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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeAug 21st 2011

stub for instanton

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeAug 21st 2011

This seems not to distinguish instantons from multiinstanton solutions ?

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeAug 21st 2011

I mention instanton number. What should we say instead?

• CommentRowNumber4.
• CommentAuthorzskoda
• CommentTimeAug 22nd 2011
• (edited Aug 22nd 2011)

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.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeAug 23rd 2011

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”.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeAug 23rd 2011

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

• CommentRowNumber7.
• CommentAuthorzskoda
• CommentTimeAug 23rd 2011

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.

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeAug 23rd 2011

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.

• CommentRowNumber9.
• CommentAuthorzskoda
• CommentTimeAug 23rd 2011

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.

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeMay 12th 2014

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.