Dirac: A command-line γ-matrix calculator

A software for simplification of Dirac matrix polynomials that arise in particle physics problems is implemented.Program summary Program Title: Dirac CPC Library link to program files: https://doi .org /10 .17632 /s5w3zyhy58 .1 Developer's repository link: https://github .com /skutnii /dirac Licensing provisions: MIT Programming language: C++20 Nature of problem: Particle physics computations require simplification of Dirac matrix polynomials. Non-commutativity and tensorial nature of Dirac matrices makes the task nontrivial. Complexity of the expressions grows quickly with the number of factors making manual computations beyond a few simplest cases unfeasible and highly error-prone. Existing software solutions are either proprietary and highly expensive or have poor if any support for Dirac matrix algebra. Solution method: The problem is solved by considering a representation of Dirac matrix algebra with 5 x 5 pseudo-matrices -matrices made of the algebra's structure constants. In this representation, multiplication of the original matrices corresponds to multiplication of pseudo-matrices and Lorentz index contraction. The problem then gets reduced to simplification of polynomials in Minkowski metric, Kronecker, and Levi-Civita symbols. Additional comments including restrictions and unusual features: The input and output have LATEX-like syntax with single-expression command line input and interactive shell modes. Scripting can be used for batched input processing and advanced LATEX formatting of the results. Example scripts demonstrate this feature and provide automated correctness tests. The software supports both rational and floating-point arithmetic. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

A software tool for simplification of Dirac matrix polynomials in particle physics problems has been implemented. It uses pseudo-matrices and algebraic calculations to simplify complex problems and enables efficient and accurate computations involving Dirac matrices in particle physics.