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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