@greatpet

I'm glad to hear that more people are excited about Maple's developments in theoretical physics. Your comment is an opportunity to shed some light on what this is about - why the words I used in this post.

Note first that four different packages converge in this development: FeynmanDiagrams, FeynmanIntegral, Physics, and new in Maple 2022: StandardModel. These packages were all developed in consultation with actual practising theoretical physicists; see the Maple Physics: Research & Development.

The FeynmanDiagrams and FeynmanIntegral packages both involve several commands for performing all or each of the steps of the computations of scattering amplitudes and Feynman integrals. We do that in both coordinates and momentum representation - feynarts cannot do that. Then FeynmanIntegral performs (with restrictions, however) the *symbolic computation of these integrals*, which is also not possible with the packages you mention. FeynmanDiagrams and FeynmanIntegral implement relevant functionality available in computer algebra for the first time, presented in Computer Algebra and Particle Physics - CAPP 2021.

Now, it is true that we didn't contact the authors of the packages you mentioned. But there is a reason. All but one are implementations in Mathematica. Still, two papers are being finished about FeynmanDiagrams and FeynmanIntegral, and as is standard in these cases, both papers include tables comparing functionality - and yes: there we talk about the packages you mention. By the way, about FeynRules (feynrules.irmp.ucl), note that in the Maple implementation, due to having functional differentiation available as a command, *the Feynman rules are computed automatically, on the flight, for any possible QFT model,* turning unnecessary a package for just that.

The fourth package you mention is implemented in FORM, not a general-purpose computer algebra system. It is not possible to implement in FORM something like what you see in Maple Physics even if you restrict the goal to what is shown above for this new StandardModel package.

Perhaps more important, each of FeynmanDiagrams, FeynmanIntegral, Physics and StandardModel has several commands that can work in *black box* or *all the steps* approach. When compared with previously existing software in other platforms, four things in this Maple Physics environment appear to be unique:

- The implementation has an emphasis not just on research but also on education. That is what I meant with
*all the steps* approach.
- The notation, both for input and output, is basically as in textbooks to the point that during presentations, sometimes people ask whether I am showing LaTeX or Maple. That this notation includes
*functional* copy (from output) & paste (on input) increases the usability significantly.
- Things can be set and changed effortlessly. For example, you can set the interaction Lagrangian for a model in 1/2 line (no need to write a text file as with feynarts) and compute scattering amplitudes in coordinates or momentum representation right away. For the StandardModel, we added a command, Lagrangian, to retrieve its different sectors or all of them. This command is relevant due to the large number of terms of the model, and because of the several different kinds of tensor indices necessary to algebraically represent it.
- The implementation of mathematical objects and related operations starts at a very deep level. Both the differentiation and product operators are redefined entirely. They handle noncommutative, anticommutative and commutative objects as we do with paper and pencil, including in that user-defined: tensors of different kinds, differential, Hermitian, Unitary, etc. quantum operators with their properties, commutator algebra rules, disjointed Hilbert spaces, etc. No wonder why for Maple 2022 we were able to implement the new StandardModel package; it is built on top of all that.

This is the help page of StandardModel-Lagrangian.mw; it illustrates the itemization above.

While, in general, I'd agree with you on the meaning of "a remarkable achievement in computational physics", the capability to represent such different mathematical objects with their properties set, as well as to perform such different operations with them in so a versatile way and so similar to what we do with paper and pencil, all that I think is indeed a remarkable achievement in computational physics.

Finally, regarding performing previously impossible novel calculations published in peer-reviewed journals, while that is possible, our approach is, as said, to implement both education and research-level capabilities with the bar as high as we can see (and for that, yes we take a peek at the existing software). In this way, it is possible to achieve a remarkable computational implementation independent of having already a previously impossible result at hand.

Edgardo S. Cheb-Terrab

Physics, Differential Equations and Mathematical Functions, Maplesoft