# Software for calculating Feynman Diagrams

Is there a software (open source preferred) where I would input something like "Ingoing: a fermion $(p1, s1)$ and a photon $(p2, s2)$. Output: A fermion $(k1, r1)$ and a photon $(k2, r2)$" and I would could then get each diagram (that is, each term in the Dyson series) up to whichever order I choose, also showing terms that evaluate to zero (just to see that they are there)?

I have tried to compute the above diagram to 2nd order and I'm just baffled with how many details there are to collect, this seems like the perfect job for a computer, but I can't find anything that would do such a symbolic calculation (hopefully showing the steps along the way) and not just the final result.

• Maybe "FORM" and in particular feynarts.de/formcalc. From wiki: The software package FormCalc which is widely used in the physics community to calculate Feynman diagrams is built on top of FORM. Feb 3, 2014 at 1:38
• This question appears to be off-topic because it is about software recommendations and not physical concepts Feb 3, 2014 at 2:30
• @tpg2114 Why would this questions be off-topic, whereas this is not off-topic? Feb 3, 2014 at 2:59
• @tpg2114 and others, we agreed in meta that questions about software exclusively used by and useful for physicists purpose are allowed. So there is no need to close this question, voted to leave open. Please do not overrule that agreement like this. Feb 3, 2014 at 8:05
• @Hunter both questions are allowed according to the meta agreement I cited, the close votes are therefore not justified. Feb 3, 2014 at 8:10

There are, of course, a lot of codes floating around. Which of them you should choose, depends on what you want to calculate exactly. Here I mention four possibilities:

1. CALHEP - this package takes you from a given Lagrangian through its Feynmann rules to the calculation of cross sections.

2. xloops - this package calculates the 1-PI Feynman diagrams with one and two closed loops for a given process in the Standard model and related theories.
Note added: as pointed out in the comments, the link does not work (as of July, 2021), will update this paragraph when a new link will be available.

3. You should also take a look at MadGraph.

4. And here is a nice paper that discusses how to generate and calculate one-loop Feynman diagrams with three software packages (each used at different steps). For example, it discusses the FormCalc package of FORM which was also mentioned by Hunter in his comment.

I hope some of these will help you with the particular calculation that you want to perform.

Edit. Let me add here also the comment of TomDickens, because this point should be stressed: Hopefully you know how to compute simple diagrams by hand already. These codes are not quite "black boxes".

• I wonder if programs applying twistor or even amplituhedron methods to evaluate Feynman diagrams are already available too ...? Feb 3, 2014 at 8:49
• @Dilaton: Good question! I don't know of any. Triggered by your question, I even made a (superficial) search on the web and didn't find such a software. I would also be interested whether such programs already exist. Feb 3, 2014 at 16:50
• @ZoltanZimboras, thanks for your answer, I will check all these. What I have done so far is work through chapters 4 and 5 in Peskin. However, I felt Peskin glosses over many of the technicalities with all steps of the way and this is precisely why I would love to have such software to compare and see that indeed everything I think I understand I really understand correctly.
– PPR
Feb 3, 2014 at 21:19
• Unfortunately I still didn't get to test the extensive software available but I made a small addition of myself which applies to calculating Feynman propagator functional derivatives in Yukawa theory up to arbitrary orders. I reckon it can be extended to QED with not much effort: github.com/yashkes/manyDerivatives
– PPR
Apr 15, 2014 at 21:46
• MadGraph does only tree level (no loops but many outgoing particles), MadGraph5_aMC@NLO can do one loop Nov 6, 2014 at 20:47