refactor: Lint
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jstoobysmith
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17 changed files with 36 additions and 43 deletions
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@ -24,7 +24,7 @@ open HepLean.Fin
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-/
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/-- Given a Wick contraction `φsΛ` for a list `φs` of `𝓕.FieldOp`,
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/-- Given a Wick contraction `φsΛ` for a list `φs` of `𝓕.FieldOp`,
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a `𝓕.FieldOp` `φ`, an `i ≤ φs.length` and a `j` which is either `none` or
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some element of `φsΛ.uncontracted`, the new Wick contraction
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`φsΛ.insertAndContract φ i j` is defined by inserting `φ` into `φs` after
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@ -285,7 +285,7 @@ lemma insert_fin_eq_self (φ : 𝓕.FieldOp) {φs : List 𝓕.FieldOp}
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rfl
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/-- For a list `φs` of `𝓕.FieldOp`, a Wick contraction `φsΛ` of `φs`, an element `φ` of
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`𝓕.FieldOp`, a `i ≤ φs.length` a sum over
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`𝓕.FieldOp`, a `i ≤ φs.length` a sum over
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Wick contractions of `φs` with `φ` inserted at `i` is equal to the sum over Wick contractions
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`φsΛ` of just `φs` and the sum over optional uncontracted elements of the `φsΛ`.
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@ -255,7 +255,7 @@ lemma sign_insert_none (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
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exact hG
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/-- For a list `φs = φ₀…φₙ` of `𝓕.FieldOp`, a graded compliant Wick contraction `φsΛ` of `φs`,
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and a `φ` in `𝓕.FieldOp`, the following relation holds
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and a `φ` in `𝓕.FieldOp`, the following relation holds
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`(φsΛ ↩Λ φ 0 none).sign = φsΛ.sign`.
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This is a direct corollary of `sign_insert_none`. -/
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@ -856,7 +856,7 @@ lemma signInsertSome_mul_filter_contracted_of_not_lt (φ : 𝓕.FieldOp) (φs :
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/--
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For a list `φs = φ₀…φₙ` of `𝓕.FieldOp`, a Wick contraction `φsΛ` of `φs`, an element `φ` of
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`𝓕.FieldOp`, a `i ≤ φs.length` and a `k` in `φsΛ.uncontracted` such that `k<i`,
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`𝓕.FieldOp`, a `i ≤ φs.length` and a `k` in `φsΛ.uncontracted` such that `k<i`,
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the sign of `φsΛ ↩Λ φ i (some k)` is equal to the product of
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- the sign associated with moving `φ` through the `φsΛ`-uncontracted `FieldOp` in `φ₀…φₖ`,
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- the sign associated with moving `φ` through all `FieldOp` in `φ₀…φᵢ₋₁`,
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@ -881,7 +881,7 @@ lemma sign_insert_some_of_lt (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
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/--
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For a list `φs = φ₀…φₙ` of `𝓕.FieldOp`, a Wick contraction `φsΛ` of `φs`, an element `φ` of
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`𝓕.FieldOp`, a `i ≤ φs.length` and a `k` in `φsΛ.uncontracted` such that `i ≤ k`,
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`𝓕.FieldOp`, a `i ≤ φs.length` and a `k` in `φsΛ.uncontracted` such that `i ≤ k`,
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the sign of `φsΛ ↩Λ φ i (some k)` is equal to the product of
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- the sign associated with moving `φ` through the `φsΛ`-uncontracted `FieldOp` in `φ₀…φₖ₋₁`,
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- the sign associated with moving `φ` through all the `FieldOp` in `φ₀…φᵢ₋₁`,
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@ -906,7 +906,7 @@ lemma sign_insert_some_of_not_lt (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
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/--
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For a list `φs = φ₀…φₙ` of `𝓕.FieldOp`, a Wick contraction `φsΛ` of `φs`, an element `φ` of
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`𝓕.FieldOp`, and a `k` in `φsΛ.uncontracted`,
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`𝓕.FieldOp`, and a `k` in `φsΛ.uncontracted`,
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the sign of `φsΛ ↩Λ φ 0 (some k)` is equal to the product of
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- the sign associated with moving `φ` through the `φsΛ`-uncontracted `FieldOp` in `φ₀…φₖ₋₁`,
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- the sign of `φsΛ`.
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@ -429,7 +429,7 @@ lemma join_sign {φs : List 𝓕.FieldOp} (φsΛ : WickContraction φs.length)
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(join φsΛ φsucΛ).sign = φsΛ.sign * φsucΛ.sign :=
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join_sign_induction φsΛ φsucΛ hc (φsΛ).1.card rfl
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/-- For a list `φs` of `𝓕.FieldOp`, a Wick contraction `φsΛ` of `φs`,
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/-- For a list `φs` of `𝓕.FieldOp`, a Wick contraction `φsΛ` of `φs`,
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and a Wick contraction `φsucΛ` of `[φsΛ]ᵘᶜ`,
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`(join φsΛ φsucΛ).sign • (join φsΛ φsucΛ).timeContract` is equal to the product of
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- `φsΛ.sign • φsΛ.timeContract` and
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@ -31,7 +31,7 @@ noncomputable def staticContract {φs : List 𝓕.FieldOp}
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superCommute_anPart_ofFieldOp_mem_center _ _⟩
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/-- For a list `φs = φ₀…φₙ` of `𝓕.FieldOp`, a Wick contraction `φsΛ` of `φs`, an element `φ` of
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`𝓕.FieldOp`, and a `i ≤ φs.length` the following relation holds
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`𝓕.FieldOp`, and a `i ≤ φs.length` the following relation holds
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`(φsΛ ↩Λ φ i none).staticContract = φsΛ.staticContract`
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@ -46,10 +46,9 @@ lemma staticContract_insert_none (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
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ext a
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simp
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/--
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For a list `φs = φ₀…φₙ` of `𝓕.FieldOp`, a Wick contraction `φsΛ` of `φs`, an element `φ` of
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`𝓕.FieldOp`, a `i ≤ φs.length` and a `k` in `φsΛ.uncontracted`, then
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`𝓕.FieldOp`, a `i ≤ φs.length` and a `k` in `φsΛ.uncontracted`, then
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`(φsΛ ↩Λ φ i (some k)).staticContract` is equal to the product of
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- `[anPart φ, φs[k]]ₛ` if `i ≤ k` or `[anPart φs[k], φ]ₛ` if `k < i`
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- `φsΛ.staticContract`.
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@ -31,7 +31,7 @@ noncomputable def timeContract {φs : List 𝓕.FieldOp}
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timeContract_mem_center _ _⟩
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/-- For a list `φs = φ₀…φₙ` of `𝓕.FieldOp`, a Wick contraction `φsΛ` of `φs`, an element `φ` of
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`𝓕.FieldOp`, and a `i ≤ φs.length` the following relation holds
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`𝓕.FieldOp`, and a `i ≤ φs.length` the following relation holds
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`(φsΛ ↩Λ φ i none).timeContract = φsΛ.timeContract`
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@ -45,8 +45,8 @@ lemma timeContract_insert_none (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
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ext a
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simp
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/-- For a list `φs = φ₀…φₙ` of `𝓕.FieldOp`, a Wick contraction `φsΛ` of `φs`, an element `φ` of
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`𝓕.FieldOp`, a `i ≤ φs.length` and a `k` in `φsΛ.uncontracted`, then
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/-- For a list `φs = φ₀…φₙ` of `𝓕.FieldOp`, a Wick contraction `φsΛ` of `φs`, an element `φ` of
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`𝓕.FieldOp`, a `i ≤ φs.length` and a `k` in `φsΛ.uncontracted`, then
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`(φsΛ ↩Λ φ i (some k)).timeContract` is equal to the product of
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- `timeContract φ φs[k]` if `i ≤ k` or `timeContract φs[k] φ` if `k < i`
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- `φsΛ.timeContract`.
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@ -80,7 +80,7 @@ lemma timeContract_empty (φs : List 𝓕.FieldOp) :
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open FieldStatistic
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/-! For a list `φs = φ₀…φₙ` of `𝓕.FieldOp`, a Wick contraction `φsΛ` of `φs`, an element `φ` of
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`𝓕.FieldOp`, a `i ≤ φs.length` and a `k` in `φsΛ.uncontracted` such that `i ≤ k`, with the
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`𝓕.FieldOp`, a `i ≤ φs.length` and a `k` in `φsΛ.uncontracted` such that `i ≤ k`, with the
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condition that `φ` has greater or equal time to `φs[k]`, then
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`(φsΛ ↩Λ φ i (some k)).timeContract` is equal to the product of
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- `[anPart φ, φs[k]]ₛ`
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@ -124,7 +124,7 @@ lemma timeContract_insert_some_of_lt
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· exact ht
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/-! For a list `φs = φ₀…φₙ` of `𝓕.FieldOp`, a Wick contraction `φsΛ` of `φs`, an element `φ` of
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`𝓕.FieldOp`, a `i ≤ φs.length` and a `k` in `φsΛ.uncontracted` such that `k < i`, with the
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`𝓕.FieldOp`, a `i ≤ φs.length` and a `k` in `φsΛ.uncontracted` such that `k < i`, with the
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condition that `φs[k]` does not have has greater or equal time to `φ`, then
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`(φsΛ ↩Λ φ i (some k)).timeContract` is equal to the product of
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- `[anPart φ, φs[k]]ₛ`
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@ -315,7 +315,7 @@ lemma take_uncontractedIndexEquiv_symm (k : c.uncontracted) :
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-/
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/-- Given a Wick Contraction `φsΛ` of a list `φs` of `𝓕.FieldOp`. The list
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`φsΛ.uncontractedListGet` of `𝓕.FieldOp` is defined as the list `φs` with
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`φsΛ.uncontractedListGet` of `𝓕.FieldOp` is defined as the list `φs` with
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all contracted positions removed, leaving the uncontracted `𝓕.FieldOp`.
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The notation `[φsΛ]ᵘᶜ` is used for `φsΛ.uncontractedListGet`. -/
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