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refactor: Rename InsertList and Insert

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jstoobysmith 2025-01-24 07:18:48 +00:00
parent 321e69e52e
commit fa7536bea9
11 changed files with 301 additions and 302 deletions
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28
HepLean/PerturbationTheory/WickContraction/TimeContract.lean
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@ -29,24 +29,24 @@ noncomputable def timeContract (𝓞 : 𝓕.ProtoOperatorAlgebra) {φs : List
𝓞.timeContract_mem_center _ _⟩
@[simp]
lemma timeContract_insertList_none (𝓞 : 𝓕.ProtoOperatorAlgebra) (φ : 𝓕.States) (φs : List 𝓕.States)
lemma timeContract_insertAndContract_none (𝓞 : 𝓕.ProtoOperatorAlgebra) (φ : 𝓕.States) (φs : List 𝓕.States)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) :
(φsΛ.insertList φ i none).timeContract 𝓞 = φsΛ.timeContract 𝓞 := by
rw [timeContract, insertList_none_prod_contractions]
(φsΛ.insertAndContract φ i none).timeContract 𝓞 = φsΛ.timeContract 𝓞 := by
rw [timeContract, insertAndContract_none_prod_contractions]
congr
ext a
simp
lemma timeConract_insertList_some (𝓞 : 𝓕.ProtoOperatorAlgebra) (φ : 𝓕.States) (φs : List 𝓕.States)
lemma timeConract_insertAndContract_some (𝓞 : 𝓕.ProtoOperatorAlgebra) (φ : 𝓕.States) (φs : List 𝓕.States)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (j : φsΛ.uncontracted) :
(φsΛ.insertList φ i (some j)).timeContract 𝓞 =
(φsΛ.insertAndContract 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 _ _⟩) * φsΛ.timeContract 𝓞 := by
rw [timeContract, insertList_some_prod_contractions]
rw [timeContract, insertAndContract_some_prod_contractions]
congr 1
· simp only [Nat.succ_eq_add_one, insertList_fstFieldOfContract_some_incl, finCongr_apply,
List.get_eq_getElem, insertList_sndFieldOfContract_some_incl, Fin.getElem_fin]
· simp only [Nat.succ_eq_add_one, insertAndContract_fstFieldOfContract_some_incl, finCongr_apply,
List.get_eq_getElem, insertAndContract_sndFieldOfContract_some_incl, Fin.getElem_fin]
split
· simp
· simp
@ -56,15 +56,15 @@ lemma timeConract_insertList_some (𝓞 : 𝓕.ProtoOperatorAlgebra) (φ : 𝓕.
open FieldStatistic
lemma timeConract_insertList_some_eq_mul_contractStateAtIndex_lt
lemma timeConract_insertAndContract_some_eq_mul_contractStateAtIndex_lt
(𝓞 : 𝓕.ProtoOperatorAlgebra) (φ : 𝓕.States) (φs : List 𝓕.States)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (k : φsΛ.uncontracted)
(ht : 𝓕.timeOrderRel φ φs[k.1]) (hik : i < i.succAbove k) :
(φsΛ.insertList φ i (some k)).timeContract 𝓞 =
(φsΛ.insertAndContract φ i (some k)).timeContract 𝓞 =
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ ⟨φs.get, (φsΛ.uncontracted.filter (fun x => x < k))⟩)
• (𝓞.contractStateAtIndex φ [φsΛ]ᵘᶜ
((uncontractedStatesEquiv φs φsΛ) (some k)) * φsΛ.timeContract 𝓞) := by
rw [timeConract_insertList_some]
rw [timeConract_insertAndContract_some]
simp only [Nat.succ_eq_add_one, Fin.getElem_fin, ite_mul, instCommGroup.eq_1,
ProtoOperatorAlgebra.contractStateAtIndex, uncontractedStatesEquiv, Equiv.optionCongr_apply,
Equiv.coe_trans, Option.map_some', Function.comp_apply, finCongr_apply, Fin.coe_cast,
@ -91,15 +91,15 @@ lemma timeConract_insertList_some_eq_mul_contractStateAtIndex_lt
simp only [exchangeSign_mul_self]
· exact ht
lemma timeConract_insertList_some_eq_mul_contractStateAtIndex_not_lt
lemma timeConract_insertAndContract_some_eq_mul_contractStateAtIndex_not_lt
(𝓞 : 𝓕.ProtoOperatorAlgebra) (φ : 𝓕.States) (φs : List 𝓕.States)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (k : φsΛ.uncontracted)
(ht : ¬ 𝓕.timeOrderRel φs[k.1] φ) (hik : ¬ i < i.succAbove k) :
(φsΛ.insertList φ i (some k)).timeContract 𝓞 =
(φsΛ.insertAndContract φ i (some k)).timeContract 𝓞 =
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ ⟨φs.get, (φsΛ.uncontracted.filter (fun x => x ≤ k))⟩)
• (𝓞.contractStateAtIndex φ [φsΛ]ᵘᶜ
((uncontractedStatesEquiv φs φsΛ) (some k)) * φsΛ.timeContract 𝓞) := by
rw [timeConract_insertList_some]
rw [timeConract_insertAndContract_some]
simp only [Nat.succ_eq_add_one, Fin.getElem_fin, ite_mul, instCommGroup.eq_1,
ProtoOperatorAlgebra.contractStateAtIndex, uncontractedStatesEquiv, Equiv.optionCongr_apply,
Equiv.coe_trans, Option.map_some', Function.comp_apply, finCongr_apply, Fin.coe_cast,