Symbolic Tensor Calculus with xAct: efficient tensor computer algebra for the Wolfram Language

Tensorial computations in General Relativity and field theory are often intricate, lengthy, and prone to error when performed by hand, especially in problems involving curvature tensors, symmetries, or perturbative expansions. The xAct suite is a powerful collection of packages for the Wolfram Language designed to carry out such calculations efficiently using abstract index notation and advanced algorithms for tensor simplification.

In this seminar, I will introduce the main ideas behind xAct and demonstrate its capabilities through a live session, including the definition of manifolds and metrics, the manipulation of curvature tensors and covariant derivatives in coordinates, generic vector bundle computations and work with differential forms. I will also briefly survey the broader ecosystem of xAct packages.