ -deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large N factorization into chiral and anti-chiral sectors. For the U(N) gauge theory on the sphere, we show that the large N phase transition persists, and that it is of third order and induced by instantons. The effect of the $$ T\overline{T} $$ T T ¯ -deformation is to decrease the critical value of the ’t Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs. The same results are shown to hold for (q, t)-deformed Yang-Mills theory. We also explicitly evaluate the entanglement entropy in the large N limit of Yang-Mills theory, showing that the $$ T\overline{T} $$ T T ¯ -deformation decreases the contribution of the Boltzmann entropy.

scholarly journals CONSISTENT INTERACTIONS IN A THREE-DIMENSIONAL THEORY WITH TENSOR GAUGE FIELDS OF DEGREES TWO AND THREE

2003 ◽  
Vol 18 (24) ◽  
pp. 4451-4468 ◽  
Author(s):  
SOLANGE-ODILE SALIU
Keyword(s):  
Three Dimensional ◽  
Simons Theory ◽  
Gauge Fields ◽  
Dimensional Theory ◽  
Gauge Symmetries ◽  
Lagrangian Action ◽  
Brst Cohomology ◽  
The Relationship ◽  
Chern Simons ◽  
Chern Simons Theory

All consistent interactions in a three-dimensional theory with tensor gauge fields of degrees two and three are obtained by means of the deformation of the solution to the master equation combined with cohomological techniques. The local BRST cohomology of this model allows the deformation of the Lagrangian action, accompanying gauge symmetries and gauge algebra. The relationship with the Chern–Simons theory is discussed.

A THREE-DIMENSIONAL COVARIANT APPROACH TO MONODROMY (SKEIN RELATIONS) IN CHERN-SIMONS THEORY

1990 ◽  
Vol 05 (32) ◽  
pp. 2747-2751 ◽  
Author(s):  
B. BRODA
Keyword(s):  
Integral Representation ◽  
Path Integral ◽  
Wilson Loop ◽  
Three Dimensional ◽  
Simons Theory ◽  
Monodromy Operator ◽  
Covariant Approach ◽  
Path Integral Representation ◽  
Chern Simons ◽  
Chern Simons Theory

A genuinely three-dimensional covariant approach to the monodromy operator (skein relations) in the context of Chern-Simons theory is proposed. A holomorphic path-integral representation for the holonomy operator (Wilson loop) and for the non-abelian Stokes theorem is used.

A three-dimensional gauge theory

1992 ◽  
Vol 70 (5) ◽  
pp. 301-304 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Gauge Theory ◽  
Scalar Field ◽  
Three Dimensional ◽  
Background Field ◽  
Field Method ◽  
Simons Theory ◽  
Point Function ◽  
Background Field Method ◽  
Chern Simons ◽  
Chern Simons Theory

We investigate a three-dimensional gauge theory modeled on Chern–Simons theory. The Lagrangian is most compactly written in terms of a two-index tensor that can be decomposed into fields with spins zero, one, and two. These all mix under the gauge transformation. The background-field method of quantization is used in conjunction with operator regularization to compute the real part of the two-point function for the scalar field.

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