Computer Algebra for Tensors in Field Theory

Abstract: Computer algebra systems are indispensable tools for modern research in mathematics and physics. This talk showcases "Alakazam", a new 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 will demonstrate several of these in this talk. Alakazam also features notable speed improvements over established systems, on which we will comment.

condensed mattergeneral literaturemathematical softwaresymbolic computationgeneral relativity and quantum cosmologyHEP - theorymathematical physicsdifferential geometrycomputational physics

Audience: advanced learners

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Europe and Pacific Theoretical Physics

Series comments: European and Pacific Theoretical Physics is a group that runs online seminars and talks across broad topics in mathematical and theoretical physics. Our goal is to share concepts across continents to bring about a deeper understanding of cutting-edge topics in physics.

The talks are informal, and anyone can participate, so please reach out if you would like to present one week!

Extended notes & presentation material are uploaded to "Past talks". Please click on the title of a talk, and then click on "paper" or "slides" to see more.

Our focus for 2025 was on Generalised (Categorical) Symmetries, following the lecture notes found here: arxiv.org/pdf/2411.09082.

Zoom link: unibe-ch.zoom.us/j/6801537904

Watch previous talks on YouTube: www.youtube.com/@eupactp

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