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 categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor galois-theory gauge-theory gebra geometric 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 string string-theory 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
    • CommentTimeOct 26th 2009

    Mike Stay kindly added the standard QM story to path integral.

    I changed the section titles a bit and added the reference to the Baer-Pfaeffle article on the QM path integral. Probably the best reference there is on this matter.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMar 16th 2010

    added more references to path integral. Also added an Idea-section

    much more needs to be added here, eventually.

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeMar 16th 2010

    In general one needs to have integration on paths in phase space, only for special Lagrangeans it reduces to integration only over paths in configuration space. Momenta integration can not be in general skipped over.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJul 11th 2013
    • (edited Jul 11th 2013)

    I have added to path integral a bunch of on the formalization in quantum mechanics by Wiener integration over stochastic processes.

    Then I started a new subsection Realization – As an integral against the Wiener measure with a (very) brief indication of that…

    …ending in an observation on what the passage from gauge coupling action functionals to the quantum propagator integral kernel looks like when viewed in higher geometric prequantum theory as an operation on correspondences in the slice (infinity,1)-topos over the moduli of circle bundles and of vector bundles, respectively.

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeJul 11th 2013
    • (edited Jul 11th 2013)

    Wiener integral needs to be analytically continued to become a QM path integral, Wiener measure certainly does not exist after the Wick rotation…I do not detect this basic idea in the entry…

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 11th 2013

    Right, I have added a “Eudlidean”-qualifier for the moment.

    • CommentRowNumber7.
    • CommentAuthorzskoda
    • CommentTimeJul 12th 2013

    Added reference

    • Theo Johnson-Freyd, The formal path integral and quantum mechanics, J. Math. Phys. 51, 122103 (2010) arxiv/1004.4305, doi; On the coordinate (in)dependence of the formal path integral, arxiv/1003.5730
    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJul 13th 2013

    added a remark stating that the expression “holonomy integrated against the Wiener measure” is precisely what appears in the worldline formalism for computing QFT scattering amplitudes.

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)