When to use Feynman or Schwinger Parametrization

In summary, Feynman parametrization is often used for integrals involving quadratic terms in Feynman diagrams, while Schwinger parametrization is advantageous for higher-order terms. The choice between the two depends on the structure of the integrand, and it is possible to use a combination of both in certain cases. However, both parametrizations have their own limitations and it is important to carefully examine the integrand before deciding which one to use.
  • #1
Elmo
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TL;DR Summary
A question about loop calculations by Feynman and Schwinger parameterization
I had been doing some calculations involving propagators with both a quadratic and a linear power of loop momentum in the denominator. In the context of HQET and QCD with strategy of regions.
The texts which I am following sometimes tend to straightaway use Schwinger and I am just wondering if there are any restrictions/conditions in the use of each of these techniques.
 
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  • #2
Hm, I'm more used to the Feynman parametrization. I don't think that it makes much of a difference which one you use.
 

1. When should I use Feynman parametrization?

Feynman parametrization is most useful when dealing with integrals involving products of several propagators, as it allows for the simplification of the integral into a more manageable form.

2. When is Schwinger parametrization preferred?

Schwinger parametrization is typically used when dealing with integrals involving exponential functions, as it allows for the integration of the exponential term and simplifies the overall integral.

3. Can I use either parametrization interchangeably?

While both Feynman and Schwinger parametrization can be used to simplify integrals, they are not interchangeable. The choice of which to use depends on the specific integral being evaluated.

4. Are there any limitations to using these parametrizations?

Both Feynman and Schwinger parametrization have their own limitations. Feynman parametrization is not suitable for integrals with singularities, while Schwinger parametrization may lead to more complicated integrals in some cases.

5. How can I determine which parametrization to use?

The choice of which parametrization to use ultimately depends on the specific integral being evaluated. It is important to understand the strengths and limitations of each parametrization and choose the one that best suits the integral at hand.

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