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 2024-10-15 13:36:48 +00:00
parent 255ea5ffd7
commit a60ade65f0
5 changed files with 21 additions and 19 deletions
Download patch file Download diff file Expand all files Collapse all files

3
HepLean/SpaceTime/LorentzVector/Complex/Contraction.lean
View file

@ -8,7 +8,6 @@ import HepLean.SpaceTime.LorentzVector.Complex.Basic
# Contraction of Lorentz vectors
-/
noncomputable section
@ -91,7 +90,7 @@ def contrCoContraction : complexContr ⊗ complexCo ⟶ 𝟙_ (Rep ℂ SL(2,ℂ)
def coContrContraction : complexCo ⊗ complexContr ⟶ 𝟙_ (Rep ℂ SL(2,ℂ)) where
hom := TensorProduct.lift contrContrCoBi
comm M := TensorProduct.ext' fun φ ψ => by
change ((LorentzGroup.toComplex (SL2C.toLorentzGroup M))⁻¹ᵀ *ᵥ φ.toFin13ℂ) ⬝ᵥ
change ((LorentzGroup.toComplex (SL2C.toLorentzGroup M))⁻¹ᵀ *ᵥ φ.toFin13ℂ) ⬝ᵥ
((LorentzGroup.toComplex (SL2C.toLorentzGroup M)) *ᵥ ψ.toFin13ℂ) = φ.toFin13ℂ ⬝ᵥ ψ.toFin13ℂ
rw [dotProduct_mulVec, mulVec_transpose, vecMul_vecMul]
rw [inv_mul_of_invertible (LorentzGroup.toComplex (SL2C.toLorentzGroup M))]

17
HepLean/SpaceTime/LorentzVector/Complex/Two.lean
View file

@ -80,9 +80,9 @@ lemma contrContrToMatrix_ρ (v : (complexContr ⊗ complexContr).V) (M : SL(2,
* contrContrToMatrix v k.1 k.2) = _
erw [Finset.sum_product]
simp_rw [kroneckerMap_apply, Matrix.mul_apply, Matrix.transpose_apply]
have h1 : ∑ x, (∑ x1 , LorentzGroup.toComplex (SL2C.toLorentzGroup M) i x1 *
have h1 : ∑ x, (∑ x1, LorentzGroup.toComplex (SL2C.toLorentzGroup M) i x1 *
contrContrToMatrix v x1 x) * LorentzGroup.toComplex (SL2C.toLorentzGroup M) j x
= ∑ x , ∑ x1 , (LorentzGroup.toComplex (SL2C.toLorentzGroup M) i x1
= ∑ x, ∑ x1, (LorentzGroup.toComplex (SL2C.toLorentzGroup M) i x1
* contrContrToMatrix v x1 x) * LorentzGroup.toComplex (SL2C.toLorentzGroup M) j x := by
congr
funext x
@ -122,9 +122,9 @@ lemma coCoToMatrix_ρ (v : (complexCo ⊗ complexCo).V) (M : SL(2,ℂ)) :
* coCoToMatrix v k.1 k.2) = _
erw [Finset.sum_product]
simp_rw [kroneckerMap_apply, Matrix.mul_apply, Matrix.transpose_apply]
have h1 : ∑ x, (∑ x1 , (LorentzGroup.toComplex (SL2C.toLorentzGroup M))⁻¹ x1 i *
have h1 : ∑ x, (∑ x1, (LorentzGroup.toComplex (SL2C.toLorentzGroup M))⁻¹ x1 i *
coCoToMatrix v x1 x) * (LorentzGroup.toComplex (SL2C.toLorentzGroup M))⁻¹ x j
= ∑ x , ∑ x1 , ((LorentzGroup.toComplex (SL2C.toLorentzGroup M))⁻¹ x1 i
= ∑ x, ∑ x1, ((LorentzGroup.toComplex (SL2C.toLorentzGroup M))⁻¹ x1 i
* coCoToMatrix v x1 x) * (LorentzGroup.toComplex (SL2C.toLorentzGroup M))⁻¹ x j := by
congr
funext x
@ -164,9 +164,9 @@ lemma contrCoToMatrix_ρ (v : (complexContr ⊗ complexCo).V) (M : SL(2,ℂ)) :
* contrCoToMatrix v k.1 k.2) = _
erw [Finset.sum_product]
simp_rw [kroneckerMap_apply, Matrix.mul_apply]
have h1 : ∑ x, (∑ x1 , LorentzGroup.toComplex (SL2C.toLorentzGroup M) i x1 *
have h1 : ∑ x, (∑ x1, LorentzGroup.toComplex (SL2C.toLorentzGroup M) i x1 *
contrCoToMatrix v x1 x) * (LorentzGroup.toComplex (SL2C.toLorentzGroup M))⁻¹ x j
= ∑ x , ∑ x1 , (LorentzGroup.toComplex (SL2C.toLorentzGroup M) i x1
= ∑ x, ∑ x1, (LorentzGroup.toComplex (SL2C.toLorentzGroup M) i x1
* contrCoToMatrix v x1 x) * (LorentzGroup.toComplex (SL2C.toLorentzGroup M))⁻¹ x j := by
congr
funext x
@ -207,9 +207,9 @@ lemma coContrToMatrix_ρ (v : (complexCo ⊗ complexContr).V) (M : SL(2,ℂ)) :
* coContrToMatrix v k.1 k.2) = _
erw [Finset.sum_product]
simp_rw [kroneckerMap_apply, Matrix.mul_apply, Matrix.transpose_apply]
have h1 : ∑ x, (∑ x1 , (LorentzGroup.toComplex (SL2C.toLorentzGroup M))⁻¹ x1 i *
have h1 : ∑ x, (∑ x1, (LorentzGroup.toComplex (SL2C.toLorentzGroup M))⁻¹ x1 i *
coContrToMatrix v x1 x) * (LorentzGroup.toComplex (SL2C.toLorentzGroup M)) j x
= ∑ x , ∑ x1 , ((LorentzGroup.toComplex (SL2C.toLorentzGroup M))⁻¹ x1 i
= ∑ x, ∑ x1, ((LorentzGroup.toComplex (SL2C.toLorentzGroup M))⁻¹ x1 i
* coContrToMatrix v x1 x) * (LorentzGroup.toComplex (SL2C.toLorentzGroup M)) j x := by
congr
funext x
@ -228,7 +228,6 @@ lemma coContrToMatrix_ρ (v : (complexCo ⊗ complexContr).V) (M : SL(2,ℂ)) :
## The symm version of the group actions.
-/
lemma contrContrToMatrix_ρ_symm (v : Matrix (Fin 1 ⊕ Fin 3) (Fin 1 ⊕ Fin 3) ℂ) (M : SL(2,ℂ)) :

4
HepLean/SpaceTime/LorentzVector/Complex/Unit.lean
View file

@ -26,7 +26,7 @@ def contrCoUnitVal : (complexContr ⊗ complexCo).V :=
/-- The contra-co unit for complex lorentz vectors as a morphism
`𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexContr ⊗ complexCo`, manifesting the invaraince under
the `SL(2, ℂ)` action. -/
def contrCoUnit : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexContr ⊗ complexCo where
def contrCoUnit : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexContr ⊗ complexCo where
hom := {
toFun := fun a =>
let a' : ℂ := a
@ -58,7 +58,7 @@ def coContrUnitVal : (complexCo ⊗ complexContr).V :=
/-- The co-contra unit for complex lorentz vectors as a morphism
`𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexCo ⊗ complexContr`, manifesting the invaraince under
the `SL(2, ℂ)` action. -/
def coContrUnit : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexCo ⊗ complexContr where
def coContrUnit : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexCo ⊗ complexContr where
hom := {
toFun := fun a =>
let a' : ℂ := a