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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 26th 2009
   • PermaLink
   Author: Urs
   Format: MarkdownMike 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.

   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.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 16th 2010
   • PermaLink
   Author: Urs
   Format: Markdownadded more references to [[path integral]]. Also added an Idea-section much more needs to be added here, eventually.

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

   much more needs to be added here, eventually.

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeMar 16th 2010
   • PermaLink
   Author: zskoda
   Format: MarkdownIn 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.

   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.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 11th 2013
   • (edited Jul 11th 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI 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](http://ncatlab.org/nlab/show/path+integral#AsAnIntegralAgainstTheWienerMeasure)_ 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.

   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.

5. • CommentRowNumber5.
   • CommentAuthorzskoda
   • CommentTimeJul 11th 2013
   • (edited Jul 11th 2013)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexWiener 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...

   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…

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJul 11th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexRight, I have added a "Eudlidean"-qualifier for the moment.

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

7. • CommentRowNumber7.
   • CommentAuthorzskoda
   • CommentTimeJul 12th 2013
   • PermaLink
   Author: zskoda
   Format: MarkdownItexAdded reference * Theo Johnson-Freyd, _The formal path integral and quantum mechanics_, J. Math. Phys. __51__, 122103 (2010) [arxiv/1004.4305](http://arxiv.org/abs/1004.4305), [doi](http://dx.doi.org/10.1063/1.3503472); _On the coordinate (in)dependence of the formal path integral_, [arxiv/1003.5730](http://arxiv.org/abs/1003.5730)

   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
8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeJul 13th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a [remark](http://ncatlab.org/nlab/show/path+integral#WorldlineFormalism) stating that the expression "holonomy integrated against the Wiener measure" is precisely what appears in the [[worldline formalism]] for computing QFT scattering amplitudes.

   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.