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## Main Question or Discussion Point

As I understand it, in order to compute a contour integral one can deform the contour of integration, such that it doesn't pass through any poles of the integrand, and the result is identical to that found using the original contour of integration considered. However, I have seen applications (particularly in QFT) where one considers an integral on the real axis, and instead of deforming the contour of integration, one shifts the poles of the integrand by a small positive/negative imaginary term in such a way that they don't pass through the contour. Is the justification for this that it is simply a convient trick that is equivalent to deforming the integration contour in the limit as the shift tends to zero and hence leads to the same result for the integral?