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].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 1 mar 2020