7.5. Dimensional regularization An alternative way to regularize the integrals encountered in perturbative series of QFT consists of the dimensional regularization. The main idea behind this approach is to consider the integrals as functions of the dimensionality d of the system, regarded as a continuous variable. Once they are evaluated in the region of the complex plane d where they converge, their values in other domains are obtained by analytic continuation. Prove the validity of the formula

 ddp

(2π)d 1

(p2 +

)n

= 1

(4π)d/2

n− d 2

(n)

 1



n−d/2

.

Discuss the analytic structure of this expression as a function of d.