Feynman Parameters

1. Mar 1, 2006

Perturbation

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

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

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

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

I get to a certain point then just can't see what to do. Gargh...

Last edited: Mar 2, 2006
2. Mar 1, 2006

Palindrom

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.

3. Mar 2, 2006

CarlB

Put $$y = A_1A_2...A_{n-1}$$, it falls right out.

Carl

4. Mar 20, 2007

athlonmp

You can find the identity:
$$\frac{1}{A\*B^n}=...$$
useful

5. Jun 2, 2011

zounnouf

http://www.physics.thetangentbundle.net/wiki/Quantum_field_theory/Schwinger-Feynman_parameters [Broken]

Last edited by a moderator: May 5, 2017
6. Jun 2, 2011

zounnouf

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