Knots and Physics |

**In General**
> s.a. Braids; chaos; knot
theory [including quantum-gravity-motivated generalizations] and knot invariants;
Links.

* __Problem__:
Express knot/link invariants in terms of physical observables.

* __In classical mechanics__:
Some trajectories of dynamical systems are closed, and can be knotted.

* __In astronomy__: Helicity invariant
used in dynamo theories of astronomical magnetic fields, and plasma theory.

@ __Reviews, books__: Amann et al ed-88;
Baez & Muniain 94;
Atiyah RMP(95);
Hirshfeld AJP(98)dec [rev];
Labastida ht/02-proc;
Cho et al IJMPA-a1803 [rev].

@ __General references__: Kauffman & Lomonaco SPIE-a1105 [quantizing knots, or more generally algebraic, combinatorial and topological structures];
Anokhina & Morozov a1802 [evolution in the space of knots].

@ __Energy spectrum__: Moffatt Nat(90)sep;
Ricca PRS(08) [energy bounds from topology];
> s.a. energy [Menger curvature].

**In Field Theory / Particle Physics** > s.a. solitons;
topological field theory.

* __In classical field theory__:
Field theories can have knotted solutions that behave like solitons.

* __In Chern-Simons theory__:
Knots are represented by operators on the Hilbert space of states; Allows
to calculate invariants.

@ __In field theory__:
Wadati et al PRP(89);
Atiyah 90; Kauffman 12;
van Baal & Wipf PLB(01) [pure gauge SU(2) configurations];
Faddeev a0805-conf [as Yang-Mills excitations];
Turaev 10;
Alves et al IJMPA(17)-a1707 [in electromagnetism and fluid dynamics];
> s.a. Feynman Diagrams.

@ __In statistical mechanics__:
Deguchi et al JPSJ(88);
Yang & Ge 89; Jones SA(90)nov;
Wu RMP(92).

@ __And path integrals__: Kauffman JMP(95).

@ __And solitons / particles__:
Wadati & Akutsu PTPS(88);
Faddeev & Niemi Nat(97)ht/96;
Battye & Sutcliffe PRL(98)ht,
PRS(99)ht/98;
Finkelstein IJMPA(07)-a0705 [and electroweak theory].

@ __And Chern-Simons theory__: Guadagnini 93;
Brügmann IJTP(95);
Gambini & Pullin CMP(97)ht/96 [skein relations, and quantum gravity];
Labastida ht/00-conf,
ht/00-proc [rev];
Hu 01.

@ __Other theories__: Ooguri & Vafa NPB(00)ht/99 [and strings];
Kauffman & Lomonaco a1904
[knotted zeros in the quantum states of hydrogen].

@ __And quantum groups__: Sawin qa/95.

> __Specific theories__: see electromagnetism;
gravitational-wave solutions; gravitomagnetism; spacetime dimension
[knotted flux tube networks].

**In Classical and Quantum Gravity**
> s.a. loop formulation of general relativity; lqg
in the connection representation and loop representation.

@ __And 3-geometry__: Hemion 93;
Toh & Anderson JMP(95)gq/94.

**Phenomenology and Knots in Other Fields**

@ __General references__:
Stasiak et al 98 [ideal knots].

@ __Molecular knots__: news sci(18)aug [classification, and knots that have been realized].

@ __Fluid knots__: news ns(13)mar [created in the lab];
video yt(14)sep [vortex knots in the lab];
news giz(16)jan [quantum knots in a superfluid].

@ __Related topics__: Gaudreau & Ledvinka a1901 [and quantum computing];
Vandans et al PRE(20) [classifying knots with neural networks].

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send feedback and suggestions to bombelli at olemiss.edu – modified 1 mar 2020