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feat: Cardinality of involutions and refactor

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jstoobysmith 2025-01-05 13:07:32 +00:00
parent 840d16a581
commit 1ab0c6f769
6 changed files with 1028 additions and 1197 deletions
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10
HepLean/PerturbationTheory/Wick/StaticTheorem.lean
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@ -25,11 +25,11 @@ lemma static_wick_nil {A : Type} [Semiring A] [Algebra ℂ A]
(S : Contractions.Splitting f le) :
F (ofListLift f [] 1) = ∑ c : Contractions [],
c.toCenterTerm f q le F S *
F (koszulOrder (fun i => q i.fst) le (ofListLift f c.normalize 1)) := by
F (koszulOrder (fun i => q i.fst) le (ofListLift f c.uncontracted 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]
dsimp [Contractions.normalize, Contractions.toCenterTerm]
dsimp [Contractions.uncontracted, Contractions.toCenterTerm]
simp [ofListLift_empty]
lemma static_wick_cons [IsTrans ((i : 𝓕) × f i) le] [IsTotal ((i : 𝓕) × f i) le]
@ -38,10 +38,10 @@ lemma static_wick_cons [IsTrans ((i : 𝓕) × f i) le] [IsTotal ((i : 𝓕) ×
(S : Contractions.Splitting f le)
(ih : F (ofListLift f φs 1) =
∑ c : Contractions φs, c.toCenterTerm f q le F S * F (koszulOrder (fun i => q i.fst) le
(ofListLift f c.normalize 1))) :
(ofListLift f c.uncontracted 1))) :
F (ofListLift f (φ :: φs) 1) = ∑ c : Contractions (φ :: φs),
c.toCenterTerm f q le F S *
F (koszulOrder (fun i => q i.fst) le (ofListLift f c.normalize 1)) := by
F (koszulOrder (fun i => q i.fst) le (ofListLift f c.uncontracted 1)) := by
rw [ofListLift_cons_eq_ofListLift, map_mul, ih, Finset.mul_sum,
← Contractions.consEquiv.symm.sum_comp]
erw [Finset.sum_sigma]
@ -88,7 +88,7 @@ theorem static_wick_theorem [IsTrans ((i : 𝓕) × f i) le] [IsTotal ((i : 𝓕
(F : FreeAlgebra ℂ (Σ i, f i) →ₐ A) [OperatorMap (fun i => q i.1) le F]
(S : Contractions.Splitting f le) :
F (ofListLift f φs 1) = ∑ c : Contractions φs, c.toCenterTerm f q le F S *
F (koszulOrder (fun i => q i.fst) le (ofListLift f c.normalize 1)) := by
F (koszulOrder (fun i => q i.fst) le (ofListLift f c.uncontracted 1)) := by
induction φs with
| nil => exact static_wick_nil q le F S
| cons a r ih => exact static_wick_cons q le r a F S ih