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refactor: Major refactor of Lorentz vecs

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jstoobysmith 2024-11-09 08:06:16 +00:00
parent 3eb5da875f
commit 5cc188146f
20 changed files with 494 additions and 1005 deletions
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6
HepLean/SpaceTime/WeylFermion/Two.lean
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@ -719,10 +719,10 @@ lemma altLeftAltRightToMatrix_ρ_symm_selfAdjoint (v : Matrix (Fin 2) (Fin 2)
(hv : IsSelfAdjoint v) (M : SL(2,ℂ)) :
TensorProduct.map (altLeftHanded.ρ M) (altRightHanded.ρ M) (altLeftAltRightToMatrix.symm v) =
altLeftAltRightToMatrix.symm
(SL2C.repSelfAdjointMatrix (M.transpose⁻¹) ⟨v, hv⟩) := by
(SL2C.toLinearMapSelfAdjointMatrix (M.transpose⁻¹) ⟨v, hv⟩) := by
rw [altLeftAltRightToMatrix_ρ_symm]
apply congrArg
simp only [SL2C.repSelfAdjointMatrix, MonoidHom.coe_mk, OneHom.coe_mk,
simp only [ MonoidHom.coe_mk, OneHom.coe_mk,
SL2C.toLinearMapSelfAdjointMatrix_apply_coe, SpecialLinearGroup.coe_inv,
SpecialLinearGroup.coe_transpose]
congr
@ -738,7 +738,7 @@ lemma leftRightToMatrix_ρ_symm_selfAdjoint (v : Matrix (Fin 2) (Fin 2) ℂ)
(hv : IsSelfAdjoint v) (M : SL(2,ℂ)) :
TensorProduct.map (leftHanded.ρ M) (rightHanded.ρ M) (leftRightToMatrix.symm v) =
leftRightToMatrix.symm
(SL2C.repSelfAdjointMatrix M ⟨v, hv⟩) := by
(SL2C.toLinearMapSelfAdjointMatrix M ⟨v, hv⟩) := by
rw [leftRightToMatrix_ρ_symm]
rfl