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refactor: Lint

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jstoobysmith 2025-01-30 11:08:10 +00:00
parent fc20099282
commit c421746f4b
11 changed files with 63 additions and 62 deletions
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23
HepLean/PerturbationTheory/Algebras/FieldOpAlgebra/SuperCommute.lean
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@ -129,7 +129,6 @@ lemma superCommute_eq_ι_superCommuteF (a b : 𝓕.CrAnAlgebra) :
-/
lemma superCommute_create_create {φ φ' : 𝓕.CrAnStates}
(h : 𝓕 |>ᶜ φ = .create) (h' : 𝓕 |>ᶜ φ' = .create) :
[ofCrAnFieldOp φ, ofCrAnFieldOp φ']ₛ = 0 := by
@ -147,7 +146,6 @@ lemma superCommute_diff_statistic {φ φ' : 𝓕.CrAnStates} (h : (𝓕 |>ₛ φ
rw [ofCrAnFieldOp, ofCrAnFieldOp]
rw [superCommute_eq_ι_superCommuteF, ι_superCommuteF_of_diff_statistic h]
lemma superCommute_ofCrAnFieldOp_ofFieldOp_diff_stat_zero (φ : 𝓕.CrAnStates) (ψ : 𝓕.States)
(h : (𝓕 |>ₛ φ) ≠ (𝓕 |>ₛ ψ)) : [ofCrAnFieldOp φ, ofFieldOp ψ]ₛ = 0 := by
rw [ofFieldOp_eq_sum, map_sum]
@ -175,8 +173,9 @@ lemma superCommute_ofCrAnFieldOp_ofCrAnFieldOp_mem_center (φ φ' : 𝓕.CrAnSta
rw [ofCrAnFieldOp, ofCrAnFieldOp, superCommute_eq_ι_superCommuteF]
exact ι_superCommuteF_ofCrAnState_ofCrAnState_mem_center φ φ'
lemma superCommute_ofCrAnFieldOp_ofCrAnFieldOp_commute (φ φ' : 𝓕.CrAnStates) (a : FieldOpAlgebra 𝓕) :
a * [ofCrAnFieldOp φ, ofCrAnFieldOp φ']ₛ = [ofCrAnFieldOp φ, ofCrAnFieldOp φ']ₛ * a := by
lemma superCommute_ofCrAnFieldOp_ofCrAnFieldOp_commute (φ φ' : 𝓕.CrAnStates)
(a : FieldOpAlgebra 𝓕) :
a * [ofCrAnFieldOp φ, ofCrAnFieldOp φ']ₛ = [ofCrAnFieldOp φ, ofCrAnFieldOp φ']ₛ * a := by
have h1 := superCommute_ofCrAnFieldOp_ofCrAnFieldOp_mem_center φ φ'
rw [@Subalgebra.mem_center_iff] at h1
exact h1 a
@ -184,7 +183,7 @@ lemma superCommute_ofCrAnFieldOp_ofCrAnFieldOp_commute (φ φ' : 𝓕.CrAnStates
lemma superCommute_ofCrAnFieldOp_ofFieldOp_mem_center (φ : 𝓕.CrAnStates) (φ' : 𝓕.States) :
[ofCrAnFieldOp φ, ofFieldOp φ']ₛ ∈ Subalgebra.center ℂ (FieldOpAlgebra 𝓕) := by
rw [ofFieldOp_eq_sum]
simp
simp only [map_sum]
refine Subalgebra.sum_mem (Subalgebra.center ℂ 𝓕.FieldOpAlgebra) ?_
intro x hx
exact superCommute_ofCrAnFieldOp_ofCrAnFieldOp_mem_center φ ⟨φ', x⟩
@ -196,7 +195,7 @@ lemma superCommute_ofCrAnFieldOp_ofFieldOp_commute (φ : 𝓕.CrAnStates) (φ' :
rw [@Subalgebra.mem_center_iff] at h1
exact h1 a
lemma superCommute_anPart_ofFieldOp_mem_center (φ φ' : 𝓕.States) :
lemma superCommute_anPart_ofFieldOp_mem_center (φ φ' : 𝓕.States) :
[anPart φ, ofFieldOp φ']ₛ ∈ Subalgebra.center ℂ (FieldOpAlgebra 𝓕) := by
match φ with
| States.inAsymp _ =>
@ -354,7 +353,6 @@ lemma superCommute_anPart_ofFieldOp (φ φ' : 𝓕.States) :
rw [superCommute_eq_ι_superCommuteF, superCommuteF_anPartF_ofState]
rfl
/-!
## Mul equal superCommute
@ -447,7 +445,7 @@ lemma superCommute_ofCrAnFieldOpList_ofCrAnFieldOpList_symm (φs φs' : List
[ofCrAnFieldOpList φs, ofCrAnFieldOpList φs']ₛ =
(- 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs')) • [ofCrAnFieldOpList φs', ofCrAnFieldOpList φs]ₛ := by
rw [ofCrAnFieldOpList, ofCrAnFieldOpList, superCommute_eq_ι_superCommuteF,
superCommuteF_ofCrAnList_ofCrAnList_symm]
superCommuteF_ofCrAnList_ofCrAnList_symm]
rfl
lemma superCommute_ofCrAnFieldOp_ofCrAnFieldOp_symm (φ φ' : 𝓕.CrAnStates) :
@ -474,22 +472,21 @@ lemma superCommute_ofCrAnFieldOpList_ofCrAnFieldOpList_eq_sum (φs φs' : List
rw [map_sum]
rfl
lemma superCommute_ofCrAnFieldOp_ofCrAnFieldOpList_eq_sum (φ : 𝓕.CrAnStates) (φs' : List 𝓕.CrAnStates) :
[ofCrAnFieldOp φ, ofCrAnFieldOpList φs']ₛ =
lemma superCommute_ofCrAnFieldOp_ofCrAnFieldOpList_eq_sum (φ : 𝓕.CrAnStates)
(φs' : List 𝓕.CrAnStates) : [ofCrAnFieldOp φ, ofCrAnFieldOpList φs']ₛ =
∑ (n : Fin φs'.length), 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs'.take n) •
[ofCrAnFieldOp φ, ofCrAnFieldOp (φs'.get n)]ₛ * ofCrAnFieldOpList (φs'.eraseIdx n) := by
conv_lhs =>
rw [← ofCrAnFieldOpList_singleton, superCommute_ofCrAnFieldOpList_ofCrAnFieldOpList_eq_sum]
congr
funext n
simp
simp only [instCommGroup.eq_1, ofList_singleton, List.get_eq_getElem, Algebra.smul_mul_assoc]
congr 1
rw [ofCrAnFieldOpList_singleton, superCommute_ofCrAnFieldOp_ofCrAnFieldOp_commute]
rw [mul_assoc, ← ofCrAnFieldOpList_append]
congr
exact Eq.symm (List.eraseIdx_eq_take_drop_succ φs' ↑n)
lemma superCommute_ofCrAnFieldOpList_ofFieldOpList_eq_sum (φs : List 𝓕.CrAnStates)
(φs' : List 𝓕.States) : [ofCrAnFieldOpList φs, ofFieldOpList φs']ₛ =
∑ (n : Fin φs'.length), 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs'.take n) •
@ -509,7 +506,7 @@ lemma superCommute_ofCrAnFieldOp_ofFieldOpList_eq_sum (φ : 𝓕.CrAnStates) (φ
rw [← ofCrAnFieldOpList_singleton, superCommute_ofCrAnFieldOpList_ofFieldOpList_eq_sum]
congr
funext n
simp
simp only [instCommGroup.eq_1, ofList_singleton, List.get_eq_getElem, Algebra.smul_mul_assoc]
congr 1
rw [ofCrAnFieldOpList_singleton, superCommute_ofCrAnFieldOp_ofFieldOp_commute]
rw [mul_assoc, ← ofFieldOpList_append]