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



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 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 α parameters


performing integrals over loop momenta using dimensional regularization, expressing the result as an expansion in ε, 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

FeynmanDiagrams, FeynmanIntegral command, PhysicalConstants, Physics, Physics conventions, Physics examples, Physics Updates, Tensors - a complete guide, Mini-Course Computer Algebra for Physicists, UsingPackages



[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.