# Schwinger parametrization

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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

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

Julian Schwinger noticed that one may simplify the integral:

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

for Re(n)>0.

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