# How do I calculate a Feynman diagram with one loop?

I'm following Peskin & Schroeder and I'm trying to calculate the momentum space representation for the following diagram, Q4 in this link. Paper

The loop is what's causing me problems. I'm not sure how to write loops in scattering amplitudes.

In general how to electron loops fit into the amplitude?

For the specific question I think the answer would be something like

$$\bar{u}(k')v(k'_+)(-ie\gamma^\mu)(-ie\gamma^\nu)(-1)\int\frac{d^4l}{(2\pi)^4}tr\left[electron-propagator\right]\bar{v}(k_+)u(k)$$

I've left out the photon propagator but the part inside the trace is what I'm unsure of.

• Loops are not treated differently from any other internal lines. What is your confusion? – ACuriousMind Feb 8 '15 at 13:43
• I've updated my question @ACuriousMind – Okazaki Feb 8 '15 at 14:39

Second, you need two photon propagators; one for each line in the diagram. One will couple to your $\gamma^\mu$ and to a new vertex with some $\gamma^\rho$ on the loop, and the other will couple to your $\gamma^\nu$ and to a new vertex with some $\gamma^\sigma$ on the loop.
As for the loop itself, it's just the product of the propagators (placed in the appropriate order with the gamma matrices): $$\frac{i(l \cdot \gamma + m)}{l^2-m^2+i\varepsilon} (-i e\gamma^\rho) \frac{i((l-q)\cdot \gamma + m)}{(l-q)^2 - m^2 + i \varepsilon} (-i e \gamma^\sigma)$$ wherein $q$ is the momentum transferred through the loop, as in the problem prompt.