I had a hard time deciding whether this question is more appropriate for physicsSE or MO, so I have cross-listed it for the time being. The physicsSE post can be found here.
In the lecture Is relativity compatible with quantum theory? on constructive quantum field theory given by Arthur Jaffe (around the timestamp 49:10) he says:
"Wavefunction renormalization entails a change of representation. In mathematical language a change to a unitarily inequivalent representation of the commutation relations or a change of Hilbert space, even in finite volume"
I found this a very interesting remark, but unfortunately could not find more about it anywhere in the literature. How does a change of representation of the commutation relations result in a kind of renormalization? I suspect the different Hilbert spaces referred to above has to do with the interacting theory being defined on a different Hilbert space as the bare theory and Haag's theorem, but how is this a (physical) renormalization?
On a related note, many introductory quantum field theory textbooks written by/for physicists use the words wavefunction renormalization and field strength renormalization interchangeably. In contrast, the constructive quantum field theory community seems to make a distinction between the two. Is there a mathematical definition that differentiates them?
