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But integration over a sheme or path (i think) is a deduction from homotopy theory and algebic topology?
??? Integration derives from measure theory. There is a link to homotopy, but I don't think homotopy is prior.Feynman said:But integration over a sheme or path (i think) is a deduction from homotopy theory and algebic topology?
Just a moment... There is an "inner product" defined on these spaces, aren't there? This inner product determines amplitudes, right? So would this inner product define a metric for this space? What is this space called, Hilbert space, Fock space, ...? ThanksMike2 said:As I recall, [tex]\phi (x,t)[/tex] is the wave function of 1st quantization. And I believe [tex]\Psi (x,t)[/tex] is called the "field" of second quantization. Are there any other names for [tex]\Psi (x,t)[/tex], for example, amplitude of something, field of something? Thanks.
The integration over [tex]D \hat \phi [/tex] is over all of "functional space", over all possible changes in the function [tex]\phi (x,t)[/tex] that gets you from the starting [tex]\phi_i (x,t)[/tex] to the ending [tex]\phi_f (x,t)[/tex]. It would appear that there is no geometry involved with this space, right? I mean, there would have to be a metric associated with this functional space in order to have geometry, right?
Citation please? Link if possible?Feynman said:But Mr selfAdjoint I have an article wich talk about the importance of the homotopy to construct the Feynman path integral
If the article is online, go to it, copy the URL (in the address box at the top of your screen), then come here and paste the url into the reply window. PF doesn't even need all the link apparatus, it automatically puts url tags before and after every url it recognizes.Feynman said:ok dextercioby , but i don't know how i send this article.
What article? Did you have a link?Feynman said:Who can i browse this article ?
The paper discusses the path-integral in so-called "multiple connected"Feynman said:Finnally this is the adrres of the article:
http://lpt1.u-strasbg.fr/kenoufi/MEMOIRES/magistere.pdf
Here's a little one-page summary of the FPI that I wrote after studying the Feynman and Hibbs text for a while. Go to the files section of my yahoo group and download the file: FPI.pdf.Feynman said:Hi
What is the physical interpretation of Feynman path integral?
Thanks
Feynman said:For Hans de Vries , so wath is the physical difference between the multiple connected and single connected and where the path integral entered in this case?:grumpy:
Grumpy?Feynman said::grumpy:.....
Feynman said:mr Hans de Vries, i have looked the memory of Dr Knoufi on path integrals,
But in this memory , it is a mathematical study for path integrals,
I still search a physical interpretation