Stable knot-like structures in classical field theory

Classical Knot Theory

This paper is a very brief introduction to knot theory. It describes knot coloring by quandles, the fundamental group of a knot complement, and handle-decompositions of knot complements.

Computation of hyperbolic structures in knot theory THIN POSITION IN THE THEORY OF CLASSICAL KNOTS

This is a preliminary version of a chapter that is intended to appear in the “Handbook of Knot Theory”, edited by William W. Menasco and Morwen B. Thistlethwaite. Comments are welcome. For our purposes, “knot theory” will have the narrowest interpretation: the study of isotopy classes of locally flat embeddings of the circle S in S. The distinctions between smooth, PL, and locally flat topologi...

A functional relation in stable knot theory

Knot Invariants from Classical Field Theories

We consider the Non-Abelian Chern-Simons term coupled to external particles, in a gauge and diffeomorphism invariant form. The classical equations of motion are perturbativelly studied, and the on-shell action is shown to produce knot-invariants associated with the sources. The first contributions are explicitely calculated, and the corresponding knot-invariants are recognized. We conclude that...

Classical Field Theory

a) Energy-momentum Based on Noether’s theorem, construct the energy-momentum tensor for classical electromagnetism from the above Lagrangian. Note that the usual procedure does not result in a symmetric tensor. To remedy that, we can add to T μν a term of the form ∂λK λμν , where K is antisymmetric in its first two indices. Such an object is automatically divergenceless, so T̂ μν = T μν + ∂λK λμ...