Alakazam: Symbolic Tensor Algebra for Field Theory in Julia

We present “Alakazam”, a Julia package for performing symbolic manipulations of tensor expressions arising in the study of field theories and quantum mechanics. This will serve as a powerful tool for studying spacetime and supersymmetric structures, including support for calculations in superspace. The package implements many key features such as raising and lowering indices, simplification of terms with dummy indices, replacement patterns, differential and variational calculus, bosonic and fermionic grading, gamma matrix identities, and Lie brackets and commutators. We present notable speed improvements over established systems. Some possible applications include the study of descendants and invariants.