The Standard Model of Particle Physics in Maple 2022

One of the most important mathematical formulations in human history is that of the Standard Model in particle physics. It describes all the elementary particles (leptons like the electron, quarks, bosons as the Higgs or the photon), which in different arrangements, form all the observable particles in nature. The formulation is not just a tremendous theoretical achievement that rendered Nobel prizes but also a practical one. Basically, all the measurements performed in the particle accelerators at CERN and the Fermilab take this mathematical, abstract formulation as the starting point. However, for computer algebra systems, the complexity of the model is somewhat extreme: is not only the number of terms in the corresponding Lagrangian impressively large but also the mathematical properties of each of these objects that represented a challenge for a long time. With hacks of different kinds, the computer algebra representation of only some aspects of the Standard Model was possible, with restricted computational capabilities.

Hidden among the novelties of Maple 2022, a breakthrough in computer algebra is the introduction of a new, fully computable representation of the Standard Model. This representation includes the accessory commands to calculate related scattering amplitudes  (the essence of the computations behind particle collision experiments) and related Feynman integrals . This is a remarkable achievement in computational physics. And from the educational point of view, it brings one more brick of knowledge from "the dark side" of the moon into "the bright side." Making the Standard Model computations be at the tip of one's fingers completely transforms the possible experience we can have with the underlying knowledge.
 

The illustration below of this new Maple 2022 StandardModel package is advanced in time with regards to the release of Maple 2022 days ago, and introduces a new command, Lagrangian, that increases one level the usability of the package. The so updated StandardModel is distributed as usual, within the Maplesoft Physics Updates for Maple 2022.
 

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft