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refactor: Spelling

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jstoobysmith 2025-02-07 15:43:59 +00:00
parent b82791d671
commit f8f1e1757f
25 changed files with 80 additions and 80 deletions
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24
HepLean/PerturbationTheory/FieldSpecification/NormalOrder.lean
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@ -43,7 +43,7 @@ instance (φ φ' : 𝓕.CrAnFieldOp) : Decidable (normalOrderRel φ φ') :=
-/
/-- For a field speciication `𝓕`, and a list `φs` of `𝓕.CrAnFieldOp`, `𝓕.normalOrderSign φs` is the
/-- For a field specification `𝓕`, and a list `φs` of `𝓕.CrAnFieldOp`, `𝓕.normalOrderSign φs` is the
sign corresponding to the number of `fermionic`-`fermionic` exchanges undertaken to normal-order
`φs` using the insertion sort algorithm. -/
def normalOrderSign (φs : List 𝓕.CrAnFieldOp) : ℂ :=
@ -91,14 +91,14 @@ lemma koszulSignInsert_append_annihilate (φ' φ : 𝓕.CrAnFieldOp)
dsimp only [List.cons_append, Wick.koszulSignInsert]
rw [koszulSignInsert_append_annihilate φ' φ hφ φs]
lemma normalOrderSign_append_annihlate (φ : 𝓕.CrAnFieldOp)
lemma normalOrderSign_append_annihilate (φ : 𝓕.CrAnFieldOp)
(hφ : 𝓕 |>ᶜ φ = CreateAnnihilate.annihilate) :
(φs : List 𝓕.CrAnFieldOp) →
normalOrderSign (φs ++ [φ]) = normalOrderSign φs
| [] => by simp
| φ' :: φs => by
dsimp only [List.cons_append, normalOrderSign, Wick.koszulSign]
have hi := normalOrderSign_append_annihlate φ hφ φs
have hi := normalOrderSign_append_annihilate φ hφ φs
dsimp only [normalOrderSign] at hi
rw [hi, koszulSignInsert_append_annihilate φ' φ hφ φs]
@ -117,7 +117,7 @@ lemma koszulSignInsert_annihilate_cons_create (φc φa : 𝓕.CrAnFieldOp)
rw [normalOrderRel, hφa, hφc]
simp [CreateAnnihilate.normalOrder]
lemma normalOrderSign_swap_create_annihlate_fst (φc φa : 𝓕.CrAnFieldOp)
lemma normalOrderSign_swap_create_annihilate_fst (φc φa : 𝓕.CrAnFieldOp)
(hφc : 𝓕 |>ᶜ φc = CreateAnnihilate.create)
(hφa : 𝓕 |>ᶜ φa = CreateAnnihilate.annihilate)
(φs : List 𝓕.CrAnFieldOp) :
@ -137,16 +137,16 @@ lemma koszulSignInsert_swap (φ φc φa : 𝓕.CrAnFieldOp) (φs φs' : List
= Wick.koszulSignInsert 𝓕.crAnStatistics normalOrderRel φ (φs ++ φc :: φa :: φs') :=
Wick.koszulSignInsert_eq_perm _ _ _ _ _ (List.Perm.append_left φs (List.Perm.swap φc φa φs'))
lemma normalOrderSign_swap_create_annihlate (φc φa : 𝓕.CrAnFieldOp)
lemma normalOrderSign_swap_create_annihilate (φc φa : 𝓕.CrAnFieldOp)
(hφc : 𝓕 |>ᶜ φc = CreateAnnihilate.create) (hφa : 𝓕 |>ᶜ φa = CreateAnnihilate.annihilate) :
(φs φs' : List 𝓕.CrAnFieldOp) → normalOrderSign (φs ++ φc :: φa :: φs') =
FieldStatistic.exchangeSign (𝓕.crAnStatistics φc) (𝓕.crAnStatistics φa) *
normalOrderSign (φs ++ φa :: φc :: φs')
| [], φs' => normalOrderSign_swap_create_annihlate_fst φc φa hφc hφa φs'
| [], φs' => normalOrderSign_swap_create_annihilate_fst φc φa hφc hφa φs'
| φ :: φs, φs' => by
rw [normalOrderSign]
dsimp only [List.cons_append, Wick.koszulSign, FieldStatistic.instCommGroup.eq_1]
rw [← normalOrderSign, normalOrderSign_swap_create_annihlate φc φa hφc hφa φs φs']
rw [← normalOrderSign, normalOrderSign_swap_create_annihilate φc φa hφc hφa φs φs']
rw [← mul_assoc, mul_comm _ (FieldStatistic.exchangeSign _ _), mul_assoc]
simp only [FieldStatistic.instCommGroup.eq_1, mul_eq_mul_left_iff]
apply Or.inl
@ -283,7 +283,7 @@ lemma normalOrderList_append_annihilate (φ : 𝓕.CrAnFieldOp)
dsimp only [normalOrderList] at hi
rw [hi, orderedInsert_append_annihilate φ' φ hφ]
lemma normalOrder_swap_create_annihlate_fst (φc φa : 𝓕.CrAnFieldOp)
lemma normalOrder_swap_create_annihilate_fst (φc φa : 𝓕.CrAnFieldOp)
(hφc : 𝓕 |>ᶜ φc = CreateAnnihilate.create)
(hφa : 𝓕 |>ᶜ φa = CreateAnnihilate.annihilate)
(φs : List 𝓕.CrAnFieldOp) :
@ -301,19 +301,19 @@ lemma normalOrder_swap_create_annihlate_fst (φc φa : 𝓕.CrAnFieldOp)
dsimp [CreateAnnihilate.normalOrder] at h
· rfl
lemma normalOrderList_swap_create_annihlate (φc φa : 𝓕.CrAnFieldOp)
lemma normalOrderList_swap_create_annihilate (φc φa : 𝓕.CrAnFieldOp)
(hφc : 𝓕 |>ᶜ φc = CreateAnnihilate.create)
(hφa : 𝓕 |>ᶜ φa = CreateAnnihilate.annihilate) :
(φs φs' : List 𝓕.CrAnFieldOp) →
normalOrderList (φs ++ φc :: φa :: φs') = normalOrderList (φs ++ φa :: φc :: φs')
| [], φs' => normalOrder_swap_create_annihlate_fst φc φa hφc hφa φs'
| [], φs' => normalOrder_swap_create_annihilate_fst φc φa hφc hφa φs'
| φ :: φs, φs' => by
dsimp only [List.cons_append, normalOrderList, List.insertionSort]
have hi := normalOrderList_swap_create_annihlate φc φa hφc hφa φs φs'
have hi := normalOrderList_swap_create_annihilate φc φa hφc hφa φs φs'
dsimp only [normalOrderList] at hi
rw [hi]
/-- For a list of creation and annihlation states, the equivalence between
/-- For a list of creation and annihilation states, the equivalence between
`Fin φs.length` and `Fin (normalOrderList φs).length` taking each position in `φs`
to it's corresponding position in the normal ordered list. This assumes that
we are using the insertion sort method.