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.

[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.