doc: Edits to Wick theorem docs
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@ -17,8 +17,8 @@ variable {𝓕 : FieldSpecification}
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/-- For a field specification `𝓕`, `𝓕.normalOrderRel` is a relation on `𝓕.CrAnFieldOp`
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representing normal ordering. It is defined such that `𝓕.normalOrderRel φ₀ φ₁`
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is true if one of the following is true
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- `φ₀` is a creation operator
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- `φ₁` is an annihilation.
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- `φ₀` is a field creation operator
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- `φ₁` is a field annihilation operator.
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Thus, colloquially `𝓕.normalOrderRel φ₀ φ₁` says the creation operators are 'less then'
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annihilation operators. -/
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@ -344,11 +344,12 @@ lemma normalOrderList_eraseIdx_normalOrderEquiv {φs : List 𝓕.CrAnFieldOp} (n
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rw [HepLean.List.eraseIdx_insertionSort_fin]
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/-- For a field specification `𝓕`, a list `φs = φ₀…φₙ` of `𝓕.CrAnFieldOp` and an `i < φs.length`,
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the following relation holds
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then
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`normalOrderSign (φ₀…φᵢ₋₁φᵢ₊₁…φₙ)` is equal to the product of
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- `normalOrderSign φ₀…φₙ`,
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- `𝓢(φᵢ, φ₀…φᵢ₋₁)` i.e. the sign needed to remove `φᵢ` from `φ₀…φₙ`,
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- `𝓢(φᵢ, _)` where `_` is the list of elements appearing before `φᵢ` after normal ordering. I.e.
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- `𝓢(φᵢ, _)` where `_` is the list of elements appearing before `φᵢ` after normal ordering,
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i.e.
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the sign needed to insert `φᵢ` back into the normal-ordered list at the correct place. -/
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lemma normalOrderSign_eraseIdx (φs : List 𝓕.CrAnFieldOp) (i : Fin φs.length) :
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normalOrderSign (φs.eraseIdx i) = normalOrderSign φs *
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