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refactor: Rename ofStateList to ofFieldOpListF

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jstoobysmith 2025-02-03 11:10:20 +00:00
parent b0735a1e13
commit 08260e709c
10 changed files with 126 additions and 126 deletions
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42
HepLean/PerturbationTheory/Algebras/FieldOpFreeAlgebra/NormalOrder.lean
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@ -527,11 +527,11 @@ lemma ofCrAnList_superCommuteF_normalOrderF_ofCrAnList (φs φs' : List 𝓕.CrA
simp [normalOrderF_ofCrAnList, map_smul, superCommuteF_ofCrAnList_ofCrAnList, ofCrAnList_append,
smul_sub, smul_smul, mul_comm]
lemma ofCrAnList_superCommuteF_normalOrderF_ofStateList (φs : List 𝓕.CrAnStates)
(φs' : List 𝓕.States) : [ofCrAnList φs, 𝓝ᶠ(ofStateList φs')]ₛca =
ofCrAnList φs * 𝓝ᶠ(ofStateList φs') -
𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • 𝓝ᶠ(ofStateList φs') * ofCrAnList φs := by
rw [ofStateList_sum, map_sum, Finset.mul_sum, Finset.smul_sum, Finset.sum_mul,
lemma ofCrAnList_superCommuteF_normalOrderF_ofFieldOpListF (φs : List 𝓕.CrAnStates)
(φs' : List 𝓕.States) : [ofCrAnList φs, 𝓝ᶠ(ofFieldOpListF φs')]ₛca =
ofCrAnList φs * 𝓝ᶠ(ofFieldOpListF φs') -
𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • 𝓝ᶠ(ofFieldOpListF φs') * ofCrAnList φs := by
rw [ofFieldOpListF_sum, map_sum, Finset.mul_sum, Finset.smul_sum, Finset.sum_mul,
← Finset.sum_sub_distrib, map_sum]
congr
funext n
@ -544,29 +544,29 @@ lemma ofCrAnList_superCommuteF_normalOrderF_ofStateList (φs : List 𝓕.CrAnSta
-/
lemma ofCrAnList_mul_normalOrderF_ofStateList_eq_superCommuteF (φs : List 𝓕.CrAnStates)
lemma ofCrAnList_mul_normalOrderF_ofFieldOpListF_eq_superCommuteF (φs : List 𝓕.CrAnStates)
(φs' : List 𝓕.States) :
ofCrAnList φs * 𝓝ᶠ(ofStateList φs') =
𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • 𝓝ᶠ(ofStateList φs') * ofCrAnList φs
+ [ofCrAnList φs, 𝓝ᶠ(ofStateList φs')]ₛca := by
simp [ofCrAnList_superCommuteF_normalOrderF_ofStateList]
ofCrAnList φs * 𝓝ᶠ(ofFieldOpListF φs') =
𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • 𝓝ᶠ(ofFieldOpListF φs') * ofCrAnList φs
+ [ofCrAnList φs, 𝓝ᶠ(ofFieldOpListF φs')]ₛca := by
simp [ofCrAnList_superCommuteF_normalOrderF_ofFieldOpListF]
lemma ofCrAnState_mul_normalOrderF_ofStateList_eq_superCommuteF (φ : 𝓕.CrAnStates)
(φs' : List 𝓕.States) : ofCrAnState φ * 𝓝ᶠ(ofStateList φs') =
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs') • 𝓝ᶠ(ofStateList φs') * ofCrAnState φ
+ [ofCrAnState φ, 𝓝ᶠ(ofStateList φs')]ₛca := by
simp [← ofCrAnList_singleton, ofCrAnList_mul_normalOrderF_ofStateList_eq_superCommuteF]
lemma ofCrAnState_mul_normalOrderF_ofFieldOpListF_eq_superCommuteF (φ : 𝓕.CrAnStates)
(φs' : List 𝓕.States) : ofCrAnState φ * 𝓝ᶠ(ofFieldOpListF φs') =
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs') • 𝓝ᶠ(ofFieldOpListF φs') * ofCrAnState φ
+ [ofCrAnState φ, 𝓝ᶠ(ofFieldOpListF φs')]ₛca := by
simp [← ofCrAnList_singleton, ofCrAnList_mul_normalOrderF_ofFieldOpListF_eq_superCommuteF]
lemma anPartF_mul_normalOrderF_ofStateList_eq_superCommuteF (φ : 𝓕.States)
lemma anPartF_mul_normalOrderF_ofFieldOpListF_eq_superCommuteF (φ : 𝓕.States)
(φs' : List 𝓕.States) :
anPartF φ * 𝓝ᶠ(ofStateList φs') =
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs') • 𝓝ᶠ(ofStateList φs' * anPartF φ)
+ [anPartF φ, 𝓝ᶠ(ofStateList φs')]ₛca := by
anPartF φ * 𝓝ᶠ(ofFieldOpListF φs') =
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs') • 𝓝ᶠ(ofFieldOpListF φs' * anPartF φ)
+ [anPartF φ, 𝓝ᶠ(ofFieldOpListF φs')]ₛca := by
rw [normalOrderF_mul_anPartF]
match φ with
| .inAsymp φ => simp
| .position φ => simp [ofCrAnState_mul_normalOrderF_ofStateList_eq_superCommuteF, crAnStatistics]
| .outAsymp φ => simp [ofCrAnState_mul_normalOrderF_ofStateList_eq_superCommuteF, crAnStatistics]
| .position φ => simp [ofCrAnState_mul_normalOrderF_ofFieldOpListF_eq_superCommuteF, crAnStatistics]
| .outAsymp φ => simp [ofCrAnState_mul_normalOrderF_ofFieldOpListF_eq_superCommuteF, crAnStatistics]
end