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Feynman Parameters

  1. Mar 1, 2006 #1
    Hey, this is a pretty simple induction problem, but I suck at induction and I think I'm missing something really obvious here, though trying to figure it out whilst having a pretty bad cold isn't much of a good idea.

    The identity

    [tex]\frac{1}{A_1\cdots A_n}=\int_0^1 dx_1\cdots dx_n \delta (\sum_i^nx_i-1) \frac{(n-1)!}{[A_1x_1+\cdots +A_nx_n]^n}[/tex]

    Can be proven inductively, given that we know it works for n=2, by the use of

    [tex]\frac{1}{AB^n}=\int^1_0 dxdy \delta (x+y-1)\frac{ny^{n-1}}{[Ax+By]^{n+1}}[/tex]

    I get to a certain point then just can't see what to do. Gargh...
    Last edited: Mar 2, 2006
  2. jcsd
  3. Mar 1, 2006 #2
    Well, whatever it is, I can't really see the more relevant parts of your post... The identity and the hint.
    Maybe you should edit and add it at the end untill Tex decides to work again.
  4. Mar 2, 2006 #3


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    Put [tex]y = A_1A_2...A_{n-1}[/tex], it falls right out.

  5. Mar 20, 2007 #4
    You can find the identity:
  6. Jun 2, 2011 #5
    http://www.physics.thetangentbundle.net/wiki/Quantum_field_theory/Schwinger-Feynman_parameters [Broken]
    Last edited by a moderator: May 5, 2017
  7. Jun 2, 2011 #6
    Or better :

    http://theoretical-physics.net/dev/src/math/feynman-parameters.html [Broken]

    Then they explain more precisely what happens to the limits of the integrals.
    Last edited by a moderator: May 5, 2017
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