refactor: Rename ofStateList to ofFieldOpListF

2025-02-03 11:10:20 +00:00 · 2025-02-03 11:10:20 +00:00 · 08260e709c
commit 08260e709c
parent b0735a1e13
10 changed files with 126 additions and 126 deletions
--- a/HepLean/PerturbationTheory/Algebras/FieldOpFreeAlgebra/SuperCommute.lean
+++ b/HepLean/PerturbationTheory/Algebras/FieldOpFreeAlgebra/SuperCommute.lean
@ -58,22 +58,22 @@ lemma superCommuteF_ofCrAnState_ofCrAnState (φ φ' : 𝓕.CrAnStates) :
  rw [FieldStatistic.ofList_singleton, FieldStatistic.ofList_singleton, smul_mul_assoc]

 lemma superCommuteF_ofCrAnList_ofStatesList (φcas : List 𝓕.CrAnStates) (φs : List 𝓕.States) :
-    [ofCrAnList φcas, ofStateList φs]ₛca = ofCrAnList φcas * ofStateList φs -
-    𝓢(𝓕 |>ₛ φcas, 𝓕 |>ₛ φs) • ofStateList φs * ofCrAnList φcas := by
-  conv_lhs => rw [ofStateList_sum]
+    [ofCrAnList φcas, ofFieldOpListF φs]ₛca = ofCrAnList φcas * ofFieldOpListF φs -
+    𝓢(𝓕 |>ₛ φcas, 𝓕 |>ₛ φs) • ofFieldOpListF φs * ofCrAnList φcas := by
+  conv_lhs => rw [ofFieldOpListF_sum]
  rw [map_sum]
  conv_lhs =>
    enter [2, x]
    rw [superCommuteF_ofCrAnList_ofCrAnList, CrAnSection.statistics_eq_state_statistics,
      ofCrAnList_append, ofCrAnList_append]
  rw [Finset.sum_sub_distrib, ← Finset.mul_sum, ← Finset.smul_sum,
-    ← Finset.sum_mul, ← ofStateList_sum]
+    ← Finset.sum_mul, ← ofFieldOpListF_sum]
  simp

-lemma superCommuteF_ofStateList_ofStatesList (φ : List 𝓕.States) (φs : List 𝓕.States) :
-    [ofStateList φ, ofStateList φs]ₛca = ofStateList φ * ofStateList φs -
-    𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) • ofStateList φs * ofStateList φ := by
-  conv_lhs => rw [ofStateList_sum]
+lemma superCommuteF_ofFieldOpListF_ofStatesList (φ : List 𝓕.States) (φs : List 𝓕.States) :
+    [ofFieldOpListF φ, ofFieldOpListF φs]ₛca = ofFieldOpListF φ * ofFieldOpListF φs -
+    𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) • ofFieldOpListF φs * ofFieldOpListF φ := by
+  conv_lhs => rw [ofFieldOpListF_sum]
  simp only [map_sum, LinearMap.coeFn_sum, Finset.sum_apply, instCommGroup.eq_1,
    Algebra.smul_mul_assoc]
  conv_lhs =>
@ -81,18 +81,18 @@ lemma superCommuteF_ofStateList_ofStatesList (φ : List 𝓕.States) (φs : List
    rw [superCommuteF_ofCrAnList_ofStatesList]
  simp only [instCommGroup.eq_1, CrAnSection.statistics_eq_state_statistics,
    Algebra.smul_mul_assoc, Finset.sum_sub_distrib]
-  rw [← Finset.sum_mul, ← Finset.smul_sum, ← Finset.mul_sum, ← ofStateList_sum]
+  rw [← Finset.sum_mul, ← Finset.smul_sum, ← Finset.mul_sum, ← ofFieldOpListF_sum]

 lemma superCommuteF_ofState_ofStatesList (φ : 𝓕.States) (φs : List 𝓕.States) :
-    [ofState φ, ofStateList φs]ₛca = ofState φ * ofStateList φs -
-    𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) • ofStateList φs * ofState φ := by
-  rw [← ofStateList_singleton, superCommuteF_ofStateList_ofStatesList, ofStateList_singleton]
+    [ofState φ, ofFieldOpListF φs]ₛca = ofState φ * ofFieldOpListF φs -
+    𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) • ofFieldOpListF φs * ofState φ := by
+  rw [← ofFieldOpListF_singleton, superCommuteF_ofFieldOpListF_ofStatesList, ofFieldOpListF_singleton]
  simp

-lemma superCommuteF_ofStateList_ofState (φs : List 𝓕.States) (φ : 𝓕.States) :
-    [ofStateList φs, ofState φ]ₛca = ofStateList φs * ofState φ -
-    𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φ) • ofState φ * ofStateList φs := by
-  rw [← ofStateList_singleton, superCommuteF_ofStateList_ofStatesList, ofStateList_singleton]
+lemma superCommuteF_ofFieldOpListF_ofState (φs : List 𝓕.States) (φ : 𝓕.States) :
+    [ofFieldOpListF φs, ofState φ]ₛca = ofFieldOpListF φs * ofState φ -
+    𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φ) • ofState φ * ofFieldOpListF φs := by
+  rw [← ofFieldOpListF_singleton, superCommuteF_ofFieldOpListF_ofStatesList, ofFieldOpListF_singleton]
  simp

 lemma superCommuteF_anPartF_crPartF (φ φ' : 𝓕.States) :
@ -202,9 +202,9 @@ lemma superCommuteF_anPartF_anPartF (φ φ' : 𝓕.States) :
    rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
    simp [crAnStatistics, ← ofCrAnList_append]

-lemma superCommuteF_crPartF_ofStateList (φ : 𝓕.States) (φs : List 𝓕.States) :
-    [crPartF φ, ofStateList φs]ₛca =
-    crPartF φ * ofStateList φs - 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) • ofStateList φs *
+lemma superCommuteF_crPartF_ofFieldOpListF (φ : 𝓕.States) (φs : List 𝓕.States) :
+    [crPartF φ, ofFieldOpListF φs]ₛca =
+    crPartF φ * ofFieldOpListF φs - 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) • ofFieldOpListF φs *
    crPartF φ := by
  match φ with
  | States.inAsymp φ =>
@ -218,10 +218,10 @@ lemma superCommuteF_crPartF_ofStateList (φ : 𝓕.States) (φs : List 𝓕.Stat
  | States.outAsymp φ =>
    simp

-lemma superCommuteF_anPartF_ofStateList (φ : 𝓕.States) (φs : List 𝓕.States) :
-    [anPartF φ, ofStateList φs]ₛca =
-    anPartF φ * ofStateList φs - 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) •
-    ofStateList φs * anPartF φ := by
+lemma superCommuteF_anPartF_ofFieldOpListF (φ : 𝓕.States) (φs : List 𝓕.States) :
+    [anPartF φ, ofFieldOpListF φs]ₛca =
+    anPartF φ * ofFieldOpListF φs - 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) •
+    ofFieldOpListF φs * anPartF φ := by
  match φ with
  | States.inAsymp φ =>
    simp
@ -238,14 +238,14 @@ lemma superCommuteF_crPartF_ofState (φ φ' : 𝓕.States) :
    [crPartF φ, ofState φ']ₛca =
    crPartF φ * ofState φ' -
    𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • ofState φ' * crPartF φ := by
-  rw [← ofStateList_singleton, superCommuteF_crPartF_ofStateList]
+  rw [← ofFieldOpListF_singleton, superCommuteF_crPartF_ofFieldOpListF]
  simp

 lemma superCommuteF_anPartF_ofState (φ φ' : 𝓕.States) :
    [anPartF φ, ofState φ']ₛca =
    anPartF φ * ofState φ' -
    𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • ofState φ' * anPartF φ := by
-  rw [← ofStateList_singleton, superCommuteF_anPartF_ofStateList]
+  rw [← ofFieldOpListF_singleton, superCommuteF_anPartF_ofFieldOpListF]
  simp

 /-!
@ -268,22 +268,22 @@ lemma ofCrAnState_mul_ofCrAnList_eq_superCommuteF (φ : 𝓕.CrAnStates) (φs' :
  rw [← ofCrAnList_singleton, ofCrAnList_mul_ofCrAnList_eq_superCommuteF]
  simp

-lemma ofStateList_mul_ofStateList_eq_superCommuteF (φs φs' : List 𝓕.States) :
-    ofStateList φs * ofStateList φs' = 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • ofStateList φs' * ofStateList φs
-    + [ofStateList φs, ofStateList φs']ₛca := by
-  rw [superCommuteF_ofStateList_ofStatesList]
+lemma ofFieldOpListF_mul_ofFieldOpListF_eq_superCommuteF (φs φs' : List 𝓕.States) :
+    ofFieldOpListF φs * ofFieldOpListF φs' = 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • ofFieldOpListF φs' * ofFieldOpListF φs
+    + [ofFieldOpListF φs, ofFieldOpListF φs']ₛca := by
+  rw [superCommuteF_ofFieldOpListF_ofStatesList]
  simp

-lemma ofState_mul_ofStateList_eq_superCommuteF (φ : 𝓕.States) (φs' : List 𝓕.States) :
-    ofState φ * ofStateList φs' = 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs') • ofStateList φs' * ofState φ
-    + [ofState φ, ofStateList φs']ₛca := by
+lemma ofState_mul_ofFieldOpListF_eq_superCommuteF (φ : 𝓕.States) (φs' : List 𝓕.States) :
+    ofState φ * ofFieldOpListF φs' = 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs') • ofFieldOpListF φs' * ofState φ
+    + [ofState φ, ofFieldOpListF φs']ₛca := by
  rw [superCommuteF_ofState_ofStatesList]
  simp

-lemma ofStateList_mul_ofState_eq_superCommuteF (φs : List 𝓕.States) (φ : 𝓕.States) :
-    ofStateList φs * ofState φ = 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φ) • ofState φ * ofStateList φs
-    + [ofStateList φs, ofState φ]ₛca := by
-  rw [superCommuteF_ofStateList_ofState]
+lemma ofFieldOpListF_mul_ofState_eq_superCommuteF (φs : List 𝓕.States) (φ : 𝓕.States) :
+    ofFieldOpListF φs * ofState φ = 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φ) • ofState φ * ofFieldOpListF φs
+    + [ofFieldOpListF φs, ofState φ]ₛca := by
+  rw [superCommuteF_ofFieldOpListF_ofState]
  simp

 lemma crPartF_mul_anPartF_eq_superCommuteF (φ φ' : 𝓕.States) :
@ -314,9 +314,9 @@ lemma anPartF_mul_anPartF_eq_superCommuteF (φ φ' : 𝓕.States) :
  rw [superCommuteF_anPartF_anPartF]
  simp

-lemma ofCrAnList_mul_ofStateList_eq_superCommuteF (φs : List 𝓕.CrAnStates) (φs' : List 𝓕.States) :
-    ofCrAnList φs * ofStateList φs' = 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • ofStateList φs' * ofCrAnList φs
-    + [ofCrAnList φs, ofStateList φs']ₛca := by
+lemma ofCrAnList_mul_ofFieldOpListF_eq_superCommuteF (φs : List 𝓕.CrAnStates) (φs' : List 𝓕.States) :
+    ofCrAnList φs * ofFieldOpListF φs' = 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • ofFieldOpListF φs' * ofCrAnList φs
+    + [ofCrAnList φs, ofFieldOpListF φs']ₛca := by
  rw [superCommuteF_ofCrAnList_ofStatesList]
  simp

@ -377,24 +377,24 @@ lemma superCommuteF_ofCrAnList_ofCrAnList_cons (φ : 𝓕.CrAnStates) (φs φs'
  rw [← ofCrAnList_cons, smul_smul, FieldStatistic.ofList_cons_eq_mul]
  simp only [instCommGroup, map_mul, mul_comm]

-lemma superCommuteF_ofCrAnList_ofStateList_cons (φ : 𝓕.States) (φs : List 𝓕.CrAnStates)
-    (φs' : List 𝓕.States) : [ofCrAnList φs, ofStateList (φ :: φs')]ₛca =
-    [ofCrAnList φs, ofState φ]ₛca * ofStateList φs' +
-    𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φ) • ofState φ * [ofCrAnList φs, ofStateList φs']ₛca := by
+lemma superCommuteF_ofCrAnList_ofFieldOpListF_cons (φ : 𝓕.States) (φs : List 𝓕.CrAnStates)
+    (φs' : List 𝓕.States) : [ofCrAnList φs, ofFieldOpListF (φ :: φs')]ₛca =
+    [ofCrAnList φs, ofState φ]ₛca * ofFieldOpListF φs' +
+    𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φ) • ofState φ * [ofCrAnList φs, ofFieldOpListF φs']ₛca := by
  rw [superCommuteF_ofCrAnList_ofStatesList]
  conv_rhs =>
    lhs
-    rw [← ofStateList_singleton, superCommuteF_ofCrAnList_ofStatesList, sub_mul, mul_assoc,
-      ← ofStateList_append]
+    rw [← ofFieldOpListF_singleton, superCommuteF_ofCrAnList_ofStatesList, sub_mul, mul_assoc,
+      ← ofFieldOpListF_append]
    rhs
-    rw [FieldStatistic.ofList_singleton, ofStateList_singleton, smul_mul_assoc,
+    rw [FieldStatistic.ofList_singleton, ofFieldOpListF_singleton, smul_mul_assoc,
      smul_mul_assoc, mul_assoc]
  conv_rhs =>
    rhs
    rw [superCommuteF_ofCrAnList_ofStatesList, mul_sub, smul_mul_assoc]
  simp only [instCommGroup, Algebra.smul_mul_assoc, List.singleton_append, Algebra.mul_smul_comm,
    sub_add_sub_cancel, sub_right_inj]
-  rw [ofStateList_cons, mul_assoc, smul_smul, FieldStatistic.ofList_cons_eq_mul]
+  rw [ofFieldOpListF_cons, mul_assoc, smul_smul, FieldStatistic.ofList_cons_eq_mul]
  simp [mul_comm]

 /--
@ -417,23 +417,23 @@ lemma superCommuteF_ofCrAnList_ofCrAnList_eq_sum (φs : List 𝓕.CrAnStates) :
    · simp [Finset.mul_sum, smul_smul, ofCrAnList_cons, mul_assoc,
        FieldStatistic.ofList_cons_eq_mul, mul_comm]

-lemma superCommuteF_ofCrAnList_ofStateList_eq_sum (φs : List 𝓕.CrAnStates) : (φs' : List 𝓕.States) →
-    [ofCrAnList φs, ofStateList φs']ₛca =
+lemma superCommuteF_ofCrAnList_ofFieldOpListF_eq_sum (φs : List 𝓕.CrAnStates) : (φs' : List 𝓕.States) →
+    [ofCrAnList φs, ofFieldOpListF φs']ₛca =
    ∑ (n : Fin φs'.length), 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs'.take n) •
-      ofStateList (φs'.take n) * [ofCrAnList φs, ofState (φs'.get n)]ₛca *
-      ofStateList (φs'.drop (n + 1))
+      ofFieldOpListF (φs'.take n) * [ofCrAnList φs, ofState (φs'.get n)]ₛca *
+      ofFieldOpListF (φs'.drop (n + 1))
  | [] => by
    simp only [superCommuteF_ofCrAnList_ofStatesList, instCommGroup, ofList_empty,
      exchangeSign_bosonic, one_smul, List.length_nil, Finset.univ_eq_empty, List.take_nil,
      List.get_eq_getElem, List.drop_nil, Finset.sum_empty]
    simp
  | φ :: φs' => by
-    rw [superCommuteF_ofCrAnList_ofStateList_cons,
-      superCommuteF_ofCrAnList_ofStateList_eq_sum φs φs']
+    rw [superCommuteF_ofCrAnList_ofFieldOpListF_cons,
+      superCommuteF_ofCrAnList_ofFieldOpListF_eq_sum φs φs']
    conv_rhs => erw [Fin.sum_univ_succ]
    congr 1
    · simp
-    · simp [Finset.mul_sum, smul_smul, ofStateList_cons, mul_assoc,
+    · simp [Finset.mul_sum, smul_smul, ofFieldOpListF_cons, mul_assoc,
        FieldStatistic.ofList_cons_eq_mul, mul_comm]

 lemma summerCommute_jacobi_ofCrAnList (φs1 φs2 φs3 : List 𝓕.CrAnStates) :