Rules to compute Feynman Diagram with the Feynman rules

[varphi42]

Hello,

I am trying to compute feynman diagrams with the feynman rules but I encounter some difficulties... Since the gamma matrices, spinnors, etc do not comute, the ordering of the different factor from feynman diagram has an importance. Is there some rules that say where to begin and in which order do we have to compute them?

I know for instance that we have to follow the particle flow but in the case of e+ e- scattering, do I begin with the e+ or the e-, etc ?

Thanks in advance

 

[andrien]

Draw a diagram and read from right to left.time increases also in going from down to up.you should care to make amplitude lorentz invariant.it should be in order of increasing time.

I know for instance that we have to follow the particle flow but in the case of e+ e- scattering, do I begin with the e+ or the e-, etc ?

it does not matter.

 

[Hepth]

My first step:
Label all internal lines with momenta.
Fermions : Label internal momenta in the DIRECTION OF THE ARROW, then use a regular
$$\frac{i (\not p + m)}{p^2-m^2}$$
propagator. Never think about internal fermions as antifermions/etc.
Bosons : I don't think it matters internally, so just choose whatever you want, I choose them so loops are directional. REALLY the delta functions at each vertex should take care of it.

Then I start at (for simple diagrams) the outgoing particles. (So start with things that are barred).

So for e+(p1) e-(p2) > gamma > e+(k1) e-(k2)


$$[\bar{u}_{k_2} (- i e Q_{\ell} \gamma_{\mu}) v_{k_1}] \times \left(-i \frac{g^{\mu \nu}}{q^2}\right) \times [\bar{v}_{p_1} (- i e Q_{\ell} \gamma_{\nu}) u_{p_2}]$$

 

[andrien]

Draw a diagram and read from right to left

correction,it should read as we read from right to left,we just follow the arrows.