refactor: Lint
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10 changed files with 120 additions and 90 deletions
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@ -85,6 +85,7 @@ lemma ofStateAlgebra_ofState (φ : 𝓕.States) :
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Roughly `[φ1, φ2]` gets sent to `(φ1ᶜ+ φ1ᵃ) * (φ2ᶜ+ φ2ᵃ)` etc. -/
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def ofStateList (φs : List 𝓕.States) : CrAnAlgebra 𝓕 := (List.map ofState φs).prod
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/-- Coercion from `List 𝓕.States` to `CrAnAlgebra 𝓕` through `ofStateList`. -/
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instance : Coe (List 𝓕.States) (CrAnAlgebra 𝓕) := ⟨ofStateList⟩
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@[simp]
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@ -36,6 +36,7 @@ def normalOrder : CrAnAlgebra 𝓕 →ₗ[ℂ] CrAnAlgebra 𝓕 :=
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Basis.constr ofCrAnListBasis ℂ fun φs =>
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normalOrderSign φs • ofCrAnList (normalOrderList φs)
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@[inherit_doc normalOrder]
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scoped[FieldSpecification.CrAnAlgebra] notation "𝓝(" a ")" => normalOrder a
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lemma normalOrder_ofCrAnList (φs : List 𝓕.CrAnStates) :
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@ -406,7 +406,7 @@ lemma superCommute_ofCrAnList_ofStateList_cons (φ : 𝓕.States) (φs : List
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/--
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Within the creation and annihilation algebra, we have that
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`[φᶜᵃs, φᶜᵃ₀ … φᶜᵃₙ]ₛca = ∑ i, sᵢ • φᶜᵃs₀ … φᶜᵃᵢ₋₁ * [φᶜᵃs, φᶜᵃᵢ]ₛca * φᶜᵃᵢ₊₁ … φᶜᵃₙ`
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`[φᶜᵃs, φᶜᵃ₀ … φᶜᵃₙ]ₛca = ∑ i, sᵢ • φᶜᵃs₀ … φᶜᵃᵢ₋₁ * [φᶜᵃs, φᶜᵃᵢ]ₛca * φᶜᵃᵢ₊₁ … φᶜᵃₙ`
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where `sᵢ` is the exchange sign for `φᶜᵃs` and `φᶜᵃs₀ … φᶜᵃᵢ₋₁`.
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-/
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lemma superCommute_ofCrAnList_ofCrAnList_eq_sum (φs : List 𝓕.CrAnStates) :
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@ -20,7 +20,7 @@ is a generalization of the operator algebra of a field theory with field specifi
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It is an algebra `A` with a map `crAnF` from the creation and annihilation free algebra
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satisfying a number of conditions with respect to super commutators.
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The true operator algebra of a field theory with field specification `𝓕`is an
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example of a proto-operator algebra.-/
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example of a proto-operator algebra. -/
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structure ProtoOperatorAlgebra where
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/-- The algebra representing the operator algebra. -/
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A : Type
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