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refactor: rm LorentzVector.Covariant

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jstoobysmith 2024-11-08 11:09:15 +00:00
parent db30edad73
commit ac7c7939a7
3 changed files with 4 additions and 109 deletions
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4
HepLean/SpaceTime/LorentzVector/Real/Contraction.lean
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@ -88,6 +88,7 @@ def contrCoContract : Contr d ⊗ Co d ⟶ 𝟙_ (Rep ℝ (LorentzGroup d)) wher
Action.tensorUnit_ρ', CategoryTheory.Category.comp_id, lift.tmul]
rfl
/-- Notation for `contrCoContract` acting on a tmul. -/
scoped[Lorentz] notation "⟪" ψ "," φ "⟫ₘ" => contrCoContract.hom (ψ ⊗ₜ φ)
lemma contrCoContract_hom_tmul (ψ : Contr d) (φ : Co d) : ⟪ψ, φ⟫ₘ = ψ.toFin1dℝ ⬝ᵥ φ.toFin1dℝ := by
@ -110,6 +111,7 @@ def coContrContract : Co d ⊗ Contr d ⟶ 𝟙_ (Rep ℝ (LorentzGroup d)) wher
Action.tensorUnit_ρ', CategoryTheory.Category.comp_id, lift.tmul]
rfl
/-- Notation for `coContrContract` acting on a tmul. -/
scoped[Lorentz] notation "⟪" φ "," ψ "⟫ₘ" => coContrContract.hom (φ ⊗ₜ ψ)
lemma coContrContract_hom_tmul (φ : Co d) (ψ : Contr d) : ⟪φ, ψ⟫ₘ = φ.toFin1dℝ ⬝ᵥ ψ.toFin1dℝ := by
@ -140,6 +142,7 @@ open CategoryTheory
def contrContrContract : Contr d ⊗ Contr d ⟶ 𝟙_ (Rep ℝ (LorentzGroup d)) :=
(Contr d ◁ Contr.toCo d) ≫ contrCoContract
/-- Notation for `contrContrContract` acting on a tmul. -/
scoped[Lorentz] notation "⟪" ψ "," φ "⟫ₘ" => contrContrContract.hom (ψ ⊗ₜ φ)
lemma contrContrContract_hom_tmul (φ : Contr d) (ψ : Contr d) :
@ -157,6 +160,7 @@ lemma contrContrContract_hom_tmul (φ : Contr d) (ψ : Contr d) :
def coCoContract : Co d ⊗ Co d ⟶ 𝟙_ (Rep ℝ (LorentzGroup d)) :=
(Co d ◁ Co.toContr d) ≫ coContrContract
/-- Notation for `coCoContract` acting on a tmul. -/
scoped[Lorentz] notation "⟪" ψ "," φ "⟫ₘ" => coCoContract.hom (ψ ⊗ₜ φ)
lemma coCoContract_hom_tmul (φ : Co d) (ψ : Co d) :