Dirac: A command-line γ-matrix calculator

Abstract

A software for simplification of Dirac matrix polynomials that arise in particle physics problems is implemented. Program summaryProgram Title: DiracCPC Library link to program files:https://doi.org/10.17632/s5w3zyhy58.1Developer's repository link:https://github.com/skutnii/diracLicensing provisions: MITProgramming language: C++20Nature 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 5×5pseudo-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 ▪-like syntax with single-expression command line input and interactive shell modes. Scripting can be used for batched input processing and advanced ▪ formatting of the results. Example scripts demonstrate this feature and provide automated correctness tests. The software supports both rational and floating-point arithmetic.