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

:$\frac=\frac\int^\infty_0 du \, u^e^,$

Julian Schwinger noticed that one may simplify the integral:

:$\int \frac=\frac\int dp \int^\infty_0 du \, u^e^=\frac\int^\infty_0 du \, u^ \int dp \, e^,$

for Re(n)>0.

Another version of Schwinger parametrization is:

:$\frac=\int^\infty_0 du \, e^,$

which is convergent as long as $\epsilon >0$ and $A \in \mathbb R$. It is easy to generalize this identity to n denominators.

See also

* Feynman parametrization

References

Quantum field theory

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