Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 21st 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexstub for [[instanton]]

   stub for instanton

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeAug 21st 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexThis seems not to distinguish instantons from multiinstanton solutions ?

   This seems not to distinguish instantons from multiinstanton solutions ?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeAug 21st 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI mention instanton number. What should we say instead?

   I mention instanton number. What should we say instead?

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeAug 22nd 2011
   • (edited Aug 22nd 2011)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexInstanton is a solution with instanton number one. Multiinstanton is a similar solution with instanton number finite $n\gt 1$. Instanton is an analogue of a soliton "solitary wave". If you nonlineary superimpose 2 you do not get an instanton but a 2-instanton solution roughly, though not linearly, composed out of 2 instantons. You do not want to call it instanton any more, though instanton solution is OK, if instanton serves as a modifier, meaning that multiinstantons are higher instanton-type solutions.

   Instanton is a solution with instanton number one. Multiinstanton is a similar solution with instanton number finite $n\gt 1$. Instanton is an analogue of a soliton “solitary wave”. If you nonlineary superimpose 2 you do not get an instanton but a 2-instanton solution roughly, though not linearly, composed out of 2 instantons. You do not want to call it instanton any more, though instanton solution is OK, if instanton serves as a modifier, meaning that multiinstantons are higher instanton-type solutions.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeAug 23rd 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexThat's not my impression of the common use of the term. As far as I am aware the common use is to say that "an instanton" is a self-dual connection. This may have any instanton number. But your point is maybe about notions of instanton's in theories other than Yang-Mills theory? I'll rename the entry into "Yang-Mills instanton".

   That’s not my impression of the common use of the term.

   As far as I am aware the common use is to say that “an instanton” is a self-dual connection. This may have any instanton number.

   But your point is maybe about notions of instanton’s in theories other than Yang-Mills theory? I’ll rename the entry into “Yang-Mills instanton”.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeAug 23rd 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexOkay, I have written a more general Idea-section at [[instanton]] and split off [[Yang-Mills instanton]].

   Okay, I have written a more general Idea-section at instanton and split off Yang-Mills instanton.

7. • CommentRowNumber7.
   • CommentAuthorzskoda
   • CommentTimeAug 23rd 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexIt is the original distinction from soliton theory, when the instantons are discovered, including I think e.g. the original ADHM paper (should be checked), and it applies both to Yang-Mills and in general. You are probably right, nowdays, the distinction is less often taken care of. Wikipedia gives 484 thousand hits for instanton and 14 thousand for the multiinstanton and 982 thousand for multi-instanton. A bit odd.

   It is the original distinction from soliton theory, when the instantons are discovered, including I think e.g. the original ADHM paper (should be checked), and it applies both to Yang-Mills and in general. You are probably right, nowdays, the distinction is less often taken care of. Wikipedia gives 484 thousand hits for instanton and 14 thousand for the multiinstanton and 982 thousand for multi-instanton. A bit odd.

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeAug 23rd 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexIf you feel like it, give a discussion of the terminology issue in the entry [[instanton]]. I think one should also keep in mind that in Yang-Mills theory the term is being used in a way rather detached from what may have been its original meaning.

   If you feel like it, give a discussion of the terminology issue in the entry instanton.

   I think one should also keep in mind that in Yang-Mills theory the term is being used in a way rather detached from what may have been its original meaning.

9. • CommentRowNumber9.
   • CommentAuthorzskoda
   • CommentTimeAug 23rd 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexSorry, I can not afford distract myself in yet another topic. I have only few hours left for math for the entire rest of the week, the rest being already occupied with other things.

   Sorry, I can not afford distract myself in yet another topic. I have only few hours left for math for the entire rest of the week, the rest being already occupied with other things.

10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeMay 12th 2014
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded some pointers to instantons in string theory (i.e. branes wrapped on spacelike cycles) to the Idea-section and the References-section of _[[instanton]]_.

    added some pointers to instantons in string theory (i.e. branes wrapped on spacelike cycles) to the Idea-section and the References-section of instanton.