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feat: Some properties of SL(2,C) and Lorentz

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jstoobysmith 2024-11-11 07:02:33 +00:00
parent 885c3ae204
commit a8243f4e79
2 changed files with 126 additions and 25 deletions
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HepLean/Lorentz/PauliMatrices/AsTensor.lean
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@ -137,7 +137,7 @@ def asConsTensor : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexContr ⊗ leftHanded ⊗
_ = ∑ x, ((∑ i, (SL2C.toLorentzGroup M).1 i x • (complexContrBasis i)) ⊗ₜ[ℂ]
∑ j, leftRightToMatrix.symm ((SL2C.toLorentzGroup M⁻¹).1 x j • (σSA j))) := by
refine Finset.sum_congr rfl (fun x _ => ?_)
rw [SL2CRep_ρ_basis, SL2C.toLinearMapSelfAdjointMatrix_σSA]
rw [SL2CRep_ρ_basis, toSelfAdjointMap_σSA]
simp only [Action.instMonoidalCategory_tensorObj_V, SL2C.toLorentzGroup_apply_coe,
Fintype.sum_sum_type, Finset.univ_unique, Fin.default_eq_zero, Fin.isValue,
Finset.sum_singleton, map_inv, lorentzGroupIsGroup_inv, AddSubgroup.coe_add,