Källen-Lehmann Representation

1. Jan 29, 2006

lonelyphysicist

I have two basic questions about the full propagator (2-point function) in QFT. Am I correct that for a scalar field, it is

$$\frac{iZ}{p^{2}-m^{2}+i \epsilon} + \int_{m^{2}}^{\infty} dX \frac{\rho[X]}{p^{2}-X+i \epsilon} ?$$

(1) Is this form of the propagator a feature of _quantum_ field theory? What if we have a nonlinear classical field theory? Would there still be something like that? Maybe Z = 1 (I'm not even sure about this) but perhaps we'd still have the term involving the integral?

(2) In QFT we seem to compute Z iteratively -- we compute 2-point function iteratively, up to a given number of loops -- and then we introduce Z's and mu's (if we're doing dimensional regularization). What about the term involving the integral? I don't recall it ever coming up except when the Källen-Lehmann rep is mentioned. Also, what about bound states; where does it come in?