refactor: Rename ofCrAnFieldOp to ofCrAnOp

2025-02-06 10:09:30 +00:00 · 2025-02-06 10:09:30 +00:00 · 2d561dd89d
commit 2d561dd89d
parent 8cc273fe38
7 changed files with 165 additions and 165 deletions
--- a/HepLean/PerturbationTheory/FieldOpAlgebra/Basic.lean
+++ b/HepLean/PerturbationTheory/FieldOpAlgebra/Basic.lean
@ -473,35 +473,35 @@ lemma ofFieldOpList_singleton (φ : 𝓕.FieldOp) :
  simp only [ofFieldOpList, ofFieldOp, ofFieldOpListF_singleton]

 /-- An element of `FieldOpAlgebra` from a `CrAnFieldOp`. -/
-def ofCrAnFieldOp (φ : 𝓕.CrAnFieldOp) : 𝓕.FieldOpAlgebra := ι (ofCrAnOpF φ)
+def ofCrAnOp (φ : 𝓕.CrAnFieldOp) : 𝓕.FieldOpAlgebra := ι (ofCrAnOpF φ)

-lemma ofCrAnFieldOp_eq_ι_ofCrAnOpF (φ : 𝓕.CrAnFieldOp) :
-    ofCrAnFieldOp φ = ι (ofCrAnOpF φ) := rfl
+lemma ofCrAnOp_eq_ι_ofCrAnOpF (φ : 𝓕.CrAnFieldOp) :
+    ofCrAnOp φ = ι (ofCrAnOpF φ) := rfl

 lemma ofFieldOp_eq_sum (φ : 𝓕.FieldOp) :
-    ofFieldOp φ = (∑ i : 𝓕.fieldOpToCrAnType φ, ofCrAnFieldOp ⟨φ, i⟩) := by
+    ofFieldOp φ = (∑ i : 𝓕.fieldOpToCrAnType φ, ofCrAnOp ⟨φ, i⟩) := by
  rw [ofFieldOp, ofFieldOpF]
  simp only [map_sum]
  rfl

 /-- An element of `FieldOpAlgebra` from a list of `CrAnFieldOp`. -/
-def ofCrAnFieldOpList (φs : List 𝓕.CrAnFieldOp) : 𝓕.FieldOpAlgebra := ι (ofCrAnListF φs)
+def ofCrAnOpList (φs : List 𝓕.CrAnFieldOp) : 𝓕.FieldOpAlgebra := ι (ofCrAnListF φs)

-lemma ofCrAnFieldOpList_eq_ι_ofCrAnListF (φs : List 𝓕.CrAnFieldOp) :
-    ofCrAnFieldOpList φs = ι (ofCrAnListF φs) := rfl
+lemma ofCrAnOpList_eq_ι_ofCrAnListF (φs : List 𝓕.CrAnFieldOp) :
+    ofCrAnOpList φs = ι (ofCrAnListF φs) := rfl

-lemma ofCrAnFieldOpList_append (φs ψs : List 𝓕.CrAnFieldOp) :
-    ofCrAnFieldOpList (φs ++ ψs) = ofCrAnFieldOpList φs * ofCrAnFieldOpList ψs := by
-  simp only [ofCrAnFieldOpList]
+lemma ofCrAnOpList_append (φs ψs : List 𝓕.CrAnFieldOp) :
+    ofCrAnOpList (φs ++ ψs) = ofCrAnOpList φs * ofCrAnOpList ψs := by
+  simp only [ofCrAnOpList]
  rw [ofCrAnListF_append]
  simp

-lemma ofCrAnFieldOpList_singleton (φ : 𝓕.CrAnFieldOp) :
-    ofCrAnFieldOpList [φ] = ofCrAnFieldOp φ := by
-  simp only [ofCrAnFieldOpList, ofCrAnFieldOp, ofCrAnListF_singleton]
+lemma ofCrAnOpList_singleton (φ : 𝓕.CrAnFieldOp) :
+    ofCrAnOpList [φ] = ofCrAnOp φ := by
+  simp only [ofCrAnOpList, ofCrAnOp, ofCrAnListF_singleton]

 lemma ofFieldOpList_eq_sum (φs : List 𝓕.FieldOp) :
-    ofFieldOpList φs = ∑ s : CrAnSection φs, ofCrAnFieldOpList s.1 := by
+    ofFieldOpList φs = ∑ s : CrAnSection φs, ofCrAnOpList s.1 := by
  rw [ofFieldOpList, ofFieldOpListF_sum]
  simp only [map_sum]
  rfl
@ -519,13 +519,13 @@ lemma anPart_negAsymp (φ : (Σ f, 𝓕.AsymptoticLabel f) × (Fin 3 → ℝ)) :
@[simp]
 lemma anPart_position (φ : (Σ f, 𝓕.PositionLabel f) × SpaceTime) :
    anPart (FieldOp.position φ) =
-    ofCrAnFieldOp ⟨FieldOp.position φ, CreateAnnihilate.annihilate⟩ := by
-  simp [anPart, ofCrAnFieldOp]
+    ofCrAnOp ⟨FieldOp.position φ, CreateAnnihilate.annihilate⟩ := by
+  simp [anPart, ofCrAnOp]

@[simp]
 lemma anPart_posAsymp (φ : (Σ f, 𝓕.AsymptoticLabel f) × (Fin 3 → ℝ)) :
-    anPart (FieldOp.outAsymp φ) = ofCrAnFieldOp ⟨FieldOp.outAsymp φ, ()⟩ := by
-  simp [anPart, ofCrAnFieldOp]
+    anPart (FieldOp.outAsymp φ) = ofCrAnOp ⟨FieldOp.outAsymp φ, ()⟩ := by
+  simp [anPart, ofCrAnOp]

 /-- The creation part of a state. -/
 def crPart (φ : 𝓕.FieldOp) : 𝓕.FieldOpAlgebra := ι (crPartF φ)
@ -534,14 +534,14 @@ lemma crPart_eq_ι_crPartF (φ : 𝓕.FieldOp) : crPart φ = ι (crPartF φ) :=

@[simp]
 lemma crPart_negAsymp (φ : (Σ f, 𝓕.AsymptoticLabel f) × (Fin 3 → ℝ)) :
-    crPart (FieldOp.inAsymp φ) = ofCrAnFieldOp ⟨FieldOp.inAsymp φ, ()⟩ := by
-  simp [crPart, ofCrAnFieldOp]
+    crPart (FieldOp.inAsymp φ) = ofCrAnOp ⟨FieldOp.inAsymp φ, ()⟩ := by
+  simp [crPart, ofCrAnOp]

@[simp]
 lemma crPart_position (φ : (Σ f, 𝓕.PositionLabel f) × SpaceTime) :
    crPart (FieldOp.position φ) =
-    ofCrAnFieldOp ⟨FieldOp.position φ, CreateAnnihilate.create⟩ := by
-  simp [crPart, ofCrAnFieldOp]
+    ofCrAnOp ⟨FieldOp.position φ, CreateAnnihilate.create⟩ := by
+  simp [crPart, ofCrAnOp]

@[simp]
 lemma crPart_posAsymp (φ : (Σ f, 𝓕.AsymptoticLabel f) × (Fin 3 → ℝ)) :
--- a/HepLean/PerturbationTheory/FieldOpAlgebra/Grading.lean
+++ b/HepLean/PerturbationTheory/FieldOpAlgebra/Grading.lean
@ -20,14 +20,14 @@ variable {𝓕 : FieldSpecification}

 /-- The submodule of `𝓕.FieldOpAlgebra` spanned by lists of field statistic `f`. -/
 def statSubmodule (f : FieldStatistic) : Submodule ℂ 𝓕.FieldOpAlgebra :=
-  Submodule.span ℂ {a | ∃ φs, a = ofCrAnFieldOpList φs ∧ (𝓕 |>ₛ φs) = f}
+  Submodule.span ℂ {a | ∃ φs, a = ofCrAnOpList φs ∧ (𝓕 |>ₛ φs) = f}

-lemma ofCrAnFieldOpList_mem_statSubmodule_of_eq (φs : List 𝓕.CrAnFieldOp) (f : FieldStatistic)
-    (h : (𝓕 |>ₛ φs) = f) : ofCrAnFieldOpList φs ∈ statSubmodule f :=
+lemma ofCrAnOpList_mem_statSubmodule_of_eq (φs : List 𝓕.CrAnFieldOp) (f : FieldStatistic)
+    (h : (𝓕 |>ₛ φs) = f) : ofCrAnOpList φs ∈ statSubmodule f :=
  Submodule.mem_span.mpr fun _ a => a ⟨φs, ⟨rfl, h⟩⟩

-lemma ofCrAnFieldOpList_mem_statSubmodule (φs : List 𝓕.CrAnFieldOp) :
-    ofCrAnFieldOpList φs ∈ statSubmodule (𝓕 |>ₛ φs) :=
+lemma ofCrAnOpList_mem_statSubmodule (φs : List 𝓕.CrAnFieldOp) :
+    ofCrAnOpList φs ∈ statSubmodule (𝓕 |>ₛ φs) :=
  Submodule.mem_span.mpr fun _ a => a ⟨φs, ⟨rfl, rfl⟩⟩

 lemma mem_bosonic_of_mem_free_bosonic (a : 𝓕.FieldOpFreeAlgebra)
@ -40,7 +40,7 @@ lemma mem_bosonic_of_mem_free_bosonic (a : 𝓕.FieldOpFreeAlgebra)
    simp only [Set.mem_setOf_eq] at hx
    obtain ⟨φs, rfl, h⟩ := hx
    simp [p]
-    apply ofCrAnFieldOpList_mem_statSubmodule_of_eq
+    apply ofCrAnOpList_mem_statSubmodule_of_eq
    exact h
  · simp only [map_zero, p]
    exact Submodule.zero_mem (statSubmodule bosonic)
@ -61,7 +61,7 @@ lemma mem_fermionic_of_mem_free_fermionic (a : 𝓕.FieldOpFreeAlgebra)
    simp only [Set.mem_setOf_eq] at hx
    obtain ⟨φs, rfl, h⟩ := hx
    simp [p]
-    apply ofCrAnFieldOpList_mem_statSubmodule_of_eq
+    apply ofCrAnOpList_mem_statSubmodule_of_eq
    exact h
  · simp only [map_zero, p]
    exact Submodule.zero_mem (statSubmodule fermionic)
@ -204,7 +204,7 @@ lemma bosonicProj_mem_bosonic (a : 𝓕.FieldOpAlgebra) (ha : a ∈ statSubmodul
    simp only [p]
    apply Subtype.eq
    simp only
-    rw [ofCrAnFieldOpList]
+    rw [ofCrAnOpList]
    rw [bosonicProj_eq_bosonicProjFree]
    rw [bosonicProjFree_eq_ι_bosonicProjF]
    rw [bosonicProjF_of_mem_bosonic]
@ -227,7 +227,7 @@ lemma fermionicProj_mem_fermionic (a : 𝓕.FieldOpAlgebra) (ha : a ∈ statSubm
    simp only [p]
    apply Subtype.eq
    simp only
-    rw [ofCrAnFieldOpList]
+    rw [ofCrAnOpList]
    rw [fermionicProj_eq_fermionicProjFree]
    rw [fermionicProjFree_eq_ι_fermionicProjF]
    rw [fermionicProjF_of_mem_fermionic]
@ -384,7 +384,7 @@ lemma directSum_eq_bosonic_plus_fermionic
    abel

 /-- For a field statistic `𝓕`, the algebra `𝓕.FieldOpAlgebra` is graded by `FieldStatistic`.
-  Those `ofCrAnFieldOpList φs` for which `φs` has `bosonic` statistics span one part of the grading,
+  Those `ofCrAnOpList φs` for which `φs` has `bosonic` statistics span one part of the grading,
  whilst those where `φs` has `fermionic` statistics span the other part of the grading. -/
 instance fieldOpAlgebraGrade : GradedAlgebra (A := 𝓕.FieldOpAlgebra) statSubmodule where
  one_mem := by
@ -392,7 +392,7 @@ instance fieldOpAlgebraGrade : GradedAlgebra (A := 𝓕.FieldOpAlgebra) statSubm
    refine Submodule.mem_span.mpr fun p a => a ?_
    simp only [Set.mem_setOf_eq]
    use []
-    simp only [ofCrAnFieldOpList, ofCrAnListF_nil, map_one, ofList_empty, true_and]
+    simp only [ofCrAnOpList, ofCrAnListF_nil, map_one, ofList_empty, true_and]
    rfl
  mul_mem f1 f2 a1 a2 h1 h2 := by
    let p (a2 : 𝓕.FieldOpAlgebra) (hx : a2 ∈ statSubmodule f2) : Prop :=
@ -404,13 +404,13 @@ instance fieldOpAlgebraGrade : GradedAlgebra (A := 𝓕.FieldOpAlgebra) statSubm
      obtain ⟨φs, rfl, h⟩ := hx
      simp only [p]
      let p (a1 : 𝓕.FieldOpAlgebra) (hx : a1 ∈ statSubmodule f1) : Prop :=
-        a1 * ofCrAnFieldOpList φs ∈ statSubmodule (f1 + f2)
+        a1 * ofCrAnOpList φs ∈ statSubmodule (f1 + f2)
      change p a1 h1
      apply Submodule.span_induction (p := p)
      · intro y hy
        obtain ⟨φs', rfl, h'⟩ := hy
        simp only [p]
-        rw [← ofCrAnFieldOpList_append]
+        rw [← ofCrAnOpList_append]
        refine Submodule.mem_span.mpr fun p a => a ?_
        simp only [Set.mem_setOf_eq]
        use φs' ++ φs
--- a/HepLean/PerturbationTheory/FieldOpAlgebra/NormalOrder/Lemmas.lean
+++ b/HepLean/PerturbationTheory/FieldOpAlgebra/NormalOrder/Lemmas.lean
@ -27,16 +27,16 @@ variable {𝓕 : FieldSpecification}
 lemma normalOrder_eq_ι_normalOrderF (a : 𝓕.FieldOpFreeAlgebra) :
    𝓝(ι a) = ι 𝓝ᶠ(a) := rfl

-lemma normalOrder_ofCrAnFieldOpList (φs : List 𝓕.CrAnFieldOp) :
-    𝓝(ofCrAnFieldOpList φs) = normalOrderSign φs • ofCrAnFieldOpList (normalOrderList φs) := by
-  rw [ofCrAnFieldOpList, normalOrder_eq_ι_normalOrderF, normalOrderF_ofCrAnListF]
+lemma normalOrder_ofCrAnOpList (φs : List 𝓕.CrAnFieldOp) :
+    𝓝(ofCrAnOpList φs) = normalOrderSign φs • ofCrAnOpList (normalOrderList φs) := by
+  rw [ofCrAnOpList, normalOrder_eq_ι_normalOrderF, normalOrderF_ofCrAnListF]
  rfl

@[simp]
 lemma normalOrder_one_eq_one : normalOrder (𝓕 := 𝓕) 1 = 1 := by
-  have h1 : 1 = ofCrAnFieldOpList (𝓕 := 𝓕) [] := by simp [ofCrAnFieldOpList]
+  have h1 : 1 = ofCrAnOpList (𝓕 := 𝓕) [] := by simp [ofCrAnOpList]
  rw [h1]
-  rw [normalOrder_ofCrAnFieldOpList]
+  rw [normalOrder_ofCrAnOpList]
  simp

@[simp]
@ -48,14 +48,14 @@ lemma normalOrder_ofFieldOpList_nil : normalOrder (𝓕 := 𝓕) (ofFieldOpList
  simp

@[simp]
-lemma normalOrder_ofCrAnFieldOpList_nil : normalOrder (𝓕 := 𝓕) (ofCrAnFieldOpList []) = 1 := by
-  rw [normalOrder_ofCrAnFieldOpList]
+lemma normalOrder_ofCrAnOpList_nil : normalOrder (𝓕 := 𝓕) (ofCrAnOpList []) = 1 := by
+  rw [normalOrder_ofCrAnOpList]
  simp only [normalOrderSign_nil, normalOrderList_nil, one_smul]
  rfl

-lemma ofCrAnFieldOpList_eq_normalOrder (φs : List 𝓕.CrAnFieldOp) :
-    ofCrAnFieldOpList (normalOrderList φs) = normalOrderSign φs • 𝓝(ofCrAnFieldOpList φs) := by
-  rw [normalOrder_ofCrAnFieldOpList, smul_smul, normalOrderSign, Wick.koszulSign_mul_self,
+lemma ofCrAnOpList_eq_normalOrder (φs : List 𝓕.CrAnFieldOp) :
+    ofCrAnOpList (normalOrderList φs) = normalOrderSign φs • 𝓝(ofCrAnOpList φs) := by
+  rw [normalOrder_ofCrAnOpList, smul_smul, normalOrderSign, Wick.koszulSign_mul_self,
    one_smul]

 lemma normalOrder_normalOrder_mid (a b c : 𝓕.FieldOpAlgebra) :
@ -165,16 +165,16 @@ lemma normalOrder_ofFieldOp_ofFieldOp_swap (φ φ' : 𝓕.FieldOp) :
  rw [ofFieldOp_mul_ofFieldOp_eq_superCommute]
  simp

-lemma normalOrder_ofCrAnFieldOp_ofCrAnFieldOpList (φ : 𝓕.CrAnFieldOp)
-    (φs : List 𝓕.CrAnFieldOp) : 𝓝(ofCrAnFieldOp φ * ofCrAnFieldOpList φs) =
-    𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) • 𝓝(ofCrAnFieldOpList φs * ofCrAnFieldOp φ) := by
-  rw [← ofCrAnFieldOpList_singleton, ofCrAnFieldOpList_mul_ofCrAnFieldOpList_eq_superCommute]
+lemma normalOrder_ofCrAnOp_ofCrAnOpList (φ : 𝓕.CrAnFieldOp)
+    (φs : List 𝓕.CrAnFieldOp) : 𝓝(ofCrAnOp φ * ofCrAnOpList φs) =
+    𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) • 𝓝(ofCrAnOpList φs * ofCrAnOp φ) := by
+  rw [← ofCrAnOpList_singleton, ofCrAnOpList_mul_ofCrAnOpList_eq_superCommute]
  simp

-lemma normalOrder_ofCrAnFieldOp_ofFieldOpList_swap (φ : 𝓕.CrAnFieldOp) (φ' : List 𝓕.FieldOp) :
-    𝓝(ofCrAnFieldOp φ * ofFieldOpList φ') = 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') •
-    𝓝(ofFieldOpList φ' * ofCrAnFieldOp φ) := by
-  rw [← ofCrAnFieldOpList_singleton, ofCrAnFieldOpList_mul_ofFieldOpList_eq_superCommute]
+lemma normalOrder_ofCrAnOp_ofFieldOpList_swap (φ : 𝓕.CrAnFieldOp) (φ' : List 𝓕.FieldOp) :
+    𝓝(ofCrAnOp φ * ofFieldOpList φ') = 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') •
+    𝓝(ofFieldOpList φ' * ofCrAnOp φ) := by
+  rw [← ofCrAnOpList_singleton, ofCrAnOpList_mul_ofFieldOpList_eq_superCommute]
  simp

 lemma normalOrder_anPart_ofFieldOpList_swap (φ : 𝓕.FieldOp) (φ' : List 𝓕.FieldOp) :
@ -184,11 +184,11 @@ lemma normalOrder_anPart_ofFieldOpList_swap (φ : 𝓕.FieldOp) (φ' : List 𝓕
    simp
  | .position φ =>
    simp only [anPart_position, instCommGroup.eq_1]
-    rw [normalOrder_ofCrAnFieldOp_ofFieldOpList_swap]
+    rw [normalOrder_ofCrAnOp_ofFieldOpList_swap]
    rfl
  | .outAsymp φ =>
    simp only [anPart_posAsymp, instCommGroup.eq_1]
-    rw [normalOrder_ofCrAnFieldOp_ofFieldOpList_swap]
+    rw [normalOrder_ofCrAnOp_ofFieldOpList_swap]
    rfl

 lemma normalOrder_ofFieldOpList_anPart_swap (φ : 𝓕.FieldOp) (φ' : List 𝓕.FieldOp) :
@ -224,18 +224,18 @@ The proof of this result ultimetly depends on
 - `superCommuteF_ofCrAnListF_ofFieldOpListF_eq_sum`
 - `normalOrderSign_eraseIdx`
 -/
-lemma ofCrAnFieldOp_superCommute_normalOrder_ofCrAnFieldOpList_sum (φ : 𝓕.CrAnFieldOp)
-    (φs : List 𝓕.CrAnFieldOp) : [ofCrAnFieldOp φ, 𝓝(ofCrAnFieldOpList φs)]ₛ = ∑ n : Fin φs.length,
-    𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ (φs.take n)) • [ofCrAnFieldOp φ, ofCrAnFieldOp φs[n]]ₛ
-    * 𝓝(ofCrAnFieldOpList (φs.eraseIdx n)) := by
-  rw [normalOrder_ofCrAnFieldOpList, map_smul]
-  rw [superCommute_ofCrAnFieldOp_ofCrAnFieldOpList_eq_sum, Finset.smul_sum,
+lemma ofCrAnOp_superCommute_normalOrder_ofCrAnOpList_sum (φ : 𝓕.CrAnFieldOp)
+    (φs : List 𝓕.CrAnFieldOp) : [ofCrAnOp φ, 𝓝(ofCrAnOpList φs)]ₛ = ∑ n : Fin φs.length,
+    𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ (φs.take n)) • [ofCrAnOp φ, ofCrAnOp φs[n]]ₛ
+    * 𝓝(ofCrAnOpList (φs.eraseIdx n)) := by
+  rw [normalOrder_ofCrAnOpList, map_smul]
+  rw [superCommute_ofCrAnOp_ofCrAnOpList_eq_sum, Finset.smul_sum,
    sum_normalOrderList_length]
  congr
  funext n
  simp only [instCommGroup.eq_1, List.get_eq_getElem, normalOrderList_get_normalOrderEquiv,
    normalOrderList_eraseIdx_normalOrderEquiv, Algebra.smul_mul_assoc, Fin.getElem_fin]
-  rw [ofCrAnFieldOpList_eq_normalOrder, mul_smul_comm, smul_smul, smul_smul]
+  rw [ofCrAnOpList_eq_normalOrder, mul_smul_comm, smul_smul, smul_smul]
  by_cases hs : (𝓕 |>ₛ φ) = (𝓕 |>ₛ φs[n])
  · congr
    erw [normalOrderSign_eraseIdx, ← hs]
@ -250,14 +250,14 @@ lemma ofCrAnFieldOp_superCommute_normalOrder_ofCrAnFieldOpList_sum (φ : 𝓕.Cr
  · erw [superCommute_diff_statistic hs]
    simp

-lemma ofCrAnFieldOp_superCommute_normalOrder_ofFieldOpList_sum (φ : 𝓕.CrAnFieldOp)
+lemma ofCrAnOp_superCommute_normalOrder_ofFieldOpList_sum (φ : 𝓕.CrAnFieldOp)
    (φs : List 𝓕.FieldOp) :
-    [ofCrAnFieldOp φ, 𝓝(ofFieldOpList φs)]ₛ = ∑ n : Fin φs.length, 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ (φs.take n)) •
-    [ofCrAnFieldOp φ, ofFieldOp φs[n]]ₛ * 𝓝(ofFieldOpList (φs.eraseIdx n)) := by
+    [ofCrAnOp φ, 𝓝(ofFieldOpList φs)]ₛ = ∑ n : Fin φs.length, 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ (φs.take n)) •
+    [ofCrAnOp φ, ofFieldOp φs[n]]ₛ * 𝓝(ofFieldOpList (φs.eraseIdx n)) := by
  conv_lhs =>
    rw [ofFieldOpList_eq_sum, map_sum, map_sum]
    enter [2, s]
-    rw [ofCrAnFieldOp_superCommute_normalOrder_ofCrAnFieldOpList_sum, CrAnSection.sum_over_length]
+    rw [ofCrAnOp_superCommute_normalOrder_ofCrAnOpList_sum, CrAnSection.sum_over_length]
    enter [2, n]
    rw [CrAnSection.take_statistics_eq_take_state_statistics, smul_mul_assoc]
  rw [Finset.sum_comm]
@ -285,13 +285,13 @@ lemma anPart_superCommute_normalOrder_ofFieldOpList_sum (φ : 𝓕.FieldOp) (φs
    simp
  | .position φ =>
    simp only [anPart_position, instCommGroup.eq_1, Fin.getElem_fin, Algebra.smul_mul_assoc]
-    rw [ofCrAnFieldOp_superCommute_normalOrder_ofFieldOpList_sum]
+    rw [ofCrAnOp_superCommute_normalOrder_ofFieldOpList_sum]
    simp only [instCommGroup.eq_1, crAnStatistics, Function.comp_apply, crAnFieldOpToFieldOp_prod,
      Fin.getElem_fin, Algebra.smul_mul_assoc]
    rfl
  | .outAsymp φ =>
    simp only [anPart_posAsymp, instCommGroup.eq_1, Fin.getElem_fin, Algebra.smul_mul_assoc]
-    rw [ofCrAnFieldOp_superCommute_normalOrder_ofFieldOpList_sum]
+    rw [ofCrAnOp_superCommute_normalOrder_ofFieldOpList_sum]
    simp only [instCommGroup.eq_1, crAnStatistics, Function.comp_apply, crAnFieldOpToFieldOp_prod,
      Fin.getElem_fin, Algebra.smul_mul_assoc]
    rfl
@ -339,7 +339,7 @@ For a field specification `𝓕`, the following relation holds in the algebra `
 `φ * 𝓝(φ₀φ₁…φₙ) = 𝓝(φφ₀φ₁…φₙ) + ∑ i, (𝓢(φ,φ₀φ₁…φᵢ₋₁) • [anPartF φ, φᵢ]ₛ) * 𝓝(φ₀φ₁…φᵢ₋₁φᵢ₊₁…φₙ)`.

 The proof of this ultimently depends on :
- `ofCrAnFieldOp_superCommute_normalOrder_ofCrAnFieldOpList_sum`
+- `ofCrAnOp_superCommute_normalOrder_ofCrAnOpList_sum`
 -/
 lemma ofFieldOp_mul_normalOrder_ofFieldOpList_eq_sum (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp) :
    ofFieldOp φ * 𝓝(ofFieldOpList φs) =
--- a/HepLean/PerturbationTheory/FieldOpAlgebra/SuperCommute.lean
+++ b/HepLean/PerturbationTheory/FieldOpAlgebra/SuperCommute.lean
@ -131,23 +131,23 @@ lemma superCommute_eq_ι_superCommuteF (a b : 𝓕.FieldOpFreeAlgebra) :

 lemma superCommute_create_create {φ φ' : 𝓕.CrAnFieldOp}
    (h : 𝓕 |>ᶜ φ = .create) (h' : 𝓕 |>ᶜ φ' = .create) :
-    [ofCrAnFieldOp φ, ofCrAnFieldOp φ']ₛ = 0 := by
-  rw [ofCrAnFieldOp, ofCrAnFieldOp]
+    [ofCrAnOp φ, ofCrAnOp φ']ₛ = 0 := by
+  rw [ofCrAnOp, ofCrAnOp]
  rw [superCommute_eq_ι_superCommuteF, ι_superCommuteF_of_create_create _ _ h h']

 lemma superCommute_annihilate_annihilate {φ φ' : 𝓕.CrAnFieldOp}
    (h : 𝓕 |>ᶜ φ = .annihilate) (h' : 𝓕 |>ᶜ φ' = .annihilate) :
-    [ofCrAnFieldOp φ, ofCrAnFieldOp φ']ₛ = 0 := by
-  rw [ofCrAnFieldOp, ofCrAnFieldOp]
+    [ofCrAnOp φ, ofCrAnOp φ']ₛ = 0 := by
+  rw [ofCrAnOp, ofCrAnOp]
  rw [superCommute_eq_ι_superCommuteF, ι_superCommuteF_of_annihilate_annihilate _ _ h h']

 lemma superCommute_diff_statistic {φ φ' : 𝓕.CrAnFieldOp} (h : (𝓕 |>ₛ φ) ≠ 𝓕 |>ₛ φ') :
-    [ofCrAnFieldOp φ, ofCrAnFieldOp φ']ₛ = 0 := by
-  rw [ofCrAnFieldOp, ofCrAnFieldOp]
+    [ofCrAnOp φ, ofCrAnOp φ']ₛ = 0 := by
+  rw [ofCrAnOp, ofCrAnOp]
  rw [superCommute_eq_ι_superCommuteF, ι_superCommuteF_of_diff_statistic h]

-lemma superCommute_ofCrAnFieldOp_ofFieldOp_diff_stat_zero (φ : 𝓕.CrAnFieldOp) (ψ : 𝓕.FieldOp)
-    (h : (𝓕 |>ₛ φ) ≠ (𝓕 |>ₛ ψ)) : [ofCrAnFieldOp φ, ofFieldOp ψ]ₛ = 0 := by
+lemma superCommute_ofCrAnOp_ofFieldOp_diff_stat_zero (φ : 𝓕.CrAnFieldOp) (ψ : 𝓕.FieldOp)
+    (h : (𝓕 |>ₛ φ) ≠ (𝓕 |>ₛ ψ)) : [ofCrAnOp φ, ofFieldOp ψ]ₛ = 0 := by
  rw [ofFieldOp_eq_sum, map_sum]
  rw [Finset.sum_eq_zero]
  intro x hx
@ -161,37 +161,37 @@ lemma superCommute_anPart_ofFieldOpF_diff_grade_zero (φ ψ : 𝓕.FieldOp)
    simp
  | FieldOp.position φ =>
    simp only [anPartF_position]
-    apply superCommute_ofCrAnFieldOp_ofFieldOp_diff_stat_zero _ _ _
+    apply superCommute_ofCrAnOp_ofFieldOp_diff_stat_zero _ _ _
    simpa [crAnStatistics] using h
  | FieldOp.outAsymp _ =>
    simp only [anPartF_posAsymp]
-    apply superCommute_ofCrAnFieldOp_ofFieldOp_diff_stat_zero _ _
+    apply superCommute_ofCrAnOp_ofFieldOp_diff_stat_zero _ _
    simpa [crAnStatistics] using h

-lemma superCommute_ofCrAnFieldOp_ofCrAnFieldOp_mem_center (φ φ' : 𝓕.CrAnFieldOp) :
-    [ofCrAnFieldOp φ, ofCrAnFieldOp φ']ₛ ∈ Subalgebra.center ℂ (FieldOpAlgebra 𝓕) := by
-  rw [ofCrAnFieldOp, ofCrAnFieldOp, superCommute_eq_ι_superCommuteF]
+lemma superCommute_ofCrAnOp_ofCrAnOp_mem_center (φ φ' : 𝓕.CrAnFieldOp) :
+    [ofCrAnOp φ, ofCrAnOp φ']ₛ ∈ Subalgebra.center ℂ (FieldOpAlgebra 𝓕) := by
+  rw [ofCrAnOp, ofCrAnOp, superCommute_eq_ι_superCommuteF]
  exact ι_superCommuteF_ofCrAnOpF_ofCrAnOpF_mem_center φ φ'

-lemma superCommute_ofCrAnFieldOp_ofCrAnFieldOp_commute (φ φ' : 𝓕.CrAnFieldOp)
+lemma superCommute_ofCrAnOp_ofCrAnOp_commute (φ φ' : 𝓕.CrAnFieldOp)
    (a : FieldOpAlgebra 𝓕) :
-    a * [ofCrAnFieldOp φ, ofCrAnFieldOp φ']ₛ = [ofCrAnFieldOp φ, ofCrAnFieldOp φ']ₛ * a := by
-  have h1 := superCommute_ofCrAnFieldOp_ofCrAnFieldOp_mem_center φ φ'
+    a * [ofCrAnOp φ, ofCrAnOp φ']ₛ = [ofCrAnOp φ, ofCrAnOp φ']ₛ * a := by
+  have h1 := superCommute_ofCrAnOp_ofCrAnOp_mem_center φ φ'
  rw [@Subalgebra.mem_center_iff] at h1
  exact h1 a

-lemma superCommute_ofCrAnFieldOp_ofFieldOp_mem_center (φ : 𝓕.CrAnFieldOp) (φ' : 𝓕.FieldOp) :
-    [ofCrAnFieldOp φ, ofFieldOp φ']ₛ ∈ Subalgebra.center ℂ (FieldOpAlgebra 𝓕) := by
+lemma superCommute_ofCrAnOp_ofFieldOp_mem_center (φ : 𝓕.CrAnFieldOp) (φ' : 𝓕.FieldOp) :
+    [ofCrAnOp φ, ofFieldOp φ']ₛ ∈ Subalgebra.center ℂ (FieldOpAlgebra 𝓕) := by
  rw [ofFieldOp_eq_sum]
  simp only [map_sum]
  refine Subalgebra.sum_mem (Subalgebra.center ℂ 𝓕.FieldOpAlgebra) ?_
  intro x hx
-  exact superCommute_ofCrAnFieldOp_ofCrAnFieldOp_mem_center φ ⟨φ', x⟩
+  exact superCommute_ofCrAnOp_ofCrAnOp_mem_center φ ⟨φ', x⟩

-lemma superCommute_ofCrAnFieldOp_ofFieldOp_commute (φ : 𝓕.CrAnFieldOp) (φ' : 𝓕.FieldOp)
-    (a : FieldOpAlgebra 𝓕) : a * [ofCrAnFieldOp φ, ofFieldOp φ']ₛ =
-    [ofCrAnFieldOp φ, ofFieldOp φ']ₛ * a := by
-  have h1 := superCommute_ofCrAnFieldOp_ofFieldOp_mem_center φ φ'
+lemma superCommute_ofCrAnOp_ofFieldOp_commute (φ : 𝓕.CrAnFieldOp) (φ' : 𝓕.FieldOp)
+    (a : FieldOpAlgebra 𝓕) : a * [ofCrAnOp φ, ofFieldOp φ']ₛ =
+    [ofCrAnOp φ, ofFieldOp φ']ₛ * a := by
+  have h1 := superCommute_ofCrAnOp_ofFieldOp_mem_center φ φ'
  rw [@Subalgebra.mem_center_iff] at h1
  exact h1 a

@ -202,9 +202,9 @@ lemma superCommute_anPart_ofFieldOp_mem_center (φ φ' : 𝓕.FieldOp) :
    simp only [anPart_negAsymp, map_zero, LinearMap.zero_apply]
    exact Subalgebra.zero_mem (Subalgebra.center ℂ _)
  | FieldOp.position φ =>
-    exact superCommute_ofCrAnFieldOp_ofFieldOp_mem_center _ _
+    exact superCommute_ofCrAnOp_ofFieldOp_mem_center _ _
  | FieldOp.outAsymp _ =>
-    exact superCommute_ofCrAnFieldOp_ofFieldOp_mem_center _ _
+    exact superCommute_ofCrAnOp_ofFieldOp_mem_center _ _

 /-!

@ -212,25 +212,25 @@ lemma superCommute_anPart_ofFieldOp_mem_center (φ φ' : 𝓕.FieldOp) :

 -/

-lemma superCommute_ofCrAnFieldOpList_ofCrAnFieldOpList (φs φs' : List 𝓕.CrAnFieldOp) :
-    [ofCrAnFieldOpList φs, ofCrAnFieldOpList φs']ₛ =
-    ofCrAnFieldOpList (φs ++ φs') - 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • ofCrAnFieldOpList (φs' ++ φs) := by
-  rw [ofCrAnFieldOpList_eq_ι_ofCrAnListF, ofCrAnFieldOpList_eq_ι_ofCrAnListF]
+lemma superCommute_ofCrAnOpList_ofCrAnOpList (φs φs' : List 𝓕.CrAnFieldOp) :
+    [ofCrAnOpList φs, ofCrAnOpList φs']ₛ =
+    ofCrAnOpList (φs ++ φs') - 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • ofCrAnOpList (φs' ++ φs) := by
+  rw [ofCrAnOpList_eq_ι_ofCrAnListF, ofCrAnOpList_eq_ι_ofCrAnListF]
  rw [superCommute_eq_ι_superCommuteF, superCommuteF_ofCrAnListF_ofCrAnListF]
  rfl

-lemma superCommute_ofCrAnFieldOp_ofCrAnFieldOp (φ φ' : 𝓕.CrAnFieldOp) :
-    [ofCrAnFieldOp φ, ofCrAnFieldOp φ']ₛ = ofCrAnFieldOp φ * ofCrAnFieldOp φ' -
-    𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • ofCrAnFieldOp φ' * ofCrAnFieldOp φ := by
-  rw [ofCrAnFieldOp, ofCrAnFieldOp]
+lemma superCommute_ofCrAnOp_ofCrAnOp (φ φ' : 𝓕.CrAnFieldOp) :
+    [ofCrAnOp φ, ofCrAnOp φ']ₛ = ofCrAnOp φ * ofCrAnOp φ' -
+    𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • ofCrAnOp φ' * ofCrAnOp φ := by
+  rw [ofCrAnOp, ofCrAnOp]
  rw [superCommute_eq_ι_superCommuteF, superCommuteF_ofCrAnOpF_ofCrAnOpF]
  rfl

-lemma superCommute_ofCrAnFieldOpList_ofFieldOpList (φcas : List 𝓕.CrAnFieldOp)
+lemma superCommute_ofCrAnOpList_ofFieldOpList (φcas : List 𝓕.CrAnFieldOp)
    (φs : List 𝓕.FieldOp) :
-    [ofCrAnFieldOpList φcas, ofFieldOpList φs]ₛ = ofCrAnFieldOpList φcas * ofFieldOpList φs -
-    𝓢(𝓕 |>ₛ φcas, 𝓕 |>ₛ φs) • ofFieldOpList φs * ofCrAnFieldOpList φcas := by
-  rw [ofCrAnFieldOpList, ofFieldOpList]
+    [ofCrAnOpList φcas, ofFieldOpList φs]ₛ = ofCrAnOpList φcas * ofFieldOpList φs -
+    𝓢(𝓕 |>ₛ φcas, 𝓕 |>ₛ φs) • ofFieldOpList φs * ofCrAnOpList φcas := by
+  rw [ofCrAnOpList, ofFieldOpList]
  rw [superCommute_eq_ι_superCommuteF, superCommuteF_ofCrAnListF_ofFieldOpFsList]
  rfl

@ -362,18 +362,18 @@ multiplication with a sign plus the super commutor.

 -/

-lemma ofCrAnFieldOpList_mul_ofCrAnFieldOpList_eq_superCommute (φs φs' : List 𝓕.CrAnFieldOp) :
-    ofCrAnFieldOpList φs * ofCrAnFieldOpList φs' =
-    𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • ofCrAnFieldOpList φs' * ofCrAnFieldOpList φs
-    + [ofCrAnFieldOpList φs, ofCrAnFieldOpList φs']ₛ := by
-  rw [superCommute_ofCrAnFieldOpList_ofCrAnFieldOpList]
-  simp [ofCrAnFieldOpList_append]
+lemma ofCrAnOpList_mul_ofCrAnOpList_eq_superCommute (φs φs' : List 𝓕.CrAnFieldOp) :
+    ofCrAnOpList φs * ofCrAnOpList φs' =
+    𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • ofCrAnOpList φs' * ofCrAnOpList φs
+    + [ofCrAnOpList φs, ofCrAnOpList φs']ₛ := by
+  rw [superCommute_ofCrAnOpList_ofCrAnOpList]
+  simp [ofCrAnOpList_append]

-lemma ofCrAnFieldOp_mul_ofCrAnFieldOpList_eq_superCommute (φ : 𝓕.CrAnFieldOp)
-    (φs' : List 𝓕.CrAnFieldOp) : ofCrAnFieldOp φ * ofCrAnFieldOpList φs' =
-    𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs') • ofCrAnFieldOpList φs' * ofCrAnFieldOp φ
-    + [ofCrAnFieldOp φ, ofCrAnFieldOpList φs']ₛ := by
-  rw [← ofCrAnFieldOpList_singleton, ofCrAnFieldOpList_mul_ofCrAnFieldOpList_eq_superCommute]
+lemma ofCrAnOp_mul_ofCrAnOpList_eq_superCommute (φ : 𝓕.CrAnFieldOp)
+    (φs' : List 𝓕.CrAnFieldOp) : ofCrAnOp φ * ofCrAnOpList φs' =
+    𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs') • ofCrAnOpList φs' * ofCrAnOp φ
+    + [ofCrAnOp φ, ofCrAnOpList φs']ₛ := by
+  rw [← ofCrAnOpList_singleton, ofCrAnOpList_mul_ofCrAnOpList_eq_superCommute]
  simp

 lemma ofFieldOpList_mul_ofFieldOpList_eq_superCommute (φs φs' : List 𝓕.FieldOp) :
@ -402,11 +402,11 @@ lemma ofFieldOpList_mul_ofFieldOp_eq_superCommute (φs : List 𝓕.FieldOp) (φ
  rw [superCommute_ofFieldOpList_ofFieldOp]
  simp

-lemma ofCrAnFieldOpList_mul_ofFieldOpList_eq_superCommute (φs : List 𝓕.CrAnFieldOp)
-    (φs' : List 𝓕.FieldOp) : ofCrAnFieldOpList φs * ofFieldOpList φs' =
-    𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • ofFieldOpList φs' * ofCrAnFieldOpList φs
-    + [ofCrAnFieldOpList φs, ofFieldOpList φs']ₛ := by
-  rw [superCommute_ofCrAnFieldOpList_ofFieldOpList]
+lemma ofCrAnOpList_mul_ofFieldOpList_eq_superCommute (φs : List 𝓕.CrAnFieldOp)
+    (φs' : List 𝓕.FieldOp) : ofCrAnOpList φs * ofFieldOpList φs' =
+    𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • ofFieldOpList φs' * ofCrAnOpList φs
+    + [ofCrAnOpList φs, ofFieldOpList φs']ₛ := by
+  rw [superCommute_ofCrAnOpList_ofFieldOpList]
  simp

 lemma crPart_mul_anPart_eq_superCommute (φ φ' : 𝓕.FieldOp) :
@ -441,17 +441,17 @@ lemma anPart_mul_anPart_swap (φ φ' : 𝓕.FieldOp) :

 -/

-lemma superCommute_ofCrAnFieldOpList_ofCrAnFieldOpList_symm (φs φs' : List 𝓕.CrAnFieldOp) :
-    [ofCrAnFieldOpList φs, ofCrAnFieldOpList φs']ₛ =
-    (- 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs')) • [ofCrAnFieldOpList φs', ofCrAnFieldOpList φs]ₛ := by
-  rw [ofCrAnFieldOpList, ofCrAnFieldOpList, superCommute_eq_ι_superCommuteF,
+lemma superCommute_ofCrAnOpList_ofCrAnOpList_symm (φs φs' : List 𝓕.CrAnFieldOp) :
+    [ofCrAnOpList φs, ofCrAnOpList φs']ₛ =
+    (- 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs')) • [ofCrAnOpList φs', ofCrAnOpList φs]ₛ := by
+  rw [ofCrAnOpList, ofCrAnOpList, superCommute_eq_ι_superCommuteF,
    superCommuteF_ofCrAnListF_ofCrAnListF_symm]
  rfl

-lemma superCommute_ofCrAnFieldOp_ofCrAnFieldOp_symm (φ φ' : 𝓕.CrAnFieldOp) :
-    [ofCrAnFieldOp φ, ofCrAnFieldOp φ']ₛ =
-    (- 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ')) • [ofCrAnFieldOp φ', ofCrAnFieldOp φ]ₛ := by
-  rw [ofCrAnFieldOp, ofCrAnFieldOp, superCommute_eq_ι_superCommuteF,
+lemma superCommute_ofCrAnOp_ofCrAnOp_symm (φ φ' : 𝓕.CrAnFieldOp) :
+    [ofCrAnOp φ, ofCrAnOp φ']ₛ =
+    (- 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ')) • [ofCrAnOp φ', ofCrAnOp φ]ₛ := by
+  rw [ofCrAnOp, ofCrAnOp, superCommute_eq_ι_superCommuteF,
    superCommuteF_ofCrAnOpF_ofCrAnOpF_symm]
  rfl

@ -461,54 +461,54 @@ lemma superCommute_ofCrAnFieldOp_ofCrAnFieldOp_symm (φ φ' : 𝓕.CrAnFieldOp)

 -/

-lemma superCommute_ofCrAnFieldOpList_ofCrAnFieldOpList_eq_sum (φs φs' : List 𝓕.CrAnFieldOp) :
-    [ofCrAnFieldOpList φs, ofCrAnFieldOpList φs']ₛ =
+lemma superCommute_ofCrAnOpList_ofCrAnOpList_eq_sum (φs φs' : List 𝓕.CrAnFieldOp) :
+    [ofCrAnOpList φs, ofCrAnOpList φs']ₛ =
    ∑ (n : Fin φs'.length), 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs'.take n) •
-    ofCrAnFieldOpList (φs'.take n) * [ofCrAnFieldOpList φs, ofCrAnFieldOp (φs'.get n)]ₛ *
-    ofCrAnFieldOpList (φs'.drop (n + 1)) := by
+    ofCrAnOpList (φs'.take n) * [ofCrAnOpList φs, ofCrAnOp (φs'.get n)]ₛ *
+    ofCrAnOpList (φs'.drop (n + 1)) := by
  conv_lhs =>
-    rw [ofCrAnFieldOpList, ofCrAnFieldOpList, superCommute_eq_ι_superCommuteF,
+    rw [ofCrAnOpList, ofCrAnOpList, superCommute_eq_ι_superCommuteF,
      superCommuteF_ofCrAnListF_ofCrAnListF_eq_sum]
  rw [map_sum]
  rfl

-lemma superCommute_ofCrAnFieldOp_ofCrAnFieldOpList_eq_sum (φ : 𝓕.CrAnFieldOp)
-    (φs' : List 𝓕.CrAnFieldOp) : [ofCrAnFieldOp φ, ofCrAnFieldOpList φs']ₛ =
+lemma superCommute_ofCrAnOp_ofCrAnOpList_eq_sum (φ : 𝓕.CrAnFieldOp)
+    (φs' : List 𝓕.CrAnFieldOp) : [ofCrAnOp φ, ofCrAnOpList φs']ₛ =
    ∑ (n : Fin φs'.length), 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs'.take n) •
-    [ofCrAnFieldOp φ, ofCrAnFieldOp (φs'.get n)]ₛ * ofCrAnFieldOpList (φs'.eraseIdx n) := by
+    [ofCrAnOp φ, ofCrAnOp (φs'.get n)]ₛ * ofCrAnOpList (φs'.eraseIdx n) := by
  conv_lhs =>
-    rw [← ofCrAnFieldOpList_singleton, superCommute_ofCrAnFieldOpList_ofCrAnFieldOpList_eq_sum]
+    rw [← ofCrAnOpList_singleton, superCommute_ofCrAnOpList_ofCrAnOpList_eq_sum]
  congr
  funext n
  simp only [instCommGroup.eq_1, ofList_singleton, List.get_eq_getElem, Algebra.smul_mul_assoc]
  congr 1
-  rw [ofCrAnFieldOpList_singleton, superCommute_ofCrAnFieldOp_ofCrAnFieldOp_commute]
-  rw [mul_assoc, ← ofCrAnFieldOpList_append]
+  rw [ofCrAnOpList_singleton, superCommute_ofCrAnOp_ofCrAnOp_commute]
+  rw [mul_assoc, ← ofCrAnOpList_append]
  congr
  exact Eq.symm (List.eraseIdx_eq_take_drop_succ φs' ↑n)

-lemma superCommute_ofCrAnFieldOpList_ofFieldOpList_eq_sum (φs : List 𝓕.CrAnFieldOp)
-    (φs' : List 𝓕.FieldOp) : [ofCrAnFieldOpList φs, ofFieldOpList φs']ₛ =
+lemma superCommute_ofCrAnOpList_ofFieldOpList_eq_sum (φs : List 𝓕.CrAnFieldOp)
+    (φs' : List 𝓕.FieldOp) : [ofCrAnOpList φs, ofFieldOpList φs']ₛ =
    ∑ (n : Fin φs'.length), 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs'.take n) •
-    ofFieldOpList (φs'.take n) * [ofCrAnFieldOpList φs, ofFieldOp (φs'.get n)]ₛ *
+    ofFieldOpList (φs'.take n) * [ofCrAnOpList φs, ofFieldOp (φs'.get n)]ₛ *
    ofFieldOpList (φs'.drop (n + 1)) := by
  conv_lhs =>
-    rw [ofCrAnFieldOpList, ofFieldOpList, superCommute_eq_ι_superCommuteF,
+    rw [ofCrAnOpList, ofFieldOpList, superCommute_eq_ι_superCommuteF,
      superCommuteF_ofCrAnListF_ofFieldOpListF_eq_sum]
  rw [map_sum]
  rfl

-lemma superCommute_ofCrAnFieldOp_ofFieldOpList_eq_sum (φ : 𝓕.CrAnFieldOp) (φs' : List 𝓕.FieldOp) :
-    [ofCrAnFieldOp φ, ofFieldOpList φs']ₛ =
+lemma superCommute_ofCrAnOp_ofFieldOpList_eq_sum (φ : 𝓕.CrAnFieldOp) (φs' : List 𝓕.FieldOp) :
+    [ofCrAnOp φ, ofFieldOpList φs']ₛ =
    ∑ (n : Fin φs'.length), 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs'.take n) •
-    [ofCrAnFieldOp φ, ofFieldOp (φs'.get n)]ₛ * ofFieldOpList (φs'.eraseIdx n) := by
+    [ofCrAnOp φ, ofFieldOp (φs'.get n)]ₛ * ofFieldOpList (φs'.eraseIdx n) := by
  conv_lhs =>
-    rw [← ofCrAnFieldOpList_singleton, superCommute_ofCrAnFieldOpList_ofFieldOpList_eq_sum]
+    rw [← ofCrAnOpList_singleton, superCommute_ofCrAnOpList_ofFieldOpList_eq_sum]
  congr
  funext n
  simp only [instCommGroup.eq_1, ofList_singleton, List.get_eq_getElem, Algebra.smul_mul_assoc]
  congr 1
-  rw [ofCrAnFieldOpList_singleton, superCommute_ofCrAnFieldOp_ofFieldOp_commute]
+  rw [ofCrAnOpList_singleton, superCommute_ofCrAnOp_ofFieldOp_commute]
  rw [mul_assoc, ← ofFieldOpList_append]
  congr
  exact Eq.symm (List.eraseIdx_eq_take_drop_succ φs' ↑n)
--- a/HepLean/PerturbationTheory/FieldOpAlgebra/TimeOrder.lean
+++ b/HepLean/PerturbationTheory/FieldOpAlgebra/TimeOrder.lean
@ -435,9 +435,9 @@ lemma timeOrder_eq_maxTimeField_mul_finset (φ : 𝓕.FieldOp) (φs : List 𝓕.

 lemma timeOrder_superCommute_eq_time_mid {φ ψ : 𝓕.CrAnFieldOp}
    (hφψ : crAnTimeOrderRel φ ψ) (hψφ : crAnTimeOrderRel ψ φ) (a b : 𝓕.FieldOpAlgebra) :
-    𝓣(a * [ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ * b) =
-    [ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ * 𝓣(a * b) := by
-  rw [ofCrAnFieldOp, ofCrAnFieldOp]
+    𝓣(a * [ofCrAnOp φ, ofCrAnOp ψ]ₛ * b) =
+    [ofCrAnOp φ, ofCrAnOp ψ]ₛ * 𝓣(a * b) := by
+  rw [ofCrAnOp, ofCrAnOp]
  rw [superCommute_eq_ι_superCommuteF]
  obtain ⟨a, rfl⟩ := ι_surjective a
  obtain ⟨b, rfl⟩ := ι_surjective b
@ -449,17 +449,17 @@ lemma timeOrder_superCommute_eq_time_mid {φ ψ : 𝓕.CrAnFieldOp}

 lemma timeOrder_superCommute_eq_time_left {φ ψ : 𝓕.CrAnFieldOp}
    (hφψ : crAnTimeOrderRel φ ψ) (hψφ : crAnTimeOrderRel ψ φ) (b : 𝓕.FieldOpAlgebra) :
-    𝓣([ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ * b) =
-    [ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ * 𝓣(b) := by
-  trans 𝓣(1 * [ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ * b)
+    𝓣([ofCrAnOp φ, ofCrAnOp ψ]ₛ * b) =
+    [ofCrAnOp φ, ofCrAnOp ψ]ₛ * 𝓣(b) := by
+  trans 𝓣(1 * [ofCrAnOp φ, ofCrAnOp ψ]ₛ * b)
  simp only [one_mul]
  rw [timeOrder_superCommute_eq_time_mid hφψ hψφ]
  simp

 lemma timeOrder_superCommute_neq_time {φ ψ : 𝓕.CrAnFieldOp}
    (hφψ : ¬ (crAnTimeOrderRel φ ψ ∧ crAnTimeOrderRel ψ φ)) :
-    𝓣([ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ) = 0 := by
-  rw [ofCrAnFieldOp, ofCrAnFieldOp]
+    𝓣([ofCrAnOp φ, ofCrAnOp ψ]ₛ) = 0 := by
+  rw [ofCrAnOp, ofCrAnOp]
  rw [superCommute_eq_ι_superCommuteF]
  rw [timeOrder_eq_ι_timeOrderF]
  trans ι (timeOrderF (1 * (superCommuteF (ofCrAnOpF φ)) (ofCrAnOpF ψ) * 1))
--- a/HepLean/PerturbationTheory/FieldOpAlgebra/WicksTheoremNormal.lean
+++ b/HepLean/PerturbationTheory/FieldOpAlgebra/WicksTheoremNormal.lean
@ -169,11 +169,11 @@ lemma wicks_theorem_normal_order_empty : 𝓣(𝓝(ofFieldOpList [])) =
  simp only [Finset.univ_unique, PUnit.default_eq_unit, List.length_nil, Equiv.coe_fn_symm_mk,
    sign_empty, timeContract_empty, OneMemClass.coe_one, one_smul, uncontractedListGet_empty,
    one_mul, Finset.sum_const, Finset.card_singleton, e2]
-  have h1' : ofFieldOpList (𝓕 := 𝓕) [] = ofCrAnFieldOpList [] := by rfl
+  have h1' : ofFieldOpList (𝓕 := 𝓕) [] = ofCrAnOpList [] := by rfl
  rw [h1']
-  rw [normalOrder_ofCrAnFieldOpList]
+  rw [normalOrder_ofCrAnOpList]
  simp only [normalOrderSign_nil, normalOrderList_nil, one_smul]
-  rw [ofCrAnFieldOpList, timeOrder_eq_ι_timeOrderF]
+  rw [ofCrAnOpList, timeOrder_eq_ι_timeOrderF]
  rw [timeOrderF_ofCrAnListF]
  simp