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Definition of Feynmann integral ?

  1. Apr 20, 2007 #1

    tpm

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    Definition of Feynmann integral ??

    Using the definition of integral as a limit of certain sums...couldn't we define an integral over paths [tex] x(t) [/tex] as the limit whenever 'epsilon' tends to 0 of the Sum:

    [tex] \sum _{i} F[x(t)] (L[x(t)+i \delta (t-t')]-L[x(t)+(i-1)\delta (t-t')]) [/tex]

    Where F is a functional and [tex] L[x(t)]=\int_{a}^{b}dtx(t) [/tex]

    Or something like that..in the sense that Riemann Path integrals are just the limit of a Riemann sum over an space of paths X(t)

    Or in terms of 'hyperreal' function so [tex] x(t)+i \epsilon \delta (t-t') [/tex]

    for i=1,2,3,4,5,6,7,8,9,....... and 'epsilon' is a infinitesimal quantity.
     
    Last edited: Apr 20, 2007
  2. jcsd
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