We have an integral over q from -[tex]\infty[/tex] to +[tex]\infty[/tex] as a contour integral in the complex q plane. If the integrand vanishes fast enough as the absolute value of q goes to infinity, we can rotate this contour counterclockwise by 90 degrees, so that it runs from -i[tex]\infty[/tex] to +i[tex]\infty[/tex].

In making this, the contour does not pass over any poles.

When I make a contour integral, the big semi-circle that I use in the upper half has the -x+iy pole in it. How does the fast vanishing of the integral and the rotation make the integral not pass over the pole? I don't see it.

thank you

In making this, the contour does not pass over any poles.

*Why?*When I make a contour integral, the big semi-circle that I use in the upper half has the -x+iy pole in it. How does the fast vanishing of the integral and the rotation make the integral not pass over the pole? I don't see it.

thank you

Last edited: