A question about Zee's book QFT in a nutshell

[ftr]

I have read( even Peter Donis mentioned it) that the derivation of the potential between two particles is not a true QFT, why is that? if not, then what is it?

Thanks in advance.

 

[PeterDonis]

I have read( even Peter Donis mentioned it)

Please give specific references.

 

[ftr]

I will search for the post. I am sure of it but I don't have the time now. I think even Zee himself makes a passing remark.

 

[atyy]

In non-relativistic QFT, there can be a potential, eg. https://www.colorado.edu/physics/phys7450/phys7450_sp10/notes/2nd_quantization.pdf

However, there is usually not a potential in relativistic QFT. This is because even in classical relativistic field theory, a potential will cause faster than light interactions. However, I am not sure whether there is a formal proof that all potentials are inconsistent with commutation of spacelike observables in relativistic QFT.

Weinberg's first QFT volume https://www.amazon.com/dp/0521670535/?tag=pfamazon01-20 discusses when the external field approximation can be used (eg. section 13.6)

 

[ftr]

I am still digging. But to add to the confusion, Zee at the beginning of Feynman Diagrams(page 41) says that so far we have been doing (in previuos chapters) non interacting theory! So I guess QFT should be interacting.