Causality for internel vertex in Feynaman diagrams

[dontknow]

Eq 4.44 in Peskin and Schroeder. My question is:
Does causality imply that time coordinates of z (internal vertex over which we doing the integration) should lie between the time coordinates of field phi(x) and phi(y)?

 

[vanhees71]

The propagators in vacuum QFT are the time-ordered propagators (which in the vacuum case are the same as the Feynman propagators). Thus there's no constraint on the times of the inner space-time point $z$.

 

[dontknow]

sorry, I was not clear. we usually interpret propagators as particle popping out in space at some spacetime, let's suppose x and then it gets annihilated at spacetime point y. so if we follow the same interpretation here the particle which pops out at some point x can go back in time gets annihilated at z (internal vertex) and then come back to spacetime point y. while integrating this kind of propagation for all values of internal vertex, Does integration contribution comes from all points in spacetime or only those lying inside the cone (timelike) of spacetime?
Or maybe I am missing a point, does time-ordered product implies that we can go in only one direction of time?
Let me know if i am still not clear.
Thanks for answering.

 

[vanhees71]

You cannot interpret the internal lines as particles. They are just clever mathematical notations to express the contributions of the perturbative series to the S-matrix element under consideration. Only the external legs stand for observable asymptotic free particle states, and only those are interpretable as particles. The causality and Poincare invariance of the scheme is guaranteed for such observable quantities through the microcausality property of the field operators.