Introducing Cadabra: a symbolic computer algebra system for field theory problems

TL;DR

Cadabra addresses a gap in symbolic computation for field-theory problems by providing a TeX-based input language and deep support for tensor and spinor algebra, including Bianchi and Schouten identities, gamma-matrix algebra, Fierz transformations, and implicit coordinate dependence. The paper demonstrates Cadabra through concrete gravity, supergravity, and quantum field theory calculations, such as Riemann-tensor polynomials, Kaluza–Klein decompositions, and fermionic rearrangements, underscoring its pencil-and-paper–like workflow. Key contributions include robust multi-term symmetries via Young tableau projectors, explicit handling of multiple index types and dummy indices, and programmable simplification control, all within an open-source, cross-platform framework. The work argues that Cadabra provides a practical, extensible toolset for field-theory calculations, enabling reproducible derivations and streamlined workflows beyond what general-purpose CAS offer.

Abstract

Cadabra is a new computer algebra system designed specifically for the solution of problems encountered in field theory. It has extensive functionality for tensor polynomial simplification taking care of Bianchi and Schouten identities, for fermions and anti-commuting variables, Clifford algebras and Fierz transformations, implicit coordinate dependence, multiple index types and many other field theory related concepts. The input format is a subset of TeX and thus easy to learn. Both a command-line and a graphical interface are available. The present paper is an introduction to the program using several concrete problems from gravity, supergravity and quantum field theory.