SpinorHelicity4D: a Mathematica toolbox for the four-dimensional spinor-helicity formalism

Abstract: We present the Mathematica package SpinorHelicity4D, a dedicated suite for analytic and numeric calculations involving four-dimensional massless and massive spinor-helicity formalism. Analytic features of the package include for example: manipulation of contracted and uncontracted spinor quantities, automated application of Schouten identities for expression simplification, contractions of spinor products into chains, re-expression of chains in terms of Dirac traces and evaluation of such traces, derivatives of arbitrary functions of spinor quantities. Numeric features of the package include among others: generation of arbitrary $n$-point numerical complex kinematics, allowing for both massless and massive external states, fully numeric or parametric kinematics, and numeric generation on either $\mathbb{R}$ or $\mathbb{Q}$, the latter providing output immediately suitable for finite field applications. Furthermore, the package features user-friendly, intuitive but also highly customizable input options, thus providing an approachable tool for the casual user while still supporting more advanced applications for more adept and frequent users. All of the output is returned in the standard bracket notation, making it easily interpretable, but at the same it retains all of the analytic properties of the objects, allowing for copy-pasted and manipulated output to be provided as new input. This makes it ideal for front-end applications on a Mathematica notebook, while still allowing for deployment on a cloud server for more heavy calculations.