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.

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.

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.

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.