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reactor: Rename anPart and crPart

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jstoobysmith 2025-01-30 06:24:17 +00:00
parent d25eab1754
commit f7e669910c
9 changed files with 252 additions and 241 deletions
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48
HepLean/PerturbationTheory/Algebras/CrAnAlgebra/Basic.lean
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@ -22,8 +22,8 @@ The main structures defined in this module are:
* `ofCrAnState` - Maps a creation/annihilation state to the algebra
* `ofCrAnList` - Maps a list of creation/annihilation states to the algebra
* `ofState` - Maps a state to a sum of creation and annihilation operators
* `crPart` - The creation part of a state in the algebra
* `anPart` - The annihilation part of a state in the algebra
* `crPartF` - The creation part of a state in the algebra
* `anPartF` - The annihilation part of a state in the algebra
* `superCommuteF` - The super commutator on the algebra
The key lemmas show how these operators interact, particularly focusing on the
@ -113,55 +113,55 @@ lemma ofStateList_sum (φs : List 𝓕.States) :
/-- The algebra map taking an element of the free-state algbra to
the part of it in the creation and annihlation free algebra
spanned by creation operators. -/
def crPart : 𝓕.States → 𝓕.CrAnAlgebra := fun φ =>
def crPartF : 𝓕.States → 𝓕.CrAnAlgebra := fun φ =>
match φ with
| States.inAsymp φ => ofCrAnState ⟨States.inAsymp φ, ()⟩
| States.position φ => ofCrAnState ⟨States.position φ, CreateAnnihilate.create⟩
| States.outAsymp _ => 0
@[simp]
lemma crPart_negAsymp (φ : 𝓕.IncomingAsymptotic) :
crPart (States.inAsymp φ) = ofCrAnState ⟨States.inAsymp φ, ()⟩ := by
simp [crPart]
lemma crPartF_negAsymp (φ : 𝓕.IncomingAsymptotic) :
crPartF (States.inAsymp φ) = ofCrAnState ⟨States.inAsymp φ, ()⟩ := by
simp [crPartF]
@[simp]
lemma crPart_position (φ : 𝓕.PositionStates) :
crPart (States.position φ) =
lemma crPartF_position (φ : 𝓕.PositionStates) :
crPartF (States.position φ) =
ofCrAnState ⟨States.position φ, CreateAnnihilate.create⟩ := by
simp [crPart]
simp [crPartF]
@[simp]
lemma crPart_posAsymp (φ : 𝓕.OutgoingAsymptotic) :
crPart (States.outAsymp φ) = 0 := by
simp [crPart]
lemma crPartF_posAsymp (φ : 𝓕.OutgoingAsymptotic) :
crPartF (States.outAsymp φ) = 0 := by
simp [crPartF]
/-- The algebra map taking an element of the free-state algbra to
the part of it in the creation and annihilation free algebra
spanned by annihilation operators. -/
def anPart : 𝓕.States → 𝓕.CrAnAlgebra := fun φ =>
def anPartF : 𝓕.States → 𝓕.CrAnAlgebra := fun φ =>
match φ with
| States.inAsymp _ => 0
| States.position φ => ofCrAnState ⟨States.position φ, CreateAnnihilate.annihilate⟩
| States.outAsymp φ => ofCrAnState ⟨States.outAsymp φ, ()⟩
@[simp]
lemma anPart_negAsymp (φ : 𝓕.IncomingAsymptotic) :
anPart (States.inAsymp φ) = 0 := by
simp [anPart]
lemma anPartF_negAsymp (φ : 𝓕.IncomingAsymptotic) :
anPartF (States.inAsymp φ) = 0 := by
simp [anPartF]
@[simp]
lemma anPart_position (φ : 𝓕.PositionStates) :
anPart (States.position φ) =
lemma anPartF_position (φ : 𝓕.PositionStates) :
anPartF (States.position φ) =
ofCrAnState ⟨States.position φ, CreateAnnihilate.annihilate⟩ := by
simp [anPart]
simp [anPartF]
@[simp]
lemma anPart_posAsymp (φ : 𝓕.OutgoingAsymptotic) :
anPart (States.outAsymp φ) = ofCrAnState ⟨States.outAsymp φ, ()⟩ := by
simp [anPart]
lemma anPartF_posAsymp (φ : 𝓕.OutgoingAsymptotic) :
anPartF (States.outAsymp φ) = ofCrAnState ⟨States.outAsymp φ, ()⟩ := by
simp [anPartF]
lemma ofState_eq_crPart_add_anPart (φ : 𝓕.States) :
ofState φ = crPart φ + anPart φ := by
lemma ofState_eq_crPartF_add_anPartF (φ : 𝓕.States) :
ofState φ = crPartF φ + anPartF φ := by
rw [ofState]
cases φ with
| inAsymp φ => simp [statesToCrAnType]