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refactor: pass at removing double spaces

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jstoobysmith 2024-07-12 10:36:39 -04:00
parent 1fe51b2e04
commit 1133b883f3
19 changed files with 121 additions and 121 deletions
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12
HepLean/SpaceTime/SL2C/Basic.lean
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@ -33,8 +33,8 @@ we can define a representation a representation of `SL(2, ℂ)` on spacetime.
-/
/-- Given an element `M ∈ SL(2, ℂ)` the linear map from `selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)` to
itself defined by `A ↦ M * A * Mᴴ`. -/
/-- Given an element `M ∈ SL(2, ℂ)` the linear map from `selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)` to
itself defined by `A ↦ M * A * Mᴴ`. -/
@[simps!]
def toLinearMapSelfAdjointMatrix (M : SL(2, ℂ)) :
selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ) →ₗ[ℝ] selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ) where
@ -50,7 +50,7 @@ def toLinearMapSelfAdjointMatrix (M : SL(2, ℂ)) :
noncomm_ring [selfAdjoint.val_smul, Algebra.mul_smul_comm, Algebra.smul_mul_assoc,
RingHom.id_apply]
/-- The representation of `SL(2, ℂ)` on `selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)` given by
/-- The representation of `SL(2, ℂ)` on `selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)` given by
`M A ↦ M * A * Mᴴ`. -/
@[simps!]
def repSelfAdjointMatrix : Representation ℝ SL(2, ℂ) $ selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ) where
@ -63,7 +63,7 @@ def repSelfAdjointMatrix : Representation ℝ SL(2, ℂ) $ selfAdjoint (Matrix (
noncomm_ring [toLinearMapSelfAdjointMatrix, SpecialLinearGroup.coe_mul, mul_assoc,
conjTranspose_mul, LinearMap.coe_mk, AddHom.coe_mk, LinearMap.mul_apply]
/-- The representation of `SL(2, ℂ)` on `spaceTime` obtained from `toSelfAdjointMatrix` and
/-- The representation of `SL(2, ℂ)` on `spaceTime` obtained from `toSelfAdjointMatrix` and
`repSelfAdjointMatrix`. -/
def repLorentzVector : Representation ℝ SL(2, ℂ) (LorentzVector 3) where
toFun M := toSelfAdjointMatrix.symm.comp ((repSelfAdjointMatrix M).comp
@ -85,7 +85,7 @@ In the next section we will restrict this homomorphism to the restricted Lorentz
-/
lemma iff_det_selfAdjoint (Λ : Matrix (Fin 1 ⊕ Fin 3) (Fin 1 ⊕ Fin 3) ℝ): Λ ∈ LorentzGroup 3 ↔
lemma iff_det_selfAdjoint (Λ : Matrix (Fin 1 ⊕ Fin 3) (Fin 1 ⊕ Fin 3) ℝ) : Λ ∈ LorentzGroup 3 ↔
∀ (x : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)),
det ((toSelfAdjointMatrix ∘
toLin LorentzVector.stdBasis LorentzVector.stdBasis Λ ∘ toSelfAdjointMatrix.symm) x).1
@ -107,7 +107,7 @@ def toLorentzGroupElem (M : SL(2, ℂ)) : LorentzGroup 3 :=
/-- The group homomorphism from ` SL(2, ℂ)` to the Lorentz group `𝓛`. -/
@[simps!]
def toLorentzGroup : SL(2, ℂ) →* LorentzGroup 3 where
def toLorentzGroup : SL(2, ℂ) →* LorentzGroup 3 where
toFun := toLorentzGroupElem
map_one' := by
simp only [toLorentzGroupElem, _root_.map_one, LinearMap.toMatrix_one]