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feat: Lots of stuff about koszul contract

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jstoobysmith 2024-12-13 10:04:26 +00:00
parent 3a76c824fc
commit 625ef5f431
4 changed files with 1618 additions and 105 deletions
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3
HepLean/Lorentz/SL2C/Basic.lean
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@ -240,7 +240,8 @@ lemma toLorentzGroup_fst_col (M : SL(2, ℂ)) :
| Sum.inr 2 => ((- ‖M.1 0 0‖ ^ 2 - ‖M.1 0 1‖ ^ 2 + ‖M.1 1 0‖ ^ 2 + ‖M.1 1 1‖ ^ 2) / 2)
change (fun μ => (toLorentzGroup M).1 μ (Sum.inl 0)) = k
have h1 : toSelfAdjointMap M (PauliMatrix.σSAL (Sum.inl 0)) = ∑ μ, k μ • PauliMatrix.σSAL μ := by
simp [Fin.sum_univ_three]
simp only [Fin.isValue, Fintype.sum_sum_type, Finset.univ_unique, Fin.default_eq_zero,
Finset.sum_singleton, Fin.sum_univ_three]
rw [toSelfAdjointMap_apply_σSAL_inl]
abel
rw [toSelfAdjointMap_basis] at h1