Knots
and Physics| Knots
and Physics |
In General > s.a. 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
link invariant used in dynamo theories of astronomical magnetic fields, and
plasma theory.
@ General references: Amann et al ed-88; Baez & Muniain 94; Atiyah RMP(95);
Hirshfeld AJP(98)
[rev]; Labastida ht/02-in.
@ Energy spectrum: Moffatt Nat(90)sep;
Ricca PRS(08) [energy bounds from topology].
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; Turaev 94; Kauffman 01;
van Baal & Wipf PLB(01)
[pure gauge SU(2) configurations]; Faddeev a0805-in [as Yang-Mills excitations].
@ 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-in,
ht/00-in
[rev]; Hu 01.
@ And strings: Ooguri & Vafa NPB(00)ht/99.
@ And quantum groups: Sawin qa/95.
In Classical and Quantum Gravity > s.a. loop
formulation of general relativity; connection and loop
representation
of quantum gravity.
@ And 3-geometry: Hemion 93; Toh & Anderson JMP(95)gq/94.
Knots in Other Fields
@ Overviews: Stasiak et al 99.
Main page – Abbreviations – Journals – Comments – Other
sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified
16 jun 2008