DibyashanuPati/PhysLean
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

refactor: Lint

Browse source
This commit is contained in:
jstoobysmith 2024-10-16 10:57:46 +00:00
parent 691b7e112e
commit a1d3616a18
10 changed files with 65 additions and 62 deletions
Download patch file Download diff file Expand all files Collapse all files

8
HepLean/SpaceTime/WeylFermion/Two.lean
View file

@ -76,7 +76,7 @@ def altRightRightToMatrix : (altRightHanded ⊗ rightHanded).V ≃ₗ[ℂ] Matri
LinearEquiv.curry ℂ ℂ (Fin 2) (Fin 2)
/-- Equivalence of `altLeftHanded ⊗ altRightHanded` to `2 x 2` complex matrices. -/
def altLeftAltRightToMatrix : (altLeftHanded ⊗ altRightHanded).V ≃ₗ[ℂ] Matrix (Fin 2) (Fin 2) ℂ :=
def altLeftAltRightToMatrix : (altLeftHanded ⊗ altRightHanded).V ≃ₗ[ℂ] Matrix (Fin 2) (Fin 2) ℂ :=
(Basis.tensorProduct altLeftBasis altRightBasis).repr ≪≫ₗ
Finsupp.linearEquivFunOnFinite ℂ ℂ (Fin 2 × Fin 2) ≪≫ₗ
LinearEquiv.curry ℂ ℂ (Fin 2) (Fin 2)
@ -465,7 +465,7 @@ lemma altLeftAltRightToMatrix_ρ (v : (altLeftHanded ⊗ altRightHanded).V) (M :
Action.instMonoidalCategory_tensorObj_V]
ring
def leftRightToMatrix_ρ (v : (leftHanded ⊗ rightHanded).V) (M : SL(2,ℂ)) :
lemma leftRightToMatrix_ρ (v : (leftHanded ⊗ rightHanded).V) (M : SL(2,ℂ)) :
leftRightToMatrix (TensorProduct.map (leftHanded.ρ M) (rightHanded.ρ M) v) =
M.1 * leftRightToMatrix v * (M.1)ᴴ := by
nth_rewrite 1 [leftRightToMatrix]
@ -490,7 +490,7 @@ def leftRightToMatrix_ρ (v : (leftHanded ⊗ rightHanded).V) (M : SL(2,ℂ)) :
erw [Finset.sum_product]
simp_rw [kroneckerMap_apply, Matrix.mul_apply]
have h1 : ∑ x : Fin 2, (∑ x1 : Fin 2, M.1 i x1 * leftRightToMatrix v x1 x) * (M.1)ᴴ x j
= ∑ x : Fin 2, ∑ x1 : Fin 2, (M.1 i x1 * leftRightToMatrix v x1 x) * (M.1)ᴴ x j := by
= ∑ x : Fin 2, ∑ x1 : Fin 2, (M.1 i x1 * leftRightToMatrix v x1 x) * (M.1)ᴴ x j := by
congr
funext x
rw [Finset.sum_mul]
@ -613,7 +613,7 @@ lemma altLeftAltRightToMatrix_ρ_symm_selfAdjoint (v : Matrix (Fin 2) (Fin 2)
rw [← @adjugate_transpose]
rfl
lemma leftRightToMatrix_ρ_symm_selfAdjoint (v : Matrix (Fin 2) (Fin 2) ℂ)
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