I have come across this post while searching for why computing the 2-point function of a free quantum field theory is the same as finding a Green's function for the equations of motion. I suppose this answer is the rigorous justification for that or is there more to it?

@PedroLauridsenRibeiro Thank you very much!

@PedroLauridsenRibeiro Thank you for the references. As a related question, do you have any resource recommendations for learning constructive QFT? I am following Glimm-Jaffe's book which is great but it would be nice to have an alternative (and easier to follow) text to supplement it.

Thank you very much for the resources!

@MartinHairer Thank you, I'm very excited to go through these notes!

@LiviuNicolaescu Thank you.

@LiviuNicolaescu Apologies for commenting on an older post but I came across this question as I am studying Gaussian measures (especially on infinite dimensional spaces and for applications to QFT). How is Gelfand's book for learning about this topic? Is it in anyway out of date or are there better resources?

@B.P. I am most interested in constructive QFT.

@B.P. I have been trying to understand the projective tensor product approach to defining nuclear spaces and nuclear operators between Banach spaces, but it seems like this isn't needed as most QFT applications only speak of nuclear spaces in the context of Hilbert spaces. Gelfand's book takes this approach and is what I am currently working through. Is this enough for most of the QFT applications? If not, are there any QFT books you can recommend that build up nuclear spaces?

@Oxonon Thank you for the reference, I will take a look at it.