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-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex-geometry computable-mathematics computer-science connection constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry goodwillie-calculus 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 history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology nonassociative 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 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
    • CommentTimeMay 31st 2011

    I badly need to polish the nnLab entries related to path integrals. Today a student asked me how the pull-push operation in string topology is a remnant of a quantum path integral. So a started writing now

    So far there is the description of the archetypical path integral for the quantum particle propagating on the line in terms of pull-tensor-push.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeMay 31st 2011

    This is very interesting. The most rich geometric theory of quantization is so far developed for finite-dimensional mechanics. The central role are the cohomological classes related to Lagrangian geometry – most notably the Maslov class. Cohomology is higher categorical subject, so can your approach predict the appearance of the Maslov class ? That would be so interesting.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 31st 2011

    I haven’t thought much about the Maslov index for a long while. Maybe I should.

    One question: in the entry you have a sentence

    Lagrangean submanifold describes the phase of short-wave oscillations.

    I am not sure what this means.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeMay 31st 2011
    • (edited May 31st 2011)

    I must have taken this phrase from somewhere. Well, it is roughly like the role of the real submanifold in the Fourier transform. My memory is that here one takes in the sense of the eikonal approximation, which is the splitting into short wave and long wave part and assigning the coordinates to each part. I should write some time an entry on eikonal. I think this is very important for us, as in the cases in which one has topological QFT, the quasiclassical approximations are exact (by localization), hence one is likely to see the connection best by looking at eikonal-like approaches.

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)