- #1

André H Gomes

- 3

- 0

## Homework Statement

We have the evaluation of the integral associated with the electron self-energy diagram and I am following Brian Hatfield's book "Quantum Field Theory of point particles and strings", and I am having problems with the integration limits after changing variables from [itex]z_2[/itex] to [itex]1-z_2[/itex], at p.388.

## Homework Equations

[itex]\int_0^\infty \frac{d\beta}{\beta} \int_0^\infty dz_2 \left[2m_o - (1-z_2)\gamma^\mu p_\mu)\right] e^{-\beta[(1-z_2)z_2 p^2 - m^2_o z_2 - \lambda^2(1-z_2)]}[/itex]

Since it may be relevant, some additional information: before this integral, we had an integration over [itex]z_1[/itex], which involved a Dirac delta function, [itex]\delta(1-z_1-z_2)[/itex].

## The Attempt at a Solution

I expected the change of variables to be as straightfoward as it seemed to be, resulting in:

[itex]\int_0^\infty \frac{d\beta}{\beta} \int_{-\infty}^1 dz \left(2m_o - z\gamma^\mu p_\mu)\right) e^{-\beta[z(1-z) p^2 - m^2_o(1-z) - \lambda^2z]}[/itex]

But, in Hatfield's book, the lower limit of the integral in [itex]z[/itex] becomes [itex]0[/itex] instead of [itex]-\infty[/itex]. I wonder if the integration from [itex]-\infty[/itex] to [itex]0[/itex] may vanish somehow, but I just can't figure it.

In advance, thank you all for the help!

(English is not my native language. I apologize any mistake.)