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refactor: building version

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jstoobysmith 2024-12-20 13:33:39 +00:00
parent a3113a791c
commit a5e0f3ceac
5 changed files with 53 additions and 42 deletions
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15
HepLean/PerturbationTheory/Wick/StaticTheorem.lean
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@ -15,16 +15,17 @@ namespace Wick
noncomputable section
open HepLean.List
open FieldStatistic
lemma static_wick_nil {I : Type} {f : I → Type} [∀ i, Fintype (f i)]
(q : I → Fin 2)
(q : I → FieldStatistic)
(le1 : (Σ i, f i) → (Σ i, f i) → Prop) [DecidableRel le1]
{A : Type} [Semiring A] [Algebra ℂ A]
(F : FreeAlgebra ℂ (Σ i, f i) →ₐ A)
(S : Contractions.Splitting f le1) :
F (ofListLift f [] 1) = ∑ c : Contractions [],
c.toCenterTerm f q le1 F S *
F (koszulOrder le1 (fun i => q i.fst) (ofListLift f c.normalize 1)) := by
F (koszulOrder (fun i => q i.fst) le1 (ofListLift f c.normalize 1)) := by
rw [← Contractions.nilEquiv.symm.sum_comp]
simp only [Finset.univ_unique, PUnit.default_eq_unit, Contractions.nilEquiv, Equiv.coe_fn_symm_mk,
Finset.sum_const, Finset.card_singleton, one_smul]
@ -32,18 +33,18 @@ lemma static_wick_nil {I : Type} {f : I → Type} [∀ i, Fintype (f i)]
simp [ofListLift_empty]
lemma static_wick_cons {I : Type} {f : I → Type} [∀ i, Fintype (f i)]
(q : I → Fin 2)
(q : I → FieldStatistic)
(le1 : (Σ i, f i) → (Σ i, f i) → Prop) [DecidableRel le1]
[IsTrans ((i : I) × f i) le1] [IsTotal ((i : I) × f i) le1]
{A : Type} [Semiring A] [Algebra ℂ A] (r : List I) (a : I)
(F : FreeAlgebra ℂ (Σ i, f i) →ₐ A) [OperatorMap (fun i => q i.1) le1 F]
(S : Contractions.Splitting f le1)
(ih : F (ofListLift f r 1) =
∑ c : Contractions r, c.toCenterTerm f q le1 F S * F (koszulOrder le1 (fun i => q i.fst)
∑ c : Contractions r, c.toCenterTerm f q le1 F S * F (koszulOrder (fun i => q i.fst) le1
(ofListLift f c.normalize 1))) :
F (ofListLift f (a :: r) 1) = ∑ c : Contractions (a :: r),
c.toCenterTerm f q le1 F S *
F (koszulOrder le1 (fun i => q i.fst) (ofListLift f c.normalize 1)) := by
F (koszulOrder (fun i => q i.fst) le1 (ofListLift f c.normalize 1)) := by
rw [ofListLift_cons_eq_ofListLift, map_mul, ih, Finset.mul_sum,
← Contractions.consEquiv.symm.sum_comp]
erw [Finset.sum_sigma]
@ -86,14 +87,14 @@ lemma static_wick_cons {I : Type} {f : I → Type} [∀ i, Fintype (f i)]
exact S.h𝓑n a
theorem static_wick_theorem {I : Type} {f : I → Type} [∀ i, Fintype (f i)]
(q : I → Fin 2)
(q : I → FieldStatistic)
(le1 : (Σ i, f i) → (Σ i, f i) → Prop) [DecidableRel le1] [IsTrans ((i : I) × f i) le1]
[IsTotal ((i : I) × f i) le1]
{A : Type} [Semiring A] [Algebra ℂ A] (r : List I)
(F : FreeAlgebra ℂ (Σ i, f i) →ₐ A) [OperatorMap (fun i => q i.1) le1 F]
(S : Contractions.Splitting f le1) :
F (ofListLift f r 1) = ∑ c : Contractions r, c.toCenterTerm f q le1 F S *
F (koszulOrder le1 (fun i => q i.fst) (ofListLift f c.normalize 1)) := by
F (koszulOrder (fun i => q i.fst) le1 (ofListLift f c.normalize 1)) := by
induction r with
| nil => exact static_wick_nil q le1 F S
| cons a r ih => exact static_wick_cons q le1 r a F S ih