Feynman parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. However, it is sometimes useful in integration in areas of pure mathematics as well.
Richard Feynman observed that:
which simplifies evaluating integrals like:
More generally, using the Dirac delta function:
Even more generally, provided that Re()>0 for all 1 ≤ j ≤ n:
See also Schwinger parametrization.
now just linearly transform integral to desired bounds
- and so
and we get the desired result.
- Kristjan Kannike. "Notes on Feynman Parametrization and the Dirac Delta Function". Archived from the original on 2007-07-29. Retrieved 2011-07-24.
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