Problem with Feynman's iε prescription

[alfredoalfred]

Homework Statement

My Problem is with Feynman's iε prescription. Trying to solve an Integral, it happens that there is a singularity s on the way. s depends on the Energy E of a particle. This integral is not convergent and doenst make any sense. To solve this Problem, one displaces the Energie from E to E - iε, with ε being very small. ( In Case of an anti particle it is E + iε).

Homework Equations

So the denominator of the dr integral looks like this: [ sqrt(r) - sqrt(2*(M-E' ) ] . now r gets integrated in such a way, that it always would hit the singularity s=sqrt(2*(M-E')). Changing E to E-iε however gets rid of the singularity. My problem is now not how to solve the Integral with the iε (which I am glad i found out already by myself), but to argue why we need such an iε in there in the first place.

The Attempt at a Solution

I tried to look up several books in Quantum field theory , but as i haven't taken such a course yet i don't understand them very well. There is so much stuff in there that I am not really sure I am missed an explanation. I am very confused :( .

Can you help to help me and give me a tip where i can find anything that explains it in maybe not a rigourous way? Trying to google feynman iε prescription has not really helped me :(

thank you very much for reading and maybe answering :)

 

[Dick]

The short answer is that the choice of the sign of i*epsilon determines whether you have chosen a propagator that propagates into the past or propagates into the future. For causalities sake you want the latter.