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jstoobysmith 2025-01-23 14:22:25 +00:00
commit fca75098f1
18 changed files with 163 additions and 314 deletions
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24
HepLean/PerturbationTheory/FieldSpecification/NormalOrder.lean
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@ -69,19 +69,14 @@ lemma koszulSignInsert_create (φ : 𝓕.CrAnStates)
lemma normalOrderSign_cons_create (φ : 𝓕.CrAnStates)
(hφ : 𝓕 |>ᶜ φ = CreateAnnihilate.create) (φs : List 𝓕.CrAnStates) :
normalOrderSign (φ :: φs) = normalOrderSign φs := by
dsimp only [normalOrderSign, Wick.koszulSign]
rw [koszulSignInsert_create φ hφ φs]
simp
simp [normalOrderSign, Wick.koszulSign, koszulSignInsert_create φ hφ φs]
@[simp]
lemma normalOrderSign_singleton (φ : 𝓕.CrAnStates) :
normalOrderSign [φ] = 1 := by
lemma normalOrderSign_singleton (φ : 𝓕.CrAnStates) : normalOrderSign [φ] = 1 := by
simp [normalOrderSign]
@[simp]
lemma normalOrderSign_nil :
normalOrderSign (𝓕 := 𝓕) [] = 1 := by
simp [normalOrderSign, Wick.koszulSign]
lemma normalOrderSign_nil : normalOrderSign (𝓕 := 𝓕) [] = 1 := rfl
lemma koszulSignInsert_append_annihilate (φ' φ : 𝓕.CrAnStates)
(hφ : 𝓕 |>ᶜ φ = CreateAnnihilate.annihilate) :
@ -139,10 +134,8 @@ lemma normalOrderSign_swap_create_annihlate_fst (φc φa : 𝓕.CrAnStates)
lemma koszulSignInsert_swap (φ φc φa : 𝓕.CrAnStates) (φs φs' : List 𝓕.CrAnStates) :
Wick.koszulSignInsert 𝓕.crAnStatistics normalOrderRel φ (φs ++ φa :: φc :: φs')
= Wick.koszulSignInsert 𝓕.crAnStatistics normalOrderRel φ (φs ++ φc :: φa :: φs') := by
apply Wick.koszulSignInsert_eq_perm
refine List.Perm.append_left φs ?h.a
exact List.Perm.swap φc φa φs'
= 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.CrAnStates)
(hφc : 𝓕 |>ᶜ φc = CreateAnnihilate.create) (hφa : 𝓕 |>ᶜ φa = CreateAnnihilate.annihilate) :
@ -157,12 +150,9 @@ lemma normalOrderSign_swap_create_annihlate (φc φa : 𝓕.CrAnStates)
rw [← mul_assoc, mul_comm _ (FieldStatistic.exchangeSign _ _), mul_assoc]
simp only [FieldStatistic.instCommGroup.eq_1, mul_eq_mul_left_iff]
apply Or.inl
conv_rhs =>
rw [normalOrderSign]
dsimp [Wick.koszulSign]
rw [← normalOrderSign]
conv_rhs => rw [normalOrderSign, Wick.koszulSign, ← normalOrderSign]
simp only [mul_eq_mul_right_iff]
apply Or.inl
left
rw [koszulSignInsert_swap]
lemma normalOrderSign_swap_create_create_fst (φc φc' : 𝓕.CrAnStates)