Here is an idea for a simple deliverable on the topics you mention:
maybe it might interest you:
computation of group invariants (Casimir, etc.) using tensors and
Feynman graphs; there is a book by Cvitanovic "Group theory" on this.
I have a closed PR https://github.com/sympy/sympy/pull/1699 on this, 
see group_factors.py and tests, in which I compute the 4 loop graph in
Cvitanovic eq.(1.1).
I did only the U(N) case, I did not write Feynman rules, so there
is a lot on work on this; one can consider also zero dimensional field
theories with 'fields' belonging to some representation.

Well, it is not really simple, but it is much simpler than doing the same 
in d=4 field theory,
it is a useful toy model for that.

On Thursday, March 20, 2014 10:48:39 AM UTC+1, Peter Petrov wrote:
>
> Hi everyone, 
>
> I just found out about GSoC several days ago and it immediately struck me 
> as being amazing. I have been trying to get involved in the open source 
> community for a while now, but haven't been able to "find the time". I am 
> currently in a PhD program working on theoretical physics (string theory), 
> but have been doing quite a lot of tinkering with computer science in 
> general lately and it has been really fascinating. GSoC seems like the 
> exact type of thing to push me and keep me on track to start contributing 
> seriously to open source projects and get my hands dirty with "real" 
> coding. I immediately jumped on the SymPy page and started playing around 
> with the packages. It's a little overwhelming how much is being developed 
> simultaneously, but I am getting a feel for some of the interesting 
> features. 
>
> I know it is a long shot to get approved for the GSoC, since I see most 
> people have started working on proposals so early on, but I am still going 
> to try and if it doesn't work I will at least have learned enough to start 
> working on something interesting even without the funding (it would help 
> though, since I will be able to devote more time to it over the summer). 
>
> I wanted to get some feedback about my ideas, which I realize might not 
> happen by the deadline (24ish hours left), but even so I would appreciate 
> it. I am trying to have a decent proposal by then, which might not be very 
> concrete (more of a conceptual plan) and hoping to have several days after 
> the melange deadline to develop it fully once I hear from you. I am not 
> sure how the review process works, but I would appreciate some feedback 
> from the mentors if you would be willing to consider a proposal modified 
> after the official deadline, since I see there is a period of several weeks 
> of review. That is so I know if I should slave away on it the days after 
> the deadline, or if there's no point. 
>
> I am also trying to fix an issue and submit a pull request by the 
> deadline, which is not going too well since I have started looking at SymPy 
> only for the past several days. Fingers crossed though. Anyways I just 
> uploaded a wiki page with my current general ideas (nothing specific yet, 
> but I have one more day). Any feedback or references to discussions 
> surrounding the topics I am looking at would be greatly appreciated. I have 
> been digging through the doc files and the mailing list, but someone with 
> experience might be able to point me to something I have not discovered 
> yet. 
>
> Thank you in advance for any help. This looks like a great community and I 
> look forward to talking with you more and hopefully contributing. 
>
> Peter Petrov  
>

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