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refactor: Lint

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jstoobysmith 2025-01-30 11:08:10 +00:00
parent fc20099282
commit c421746f4b
11 changed files with 63 additions and 62 deletions
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21
HepLean/PerturbationTheory/WicksTheorem.lean
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@ -39,11 +39,11 @@ lemma normalOrder_uncontracted_none (φ : 𝓕.States) (φs : List 𝓕.States)
(i : Fin φs.length.succ) (φsΛ : WickContraction φs.length) :
𝓝(ofFieldOpList [φsΛ ↩Λ φ i none]ᵘᶜ)
= 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ ⟨φs.get, φsΛ.uncontracted.filter (fun x => i.succAbove x < i)⟩) •
𝓝(ofFieldOpList (φ :: [φsΛ]ᵘᶜ)) := by
𝓝(ofFieldOpList (φ :: [φsΛ]ᵘᶜ)) := by
simp only [Nat.succ_eq_add_one, instCommGroup.eq_1]
rw [ofFieldOpList_normalOrder_insert φ [φsΛ]ᵘᶜ
⟨(φsΛ.uncontractedListOrderPos i), by simp [uncontractedListGet]⟩, smul_smul]
trans (1 : ℂ) • (𝓝(ofFieldOpList [φsΛ ↩Λ φ i none]ᵘᶜ))
trans (1 : ℂ) • (𝓝(ofFieldOpList [φsΛ ↩Λ φ i none]ᵘᶜ))
· simp
congr 1
simp only [instCommGroup.eq_1, uncontractedListGet]
@ -108,7 +108,7 @@ where `k'` is the position in `c.uncontractedList` corresponding to `k`.
lemma normalOrder_uncontracted_some (φ : 𝓕.States) (φs : List 𝓕.States)
(i : Fin φs.length.succ) (φsΛ : WickContraction φs.length) (k : φsΛ.uncontracted) :
𝓝(ofFieldOpList [φsΛ ↩Λ φ i (some k)]ᵘᶜ)
= 𝓝(ofFieldOpList (optionEraseZ [φsΛ]ᵘᶜ φ ((uncontractedStatesEquiv φs φsΛ) k))) := by
= 𝓝(ofFieldOpList (optionEraseZ [φsΛ]ᵘᶜ φ ((uncontractedStatesEquiv φs φsΛ) k))) := by
simp only [Nat.succ_eq_add_one, insertAndContract, optionEraseZ, uncontractedStatesEquiv,
Equiv.optionCongr_apply, Equiv.coe_trans, Option.map_some', Function.comp_apply, finCongr_apply,
Fin.coe_cast, uncontractedListGet]
@ -153,9 +153,9 @@ The proof of this result relies primarily on:
lemma wick_term_none_eq_wick_term_cons (φ : 𝓕.States) (φs : List 𝓕.States)
(i : Fin φs.length.succ) (φsΛ : WickContraction φs.length) :
(φsΛ ↩Λ φ i none).sign • (φsΛ ↩Λ φ i none).timeContract
* 𝓝(ofFieldOpList [φsΛ ↩Λ φ i none]ᵘᶜ) =
* 𝓝(ofFieldOpList [φsΛ ↩Λ φ i none]ᵘᶜ) =
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ ⟨φs.get, (Finset.univ.filter (fun k => i.succAbove k < i))⟩)
• (φsΛ.sign • φsΛ.timeContract * 𝓝(ofFieldOpList (φ :: [φsΛ]ᵘᶜ))) := by
• (φsΛ.sign • φsΛ.timeContract * 𝓝(ofFieldOpList (φ :: [φsΛ]ᵘᶜ))) := by
by_cases hg : GradingCompliant φs φsΛ
· rw [normalOrder_uncontracted_none, sign_insert_none]
simp only [Nat.succ_eq_add_one, timeContract_insertAndContract_none, instCommGroup.eq_1,
@ -203,7 +203,7 @@ lemma wick_term_some_eq_wick_term_optionEraseZ (φ : 𝓕.States) (φs : List
(hlt : ∀ (k : Fin φs.length), timeOrderRel φ φs[k])
(hn : ∀ (k : Fin φs.length), i.succAbove k < i → ¬ timeOrderRel φs[k] φ) :
(φsΛ ↩Λ φ i (some k)).sign • (φsΛ ↩Λ φ i (some k)).timeContract
* 𝓝(ofFieldOpList [φsΛ ↩Λ φ i (some k)]ᵘᶜ) =
* 𝓝(ofFieldOpList [φsΛ ↩Λ φ i (some k)]ᵘᶜ) =
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ ⟨φs.get, (Finset.univ.filter (fun x => i.succAbove x < i))⟩)
• (φsΛ.sign • (contractStateAtIndex φ [φsΛ]ᵘᶜ
((uncontractedStatesEquiv φs φsΛ) (some k)) * φsΛ.timeContract)
@ -277,7 +277,7 @@ The proof of this result primarily depends on
lemma wick_term_cons_eq_sum_wick_term (φ : 𝓕.States) (φs : List 𝓕.States) (i : Fin φs.length.succ)
(φsΛ : WickContraction φs.length) (hlt : ∀ (k : Fin φs.length), timeOrderRel φ φs[k])
(hn : ∀ (k : Fin φs.length), i.succAbove k < i → ¬timeOrderRel φs[k] φ) :
(φsΛ.sign • φsΛ.timeContract) * ((ofFieldOp φ) * 𝓝(ofFieldOpList [φsΛ]ᵘᶜ)) =
(φsΛ.sign • φsΛ.timeContract) * ((ofFieldOp φ) * 𝓝(ofFieldOpList [φsΛ]ᵘᶜ)) =
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ ⟨φs.get, (Finset.univ.filter (fun x => i.succAbove x < i))⟩) •
∑ (k : Option φsΛ.uncontracted), ((φsΛ ↩Λ φ i k).sign •
(φsΛ ↩Λ φ i k).timeContract * (𝓝(ofFieldOpList [φsΛ ↩Λ φ i k]ᵘᶜ))) := by
@ -318,7 +318,7 @@ lemma wick_term_cons_eq_sum_wick_term (φ : 𝓕.States) (φs : List 𝓕.States
/-- Wick's theorem for the empty list. -/
lemma wicks_theorem_nil :
𝓣(ofFieldOpList (𝓕 := 𝓕) []) = ∑ (nilΛ : WickContraction [].length),
(nilΛ.sign (𝓕 := 𝓕) • nilΛ.timeContract) * 𝓝(ofFieldOpList [nilΛ]ᵘᶜ) := by
(nilΛ.sign (𝓕 := 𝓕) • nilΛ.timeContract) * 𝓝(ofFieldOpList [nilΛ]ᵘᶜ) := by
rw [timeOrder_ofFieldOpList_nil]
simp only [map_one, List.length_nil, Algebra.smul_mul_assoc]
rw [sum_WickContraction_nil, uncontractedListGet, nil_zero_uncontractedList]
@ -333,8 +333,7 @@ lemma wicks_theorem_nil :
rfl
lemma wicks_theorem_congr {φs φs' : List 𝓕.States} (h : φs = φs') :
∑ (φsΛ : WickContraction φs.length), (φsΛ.sign • φsΛ.timeContract) *
𝓝(ofFieldOpList [φsΛ]ᵘᶜ)
∑ (φsΛ : WickContraction φs.length), (φsΛ.sign • φsΛ.timeContract) * 𝓝(ofFieldOpList [φsΛ]ᵘᶜ)
= ∑ (φs'Λ : WickContraction φs'.length), (φs'Λ.sign • φs'Λ.timeContract) *
𝓝(ofFieldOpList [φs'Λ]ᵘᶜ) := by
subst h
@ -379,7 +378,7 @@ theorem wicks_theorem : (φs : List 𝓕.States) → 𝓣(ofFieldOpList φs) =
trans (1 : ℂ) • ∑ k : Option { x // x ∈ c.uncontracted }, sign
(List.insertIdx (↑(maxTimeFieldPosFin φ φs)) (maxTimeField φ φs) (eraseMaxTimeField φ φs))
(c ↩Λ (maxTimeField φ φs) (maxTimeFieldPosFin φ φs) k) •
↑((c ↩Λ (maxTimeField φ φs) (maxTimeFieldPosFin φ φs) k).timeContract ) *
↑((c ↩Λ (maxTimeField φ φs) (maxTimeFieldPosFin φ φs) k).timeContract) *
𝓝(ofFieldOpList (List.map (List.insertIdx (↑(maxTimeFieldPosFin φ φs))
(maxTimeField φ φs) (eraseMaxTimeField φ φs)).get
(c ↩Λ (maxTimeField φ φs) (maxTimeFieldPosFin φ φs) k).uncontractedList))