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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. See Also References

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