Feynman parametrization: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>David Eppstein
{{applied-math-stub}}
Added the symmetric form of the parametrization, used in some QED papers from the 60's.
 
Line 1: Line 1:
{{unreferenced|date=August 2012}}
Alyson Meagher is the title her mothers and fathers gave her but she doesn't like when people use her full name. Some time  free psychic readings ([http://mybrandcp.com/xe/board_XmDx25/107997 please click the up coming website page]) ago he chose to live in North Carolina and he doesn't strategy on changing it. It's not a common thing but what I like doing is to climb but I don't have the time recently. She works as a travel  psychic love readings ([http://165.132.39.93/xe/visitors/372912 please click the up coming website page]) agent but quickly she'll be on her own.<br><br>My web page ... clairvoyance - [http://www.edmposts.com/build-a-beautiful-organic-garden-using-these-ideas/ just click the up coming document],
'''Schwinger parametrization''' is a technique for evaluating [[loop integral]]s which arise from [[Feynman diagram]]s with one or more loops.
 
Using the well-known observation that
 
:<math>\frac{1}{A^n}=\frac{1}{(n-1)!}\int^\infty_0 du \, u^{n-1}e^{-uA},</math>
 
[[Julian Schwinger]] noticed that one may simplify the integral:
 
:<math>\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)},</math>
 
for Re(n)>0.
 
Another version of Schwinger parametrization is:
 
:<math>\frac{1}{A}=-i\int^\infty_0 du \, e^{iuA},</math>
 
and it is easy to generalize this identity to n denominators.
 
See also [[Feynman parametrization]].
 
[[Category:Quantum field theory]]
 
 
{{applied-math-stub}}
{{quantum-stub}}

Latest revision as of 15:23, 8 November 2014

Alyson Meagher is the title her mothers and fathers gave her but she doesn't like when people use her full name. Some time free psychic readings (please click the up coming website page) ago he chose to live in North Carolina and he doesn't strategy on changing it. It's not a common thing but what I like doing is to climb but I don't have the time recently. She works as a travel psychic love readings (please click the up coming website page) agent but quickly she'll be on her own.

My web page ... clairvoyance - just click the up coming document,

Retrieved from "https://en.formulasearchengine.com/index.php?title=Feynman_parametrization&oldid=243204"