This may be more of a maths question, but because I may actually just be interpreting the expression wrong, I think I'd better post it here.(adsbygoogle = window.adsbygoogle || []).push({});

I'm reading Quantum Field Theory in a Nutshell by A. Zee and I'm stuck on a bit of maths he does. He provides an expression for the free propagator for a particles described by the Klein-Gordon equation,

[tex]

D(x-y) = \int \frac{d^4 k}{(2 \pi)^4} \frac{e^{i k (x-y)}}{k^2 - m^2 + i \epsilon}.

[/tex]

Now, if I am not mistaken, the integral over four counts of [itex]k[/itex] means integrating over [itex]k^0, k^1, k^2, k^3[/itex], each with integration limits [itex]-\infty[/itex] and [itex]\infty[/itex].

He goes on to perform the integral over [itex]k^0[/itex], and he describes this as a contour integral in the complex plain. He takes this contour to be the real axis and an infinite semicircle to get back to [itex]-\infty[/itex]. My question is, why does he add that semicircle? Once you've integrated over the real line, since the integration limits are [itex]-\infty[/itex] and [itex]\infty[/itex], aren't you done? Or have I perhaps misinterpreted what he means to integrate over?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Integral for the free propagator

**Physics Forums | Science Articles, Homework Help, Discussion**