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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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28
HepLean/PerturbationTheory/Algebras/FieldOpFreeAlgebra/Basic.lean
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@ -72,27 +72,27 @@ def ofState (φ : 𝓕.States) : FieldOpFreeAlgebra 𝓕 :=
/-- Maps a list of states to the creation and annihilation free-algebra by taking
the product of their sums of creation and annihlation operators.
Roughly `[φ1, φ2]` gets sent to `(φ1ᶜ+ φ1ᵃ) * (φ2ᶜ+ φ2ᵃ)` etc. -/
def ofStateList (φs : List 𝓕.States) : FieldOpFreeAlgebra 𝓕 := (List.map ofState φs).prod
def ofFieldOpListF (φs : List 𝓕.States) : FieldOpFreeAlgebra 𝓕 := (List.map ofState φs).prod
/-- Coercion from `List 𝓕.States` to `FieldOpFreeAlgebra 𝓕` through `ofStateList`. -/
instance : Coe (List 𝓕.States) (FieldOpFreeAlgebra 𝓕) := ⟨ofStateList⟩
/-- Coercion from `List 𝓕.States` to `FieldOpFreeAlgebra 𝓕` through `ofFieldOpListF`. -/
instance : Coe (List 𝓕.States) (FieldOpFreeAlgebra 𝓕) := ⟨ofFieldOpListF⟩
@[simp]
lemma ofStateList_nil : ofStateList ([] : List 𝓕.States) = 1 := rfl
lemma ofFieldOpListF_nil : ofFieldOpListF ([] : List 𝓕.States) = 1 := rfl
lemma ofStateList_cons (φ : 𝓕.States) (φs : List 𝓕.States) :
ofStateList (φ :: φs) = ofState φ * ofStateList φs := rfl
lemma ofFieldOpListF_cons (φ : 𝓕.States) (φs : List 𝓕.States) :
ofFieldOpListF (φ :: φs) = ofState φ * ofFieldOpListF φs := rfl
lemma ofStateList_singleton (φ : 𝓕.States) :
ofStateList [φ] = ofState φ := by simp [ofStateList]
lemma ofFieldOpListF_singleton (φ : 𝓕.States) :
ofFieldOpListF [φ] = ofState φ := by simp [ofFieldOpListF]
lemma ofStateList_append (φs φs' : List 𝓕.States) :
ofStateList (φs ++ φs') = ofStateList φs * ofStateList φs' := by
dsimp only [ofStateList]
lemma ofFieldOpListF_append (φs φs' : List 𝓕.States) :
ofFieldOpListF (φs ++ φs') = ofFieldOpListF φs * ofFieldOpListF φs' := by
dsimp only [ofFieldOpListF]
rw [List.map_append, List.prod_append]
lemma ofStateList_sum (φs : List 𝓕.States) :
ofStateList φs = ∑ (s : CrAnSection φs), ofCrAnList s.1 := by
lemma ofFieldOpListF_sum (φs : List 𝓕.States) :
ofFieldOpListF φs = ∑ (s : CrAnSection φs), ofCrAnList s.1 := by
induction φs with
| nil => simp
| cons φ φs ih =>
@ -101,7 +101,7 @@ lemma ofStateList_sum (φs : List 𝓕.States) :
conv_rhs =>
enter [2, x]
rw [← Finset.mul_sum]
rw [← Finset.sum_mul, ofStateList_cons, ← ih]
rw [← Finset.sum_mul, ofFieldOpListF_cons, ← ih]
rfl
/-!