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refactor: Rename asymptotic states

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jstoobysmith 2025-01-23 10:46:50 +00:00
parent ba51484b1f
commit c9deac6cfe
14 changed files with 279 additions and 155 deletions
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48
HepLean/PerturbationTheory/Algebras/CrAnAlgebra/SuperCommute.lean
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@ -101,26 +101,26 @@ lemma superCommute_anPart_crPart (φ φ' : 𝓕.States) :
anPart (StateAlgebra.ofState φ) * crPart (StateAlgebra.ofState φ') -
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • crPart (StateAlgebra.ofState φ') * anPart (StateAlgebra.ofState φ) := by
match φ, φ' with
| States.negAsymp φ, _ =>
| States.inAsymp φ, _ =>
simp
| _, States.posAsymp φ =>
| _, States.outAsymp φ =>
simp only [crPart_posAsymp, map_zero, mul_zero, instCommGroup.eq_1, smul_zero, zero_mul,
sub_self]
| States.position φ, States.position φ' =>
simp only [anPart_position, crPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp [crAnStatistics, ← ofCrAnList_append]
| States.posAsymp φ, States.position φ' =>
| States.outAsymp φ, States.position φ' =>
simp only [anPart_posAsymp, crPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp [crAnStatistics, ← ofCrAnList_append]
| States.position φ, States.negAsymp φ' =>
| States.position φ, States.inAsymp φ' =>
simp only [anPart_position, crPart_negAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp only [List.singleton_append, instCommGroup.eq_1, crAnStatistics,
FieldStatistic.ofList_singleton, Function.comp_apply, crAnStatesToStates_prod, ←
ofCrAnList_append]
| States.posAsymp φ, States.negAsymp φ' =>
| States.outAsymp φ, States.inAsymp φ' =>
simp only [anPart_posAsymp, crPart_negAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp [crAnStatistics, ← ofCrAnList_append]
@ -131,25 +131,25 @@ lemma superCommute_crPart_anPart (φ φ' : 𝓕.States) :
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') •
anPart (StateAlgebra.ofState φ') * crPart (StateAlgebra.ofState φ) := by
match φ, φ' with
| States.posAsymp φ, _ =>
| States.outAsymp φ, _ =>
simp only [crPart_posAsymp, map_zero, LinearMap.zero_apply, zero_mul, instCommGroup.eq_1,
mul_zero, sub_self]
| _, States.negAsymp φ =>
| _, States.inAsymp φ =>
simp only [anPart_negAsymp, map_zero, mul_zero, instCommGroup.eq_1, smul_zero, zero_mul,
sub_self]
| States.position φ, States.position φ' =>
simp only [crPart_position, anPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp [crAnStatistics, ← ofCrAnList_append]
| States.position φ, States.posAsymp φ' =>
| States.position φ, States.outAsymp φ' =>
simp only [crPart_position, anPart_posAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp [crAnStatistics, ← ofCrAnList_append]
| States.negAsymp φ, States.position φ' =>
| States.inAsymp φ, States.position φ' =>
simp only [crPart_negAsymp, anPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp [crAnStatistics, ← ofCrAnList_append]
| States.negAsymp φ, States.posAsymp φ' =>
| States.inAsymp φ, States.outAsymp φ' =>
simp only [crPart_negAsymp, anPart_posAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp [crAnStatistics, ← ofCrAnList_append]
@ -160,24 +160,24 @@ lemma superCommute_crPart_crPart (φ φ' : 𝓕.States) :
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') •
crPart (StateAlgebra.ofState φ') * crPart (StateAlgebra.ofState φ) := by
match φ, φ' with
| States.posAsymp φ, _ =>
| States.outAsymp φ, _ =>
simp only [crPart_posAsymp, map_zero, LinearMap.zero_apply, zero_mul, instCommGroup.eq_1,
mul_zero, sub_self]
| _, States.posAsymp φ =>
| _, States.outAsymp φ =>
simp only [crPart_posAsymp, map_zero, mul_zero, instCommGroup.eq_1, smul_zero, zero_mul, sub_self]
| States.position φ, States.position φ' =>
simp only [crPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp [crAnStatistics, ← ofCrAnList_append]
| States.position φ, States.negAsymp φ' =>
| States.position φ, States.inAsymp φ' =>
simp only [crPart_position, crPart_negAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp [crAnStatistics, ← ofCrAnList_append]
| States.negAsymp φ, States.position φ' =>
| States.inAsymp φ, States.position φ' =>
simp only [crPart_negAsymp, crPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp [crAnStatistics, ← ofCrAnList_append]
| States.negAsymp φ, States.negAsymp φ' =>
| States.inAsymp φ, States.inAsymp φ' =>
simp only [crPart_negAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp [crAnStatistics, ← ofCrAnList_append]
@ -188,23 +188,23 @@ lemma superCommute_anPart_anPart (φ φ' : 𝓕.States) :
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') •
anPart (StateAlgebra.ofState φ') * anPart (StateAlgebra.ofState φ) := by
match φ, φ' with
| States.negAsymp φ, _ =>
| States.inAsymp φ, _ =>
simp
| _, States.negAsymp φ =>
| _, States.inAsymp φ =>
simp
| States.position φ, States.position φ' =>
simp only [anPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp [crAnStatistics, ← ofCrAnList_append]
| States.position φ, States.posAsymp φ' =>
| States.position φ, States.outAsymp φ' =>
simp only [anPart_position, anPart_posAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp [crAnStatistics, ← ofCrAnList_append]
| States.posAsymp φ, States.position φ' =>
| States.outAsymp φ, States.position φ' =>
simp only [anPart_posAsymp, anPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp [crAnStatistics, ← ofCrAnList_append]
| States.posAsymp φ, States.posAsymp φ' =>
| States.outAsymp φ, States.outAsymp φ' =>
simp only [anPart_posAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList]
simp [crAnStatistics, ← ofCrAnList_append]
@ -214,7 +214,7 @@ lemma superCommute_crPart_ofStateList (φ : 𝓕.States) (φs : List 𝓕.States
crPart (StateAlgebra.ofState φ) * ofStateList φs - 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) • ofStateList φs *
crPart (StateAlgebra.ofState φ) := by
match φ with
| States.negAsymp φ =>
| States.inAsymp φ =>
simp only [crPart_negAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, superCommute_ofCrAnList_ofStatesList]
simp [crAnStatistics]
@ -222,7 +222,7 @@ lemma superCommute_crPart_ofStateList (φ : 𝓕.States) (φs : List 𝓕.States
simp only [crPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, superCommute_ofCrAnList_ofStatesList]
simp [crAnStatistics]
| States.posAsymp φ =>
| States.outAsymp φ =>
simp
lemma superCommute_anPart_ofStateList (φ : 𝓕.States) (φs : List 𝓕.States) :
@ -230,13 +230,13 @@ lemma superCommute_anPart_ofStateList (φ : 𝓕.States) (φs : List 𝓕.States
anPart (StateAlgebra.ofState φ) * ofStateList φs - 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) •
ofStateList φs * anPart (StateAlgebra.ofState φ) := by
match φ with
| States.negAsymp φ =>
| States.inAsymp φ =>
simp
| States.position φ =>
simp only [anPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, superCommute_ofCrAnList_ofStatesList]
simp [crAnStatistics]
| States.posAsymp φ =>
| States.outAsymp φ =>
simp only [anPart_posAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
rw [← ofCrAnList_singleton, superCommute_ofCrAnList_ofStatesList]
simp [crAnStatistics]