sci.physics.particle

On Thu, 15 Nov 2007 22:17:48 +0100, chilldown wrote:

> Hello,
>
> Can anyone explain to me that why is "ioata-epsilon" added to the euclidean
> propagator in
> k or p space?
> Without it, the Euclidean porpagator has poles on real axis and it can be
> integrated
> with countour integration as I see it by deforming the countour. Then why
> are the poles shifted from real axis
> by adding "ioata-epsilon" ?? OR is it postulated for reasons not obvious
> until the one
> goes from Euclidean to Minkowski
> and t in introduced?

It would be easier if I could see the equation you were looking at, but if
you have poles you need to go around, the result of the integral depends on
which way you go around the poles. You can specify how to deform the
contour, or equivalently you can deform the function by adding an i*epsilon
term and integrate along the real axis. The i*epsilon way of writing it is
shorter.

Is this a propagator for a massless particle? For a massive particle, if
you Wick rotate it into Euclidean space, I don't believe there are any
poles in the integrand.

> Is "ioata-epsilon" always added or it may also be subtracted?

If you changed the sign of the i*epsilon term, that would be equivalent to
integrating around the pole the other way, and you'd get a different
propagator.

> The course I am following is Introduction to QFT.

It would be good to know what textbook you're using so those who have the
textbook can refer to it. Note that there are several texts with that same
title.

> Thanks.
>
> PS: I forgot the I can't post the symbols thats why this is duplicate with
> correction to symbols!

LaTeX is good for expressing complicated equations in text form. I often
write equations in a LaTeX-like form in which I omit things like
backslashes and dollar signs which help the computer read it, but not other
people.

--
Jim E. Black