Schwinger parametrization

Schwinger parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops.

Using the well-known observation that

: $frac{1}{A^n}=frac{1}{(n-1)!}int^infty_0 du , u^{n-1}e^{-uA},$

Julian Schwinger noticed that one may simplify the integral:

: $int frac{dp}{A(p)^n}=frac{1}{Gamma(n)}int dp int^infty_0 du , u^{n-1}e^{-uA(p)}=frac{1}{Gamma(n)}int^infty_0 du , u^{n-1} int dp , e^{-uA(p)},$

for Re(n)>0.

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