HepLean: Digitalising high energy physics

TL;DR

HEPLean addresses the challenge of making high energy physics results machine-checkable and easily searchable by encoding definitions, theorems, proofs, and calculations in Lean 4 with the MathLib foundation. The approach builds a reusable formal library around CKM matrices, anomaly cancellation conditions, and Higgs physics, enabling formal verification, automated proving, and pedagogy. Key contributions include concrete CKM definitions, an equivalence framework for CKM matrices, invariant formalisms for ACCs under family permutations, and a rigorous Higgs potential and field framework with smoothness properties. The work lays groundwork for future expansion to 2HDM, Lorentz/group representations, generalized symmetries, and experimental-data integration, while inviting community participation through Lean-based education and collaboration.

Abstract

We introduce HepLean, an open-source project to digitalise definitions, theorems, proofs, and calculations in high energy physics using the interactive theorem prover Lean 4. HepLean has the potential to benefit the high energy physics community in four ways: making it easier to find existing results, allowing the creation of new results using artificial intelligence and automated methods, allowing easy review of papers for mathematical correctness, and providing new ways to teach high energy physics. We will discuss these in detail. We will also demonstrate the digitalisation of three areas of high energy physics in HepLean: Cabibbo-Kobayashi-Maskawa matrices in flavour physics, local anomaly cancellation, and Higgs physics.