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In quantum theory we have some principles that guides us, e.g. Pauli's principle. What I am after in this question is a list of fundamental results, be it equation or identities that must hold in a respectable QFT. I am thinking for instance of the Wards identities or Adler-Bell-Jackiw anomaly and similar things.

Please could you make a list of these types of identities and comment on how fundamental these are (say on a scale 1-3 normalized such that Pauli=1).

Also, please comment on how these identities arise and if there are any analogs of these in other theories (e.g. in the classical limit, or in String Theory or whatever)

Finally I would appreciate if you comment on and discuss what would happen in a theory where the pertinent identities are not satisfied.

Please don't close this question as being vague and not explicitly a solvable problem. In my opinion, these types of question are also needed here, apart from the usual "why is F=ma"-questions.

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    $\begingroup$ High level questions are great, but not ones that would take an entire book to answer. I'd recommend splitting the question up a bit and removing the purely opinion-based part (fundamental ranking from 1-3). I see 3 great questions here that should probably stand on their own. $\endgroup$
    – tpg2114
    Commented Nov 11, 2013 at 17:58
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    $\begingroup$ I edited this out of the question but an putting it as a comment to maintain the original intent of the poster: " Please don't close this question as being vague and not explicitly a solvable problem. In my opinion, these types of question are also needed here, apart from the usual "why is F=ma"-questions. " $\endgroup$
    – tpg2114
    Commented Nov 11, 2013 at 17:59
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    $\begingroup$ A classic one thinks of: 't Hooft anomaly matching. From unitarity we get the optical theorem, Froissart bound, the a-theorem, Cutkosky rules, BCFW... In specific theories, there are much stronger principles: in QCD there are sum rules, scattering factorizes etc. Specific quantities in SUSY theories have nonrenormalization theorems, those are also very strong results. $\endgroup$
    – Vibert
    Commented Nov 11, 2013 at 18:19
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    $\begingroup$ @tgp2114: Oh, shoo. This question is perfectly fine. $\endgroup$
    – Abhimanyu Pallavi Sudhir
    Commented Nov 12, 2013 at 12:07
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    $\begingroup$ Shoe${}{}{}{}$. $\endgroup$
    – Abhimanyu Pallavi Sudhir
    Commented Nov 16, 2013 at 14:19

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