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• 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.

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