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Physics[FeynmanIntegral] - Package of commands for the evaluation of Feynman integrals

Description

 • FeynmanIntegral is both a command and a package of commands for the computation of Feynman integrals, i.e. the (loop) integrals that appear in quantum field theory when performing perturbative calculations with the S-matrix in momentum representation. Feynman integrals are often divergent and must be regularized to extract physically meaningful quantities.
 • In this context, the FeynmanIntegral command computes a Feynman integral using dimensional regularization, rewriting the integrand using tensor reduction, Feynman parameters, and expanding in the dimensional parameter $\mathrm{ϵ}$.
 • As a package, FeynmanIntegral includes commands for performing the relevant steps of that computation; i.e.:
 • expressing the integrands of Feynman integrals as integrals over auxiliary Feynman or $\mathrm{\alpha }$ parameters
 • performing integrals over loop momenta using dimensional regularization, expressing the result as an expansion in $\mathrm{\epsilon }$, the dimensional parameter.
 • expressing tensor integrals in a basis of scalar integrals
 • The FeynmanIntegral package contains the following commands:

 You can load the FeynmanIntegral package using the with command, or invoke FeynmanIntegral commands using the long form, e.g. as in FeynmanIntegral:-Parametrize.

Brief description of the commands of the FeynmanIntegral package

 • Evaluate evaluates the Feynman integrals of a given expression, typically the output of the FeynmanDiagrams command, by parametrizing each of those integrals then evaluating them in dimension $d$ and expanding around $d=4$.
 • Parametrize replaces the propagators within a Feynman integral by integrals on Feynman or alpha parameters.

References

 [1] Smirnov, V.A., Feynman Integral Calculus. Springer, 2006.
 [2] Weinberg, S., The Quantum Theory Of Fields. Cambridge University Press, 2005.
 [3] Bogoliubov, N.N., and Shirkov, D.V. Quantum Fields. Benjamin Cummings, 1982.