Not signed in (Sign In)

Start a new discussion

Not signed in

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

  • Sign in using OpenID

Site Tag Cloud

2-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science connection constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality education elliptic-cohomology enriched fibration foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck 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 infinity integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monad monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar 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-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • 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>1n\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.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)