- 164

- 10

## Main Question or Discussion Point

I know this question has been asked, in several ways, many times before. I have read many of the posts. And still I do not fully understand the situation: is QM in any way a subset of QFT?

Apparently no: QM uses position variables, while QFT does not. QM has the Born rule and a wave function, while QFT does not.

But then, many of the postulates in both (unitarity, cluster decomposition ...) are common. It seems here that the difference is Galilean invariance on QM vs Poincaré invariance in QFT, but that is ok.

Classical mechanics is easily derived, in the path integral formalism, from QFT. But I have never seen the same for QM from QFT.

But then, there is a "second quantization" in QM, mostly in condensed matter, where QM becomes a field theory.

So, my question is then: are QM and QFT different theories? If so, how does this observation with Weinberg's "theorem" that "everything" is an effective field theory?

Apparently no: QM uses position variables, while QFT does not. QM has the Born rule and a wave function, while QFT does not.

But then, many of the postulates in both (unitarity, cluster decomposition ...) are common. It seems here that the difference is Galilean invariance on QM vs Poincaré invariance in QFT, but that is ok.

Classical mechanics is easily derived, in the path integral formalism, from QFT. But I have never seen the same for QM from QFT.

But then, there is a "second quantization" in QM, mostly in condensed matter, where QM becomes a field theory.

So, my question is then: are QM and QFT different theories? If so, how does this observation with Weinberg's "theorem" that "everything" is an effective field theory?