DibyashanuPati/PhysLean
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

refactor: ofState rename to ofFieldOpF

Browse source
This commit is contained in:
jstoobysmith 2025-02-03 11:13:23 +00:00
parent 08260e709c
commit 93d06895c6
12 changed files with 85 additions and 85 deletions
Download patch file Download diff file Expand all files Collapse all files

16
HepLean/PerturbationTheory/Algebras/FieldOpFreeAlgebra/Basic.lean
View file

@ -21,7 +21,7 @@ The main structures defined in this module are:
* `FieldOpFreeAlgebra` - The creation and annihilation algebra
* `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
* `ofFieldOpF` - Maps a state to a sum of creation and annihilation operators
* `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
@ -66,13 +66,13 @@ lemma ofCrAnList_singleton (φ : 𝓕.CrAnStates) :
/-- Maps a state to the sum of creation and annihilation operators in
creation and annihilation free-algebra. -/
def ofState (φ : 𝓕.States) : FieldOpFreeAlgebra 𝓕 :=
def ofFieldOpF (φ : 𝓕.States) : FieldOpFreeAlgebra 𝓕 :=
∑ (i : 𝓕.statesToCrAnType φ), ofCrAnState ⟨φ, i⟩
/-- Maps a list of states to the creation and annihilation free-algebra by taking
the product of their sums of creation and annihlation operators.
Roughly `[φ1, φ2]` gets sent to `(φ1ᶜ+ φ1ᵃ) * (φ2ᶜ+ φ2ᵃ)` etc. -/
def ofFieldOpListF (φs : List 𝓕.States) : FieldOpFreeAlgebra 𝓕 := (List.map ofState φs).prod
def ofFieldOpListF (φs : List 𝓕.States) : FieldOpFreeAlgebra 𝓕 := (List.map ofFieldOpF φs).prod
/-- Coercion from `List 𝓕.States` to `FieldOpFreeAlgebra 𝓕` through `ofFieldOpListF`. -/
instance : Coe (List 𝓕.States) (FieldOpFreeAlgebra 𝓕) := ⟨ofFieldOpListF⟩
@ -81,10 +81,10 @@ instance : Coe (List 𝓕.States) (FieldOpFreeAlgebra 𝓕) := ⟨ofFieldOpListF
lemma ofFieldOpListF_nil : ofFieldOpListF ([] : List 𝓕.States) = 1 := rfl
lemma ofFieldOpListF_cons (φ : 𝓕.States) (φs : List 𝓕.States) :
ofFieldOpListF (φ :: φs) = ofState φ * ofFieldOpListF φs := rfl
ofFieldOpListF (φ :: φs) = ofFieldOpF φ * ofFieldOpListF φs := rfl
lemma ofFieldOpListF_singleton (φ : 𝓕.States) :
ofFieldOpListF [φ] = ofState φ := by simp [ofFieldOpListF]
ofFieldOpListF [φ] = ofFieldOpF φ := by simp [ofFieldOpListF]
lemma ofFieldOpListF_append (φs φs' : List 𝓕.States) :
ofFieldOpListF (φs ++ φs') = ofFieldOpListF φs * ofFieldOpListF φs' := by
@ -160,9 +160,9 @@ lemma anPartF_posAsymp (φ : 𝓕.OutgoingAsymptotic) :
anPartF (States.outAsymp φ) = ofCrAnState ⟨States.outAsymp φ, ()⟩ := by
simp [anPartF]
lemma ofState_eq_crPartF_add_anPartF (φ : 𝓕.States) :
ofState φ = crPartF φ + anPartF φ := by
rw [ofState]
lemma ofFieldOpF_eq_crPartF_add_anPartF (φ : 𝓕.States) :
ofFieldOpF φ = crPartF φ + anPartF φ := by
rw [ofFieldOpF]
cases φ with
| inAsymp φ => simp [statesToCrAnType]
| position φ => simp [statesToCrAnType, CreateAnnihilate.sum_eq]