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refactor: Simplify some notation

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jstoobysmith 2025-01-24 05:19:04 +00:00
parent 7d053695dd
commit 6701ee7b37
8 changed files with 106 additions and 111 deletions
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8
HepLean/PerturbationTheory/WickContraction/TimeContract.lean
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@ -30,7 +30,7 @@ noncomputable def timeContract (𝓞 : 𝓕.ProtoOperatorAlgebra) {φs : List
@[simp]
lemma timeContract_insertList_none (𝓞 : 𝓕.ProtoOperatorAlgebra) (φ : 𝓕.States) (φs : List 𝓕.States)
(c : WickContraction φs.length) (i : Fin φs.length.succ) :
(c.insertList φ φs i none).timeContract 𝓞 = c.timeContract 𝓞 := by
(c.insertList φ i none).timeContract 𝓞 = c.timeContract 𝓞 := by
rw [timeContract, insertList_none_prod_contractions]
congr
ext a
@ -38,7 +38,7 @@ lemma timeContract_insertList_none (𝓞 : 𝓕.ProtoOperatorAlgebra) (φ : 𝓕
lemma timeConract_insertList_some (𝓞 : 𝓕.ProtoOperatorAlgebra) (φ : 𝓕.States) (φs : List 𝓕.States)
(c : WickContraction φs.length) (i : Fin φs.length.succ) (j : c.uncontracted) :
(c.insertList φ φs i (some j)).timeContract 𝓞 =
(c.insertList φ i (some j)).timeContract 𝓞 =
(if i < i.succAbove j then
⟨𝓞.timeContract φ φs[j.1], 𝓞.timeContract_mem_center _ _⟩
else ⟨𝓞.timeContract φs[j.1] φ, 𝓞.timeContract_mem_center _ _⟩) * c.timeContract 𝓞 := by
@ -59,7 +59,7 @@ lemma timeConract_insertList_some_eq_mul_contractStateAtIndex_lt
(𝓞 : 𝓕.ProtoOperatorAlgebra) (φ : 𝓕.States) (φs : List 𝓕.States)
(c : WickContraction φs.length) (i : Fin φs.length.succ) (k : c.uncontracted)
(ht : 𝓕.timeOrderRel φ φs[k.1]) (hik : i < i.succAbove k) :
(c.insertList φ φs i (some k)).timeContract 𝓞 =
(c.insertList φ i (some k)).timeContract 𝓞 =
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ ⟨φs.get, (c.uncontracted.filter (fun x => x < k))⟩)
• (𝓞.contractStateAtIndex φ (List.map φs.get c.uncontractedList)
((uncontractedStatesEquiv φs c) (some k)) * c.timeContract 𝓞) := by
@ -94,7 +94,7 @@ lemma timeConract_insertList_some_eq_mul_contractStateAtIndex_not_lt
(𝓞 : 𝓕.ProtoOperatorAlgebra) (φ : 𝓕.States) (φs : List 𝓕.States)
(c : WickContraction φs.length) (i : Fin φs.length.succ) (k : c.uncontracted)
(ht : ¬ 𝓕.timeOrderRel φs[k.1] φ) (hik : ¬ i < i.succAbove k) :
(c.insertList φ φs i (some k)).timeContract 𝓞 =
(c.insertList φ i (some k)).timeContract 𝓞 =
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ ⟨φs.get, (c.uncontracted.filter (fun x => x ≤ k))⟩)
• (𝓞.contractStateAtIndex φ (List.map φs.get c.uncontractedList)
((uncontractedStatesEquiv φs c) (some k)) * c.timeContract 𝓞) := by