92 lines
6 KiB
Markdown
92 lines
6 KiB
Markdown
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[](https://heplean.com)
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[](https://heplean.com/GetInvolved.html)
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[](https://leanprover.zulipchat.com)
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[](https://heplean.com/TODOList)
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[](https://heplean.com/InformalGraph)
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[](https://heplean.com/Stats)
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[](https://github.com/leanprover/lean4/releases/tag/v4.18.0)
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[](https://gitpod.io/#https://github.com/HEPLean/HepLean)
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A project to digitalize physics.
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*(Formerly called HepLean)*
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## Aims of this project
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🎯 __Digitalize__ results (meaning calculations, definitions, and theorems) from physics
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into Lean 4.
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🎯 Develop structures to aid the __creation__ of new results in physics using Lean,
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with the potential future use of AI.
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🎯 Create good documentation so that the project can be used for __pedagogical__ purposes.
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## Some parts of PhysLean
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PhysLean _currently_ includes, but is not limited to, the following parts:
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__Lorentz [🗂️](https://physlean.com/docs/PhysLean/Relativity/Lorentz/Group/Basic.html):__ The Lorentz group, Lorentz algebra, Weyl fermions, Real Lorentz vectors, complex Lorentz vectors, complex Lorentz tensors, bispinors, Pauli matrices, etc.
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__Index notation [🗂️](https://physlean.com/docs/PhysLean/Relativity/Tensors/OverColor/Basic.html) [📄](https://arxiv.org/abs/2411.07667):__ Formalization of index notation using category theory allowing commands like
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```Lean
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{A | μ ν ⊗ S | μ ν = - A | μ ν ⊗ S | μ ν}ᵀ
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```
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__Anomaly cancellation [🗂️](https://physlean.com/docs/PhysLean/QFT/AnomalyCancellation/Basic.html):__ Results related to solutions to the anomaly cancellation conditions of several theories.
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__Standard Model physics [🗂️](https://physlean.com/docs/PhysLean/Particles/StandardModel/Basic.html):__ Properties of the Higgs potential.
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__BSM physics [🗂️](https://physlean.com/docs/PhysLean/Particles/BeyondTheStandardModel/TwoHDM/Basic.html):__ Starts to: Georgi Glashow model, Pati-Salam, Spin(10), Two Higgs doublet model.
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__Flavor physics [🗂️](https://physlean.com/docs/PhysLean/Particles/FlavorPhysics/CKMMatrix/Basic.html):__ Properties of the CKM matrix.
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__Perturbation Theory [🗂️](https://physlean.com/docs/PhysLean/QFT/PerturbationTheory/WickContraction/Basic.html):__ Time-dependent version of Wick's theorem for both fermions and bosons.
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## Associated media and publications
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- [📄](https://arxiv.org/abs/2405.08863) Joseph Tooby-Smith,
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__HepLean: Digitalising high energy physics__, Computer Physics Communications, Volume 308,
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2025, 109457, ISSN 0010-4655, https://doi.org/10.1016/j.cpc.2024.109457. \[arXiv:2405.08863\]
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- [📄](https://arxiv.org/abs/2411.07667) Joseph Tooby-Smith, __Formalization of physics index notation in Lean 4__, arXiv:2411.07667
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- [💻](https://live.lean-lang.org/#code=import%20Mathlib.Tactic.Polyrith%20%0A%0Atheorem%20threeFamily%20(a%20b%20c%20%3A%20ℚ)%20(h%20%3A%20a%20%2B%20b%20%2B%20c%20%3D%200)%20(h3%20%3A%20a%20%5E%203%20%2B%20b%20%5E%203%20%2B%20c%20%5E%203%20%3D%200)%20%3A%20%0A%20%20%20%20a%20%3D%200%20∨%20b%20%3D%200%20∨%20c%20%3D%200%20%20%3A%3D%20by%20%0A%20%20have%20h1%20%3A%20c%20%3D%20-%20(a%20%2B%20b)%20%3A%3D%20by%20%0A%20%20%20%20linear_combination%20h%20%0A%20%20have%20h4%20%3A%20%203%20*%20a%20*%20b%20*%20c%20%3D%200%20%3A%3D%20by%20%0A%20%20%20%20rw%20%5B←%20h3%2C%20h1%5D%0A%20%20%20%20ring%20%0A%20%20simp%20at%20h4%20%0A%20%20exact%20or_assoc.mp%20h4%0A%20%20%0A) Example code snippet related to Anomaly cancellation conditions.
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- [🎥](https://www.youtube.com/watch?v=W2cObnopqas) Seminar recording of "HepLean: Lean and high energy physics" by J. Tooby-Smith
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### Papers referencing PhysLean
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- Hu, Jiewen, Thomas Zhu, and Sean Welleck. "miniCTX: Neural Theorem Proving with (Long-) Contexts." arXiv preprint [arXiv:2408.03350](https://www.arxiv.org/abs/2408.03350) (2024). [Project page]( https://cmu-l3.github.io/minictx/)
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How HepLean was used: *Theorems from the space-time files of HepLean were included in a data set used to evaluate the ability of models to prove theorems from real-world repositories, which requires working with definitions, theorems, and other context not seen in training.*
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## Contributing
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We would love to have you involved! See the [Get Involved](https://heplean.com/GetInvolved.html) page to see how you can get involved.
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Any contributions are welcome! If you have any questions or want permission permission to create a pull-request for this
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repository contact Joseph Tooby-Smith on the [Lean Zulip](https://leanprover.zulipchat.com), or email.
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## Installation
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If you want to play around with HepLean, but do not want to download Lean, then you can use [GitPod](https://gitpod.io/#https://github.com/HEPLean/HepLean).
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### Installing Lean 4
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Installation instructions for Lean 4 can be found:
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- https://lean-lang.org/lean4/doc/quickstart.html
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or
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- https://leanprover-community.github.io/get_started.html
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### Installing PhysLean
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- Clone this repository (or download the repository as a Zip file)
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- Open a terminal at the top-level in the corresponding directory.
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- Run `lake exe cache get`. The command `lake` should have been installed when you installed Lean.
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- Run `lake build`.
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- Open the directory (not a single file) in Visual Studio Code (or another Lean compatible code editor).
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### Optional extras
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- [Lean Copilot](https://github.com/lean-dojo/LeanCopilot) and [LLMLean](https://github.com/cmu-l3/llmlean) allow for the use of large language models in Lean
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- [tryAtEachStep](https://github.com/dwrensha/tryAtEachStep) allows one to apply a tactic, e.g. `exact?` at each step of a lemma in a file to see if it completes the goal. This is useful for golfing proofs.
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