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First off, I'm not sure if this is the right sub to talk about QFT. Apologies if t isn't.

I'm halfway through an introductory QFT course and I still don't get what it is. What is different

*in its formalism*that makes it able to tackle problems that quantum mehanics can't deal with?

From what I know so far I would say that QFT is a generalization of quantum mechanics in which you can "choose" a different equation of evolution, so that QM is a particular case of QFT in which the equation evolution is Schrödinger's equation (or Heisenberg, depending on the picture you choose).

I know this is wrong, though, because another important difference is that the position in space is "demoted" from a operator to a variable, so that it is on the same foot as time. But this makes me wonder many things:

What do we mean exactly when we write Φ(x)?

Are they still wavefunctions or should I think of them as a different concept?

Can these functions be expressed as a scalar product of kets <x|Φ>, as wavefunctions are? If they can what do we substitute the position eigenkets with, since we don't have a position operator anymore?

As you see I am completely lost when I try to see the "big picture". I thought I would find an explicit formalism for QFT somewhere, that is, a presentation of some postulates and the conclusions that follow from them, as there is for quantum mechanics, but every book I've found so far has been unsatisfactory in this regard.

I'd love to hear your thoughts on this.

Thank you for your time.