refactor: Lint
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12 changed files with 30 additions and 38 deletions
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@ -29,7 +29,7 @@ def staticWickTerm {φs : List 𝓕.FieldOp} (φsΛ : WickContraction φs.length
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/-- The static Wick term for the empty contraction of the empty list is `1`. -/
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@[simp]
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lemma staticWickTerm_empty_nil :
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lemma staticWickTerm_empty_nil :
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staticWickTerm (empty (n := ([] : List 𝓕.FieldOp).length)) = 1 := by
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rw [staticWickTerm, uncontractedListGet, nil_zero_uncontractedList]
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simp [sign, empty, staticContract]
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@ -51,7 +51,7 @@ lemma staticWickTerm_insert_zero_none (φ : 𝓕.FieldOp) (φs : List 𝓕.Field
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simp only [staticContract_insert_none, insertAndContract_uncontractedList_none_zero,
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Algebra.smul_mul_assoc]
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/-- Let `φsΛ` be a Wick contraction for `φs = φ₀φ₁…φₙ`. Then`(φsΛ ↩Λ φ 0 (some k)).wickTerm`
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/-- Let `φsΛ` be a Wick contraction for `φs = φ₀φ₁…φₙ`. Then`(φsΛ ↩Λ φ 0 (some k)).wickTerm`
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is equal the product of
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- the sign `𝓢(φ, φ₀…φᵢ₋₁) `
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- the sign `φsΛ.sign`
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@ -62,7 +62,7 @@ is equal the product of
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The proof of this result relies on
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- `staticContract_insert_some_of_lt` to rewrite static
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contractions.
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contractions.
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- `normalOrder_uncontracted_some` to rewrite normal orderings.
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- `sign_insert_some_zero` to rewrite signs.
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-/
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@ -105,14 +105,13 @@ lemma staticWickTerm_insert_zero_some (φ : 𝓕.FieldOp) (φs : List 𝓕.Field
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rw [h1]
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simp
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/--
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Let `φsΛ` be a Wick contraction for `φs = φ₀φ₁…φₙ`. Then
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Let `φsΛ` be a Wick contraction for `φs = φ₀φ₁…φₙ`. Then
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`φ * φsΛ.staticWickTerm = ∑ k, (φsΛ ↩Λ φ i k).wickTerm`
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where the sum is over all `k` in `Option φsΛ.uncontracted` (so either `none` or `some k`).
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The proof of proceeds as follows:
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- `ofFieldOp_mul_normalOrder_ofFieldOpList_eq_sum` is used to expand `φ 𝓝([φsΛ]ᵘᶜ)` as
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- `ofFieldOp_mul_normalOrder_ofFieldOpList_eq_sum` is used to expand `φ 𝓝([φsΛ]ᵘᶜ)` as
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a sum over `k` in `Option φsΛ.uncontracted` of terms involving `[φ, φs[k]]` etc.
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- Then `staticWickTerm_insert_zero_none` and `staticWickTerm_insert_zero_some` are
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used to equate terms.
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