HepLean: Digitalising high energy physics
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.
- The lean theorem prover (system description). In Automated Deduction-CADE-25: 25th International Conference on Automated Deduction, Berlin, Germany, August 1-7, 2015, Proceedings 25, pages 378–388. Springer, 2015. doi:10.1007/978-3-319-21401-6_26.
- The mathlib Community. The lean mathematical library. In Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2020, page 367–381, New York, NY, USA, 2020. Association for Computing Machinery. doi:10.1145/3372885.3373824.
- Formalizing chemical physics using the lean theorem prover. Digital Discovery, 3(2):264–280, 2024. doi:/10.1039/D3DD00077J.
- Tomáš Skřivan. Scilean: Scientific computing assistant. GitHub repository. URL: https://github.com/lecopivo/SciLean.
- Eric Hanqing Lu. A formalization of elements of special relativity in coq. 2017. URL: http://nrs.harvard.edu/urn-3:HUL.InstRepos:38811518.
- Kevin Hartnett. Building the mathematical library of the future. Quanta Magazine, 2020.
- Joachim Breitner. loogle. GitHub repository. URL: https://github.com/nomeata/loogle.
- Leandojo: Theorem proving with retrieval-augmented language models. 2023. arXiv:2306.15626.
- Lean game server. URL: https://adam.math.hhu.de/#/.
- The natural number game. URL: https://adam.math.hhu.de/#/g/leanprover-community/nng4.
- Daniel J. Velleman. The set theory game. URL: https://adam.math.hhu.de/#/g/djvelleman/stg4.
- C. Jarlskog. Commutator of the quark mass matrices in the standard electroweak model and a measure of maximal CPCP\mathrm{CP}roman_CP nonconservation. Phys. Rev. Lett., 55:1039–1042, Sep 1985. doi:10.1103/PhysRevLett.55.1039.
- Comments on the parametrization of the kobayashi-maskawa matrix. Phys. Rev. Lett., 53:1802–1805, Nov 1984. doi:10.1103/PhysRevLett.53.1802.
- General Solution to the U(1) Anomaly Equations. Phys. Rev. Lett., 123(15):151601, 2019. arXiv:1905.13729, doi:10.1103/PhysRevLett.123.151601.
- Geometric General Solution to the U(1)𝑈1U(1)italic_U ( 1 ) Anomaly Equations. JHEP, 05:065, 2020. arXiv:1912.04804, doi:10.1007/JHEP05(2020)065.
- Anomaly cancellation with an extra gauge boson. Phys. Rev. Lett., 125(16):161601, 2020. arXiv:2006.03588, doi:10.1103/PhysRevLett.125.161601.
- A ν𝜈\nuitalic_ν supersymmetric anomaly-free atlas. JHEP, 02:144, 2022. arXiv:2107.07926, doi:10.1007/JHEP02(2022)144.
- Hypercharge Quantisation and Fermat’s Last Theorem. SciPost Phys., 8(1):009, 2020. arXiv:1907.00514, doi:10.21468/SciPostPhys.8.1.009.
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