Merge pull request #265 from HEPLean/NotesEdit

feat: Add contract in field algebra

HepLean/PerturbationTheory/Wick/Algebra.lean

@@ -286,10 +286,6 @@ def normalOrder (q : index S → Fin 2) : S.ConstDestAlgebra →ₗ[ℂ] S.Const
 def contract (q : index S → Fin 2) : S.ConstDestAlgebra →ₗ[ℂ] S.ConstDestAlgebra :=
   timeOrder q - normalOrder q
 
-informal_lemma timeOrder_comm_normalOrder where
-  math :≈ "time ordering and normal ordering commute."
-  deps :≈ [``timeOrder, ``normalOrder]
-
 end
 
 end ConstDestAlgebra
@@ -644,6 +640,11 @@ lemma timeOrder_comm_toConstDestAlgebra (q : index S → Fin 2) :
   · simp only [mul_eq_mul_right_iff]
     exact Or.inl (listToConstDestList_koszulSign q l f)
 
+/-- The contraction of fields defined as the time order minus normal order once mapped down
+  to constructive and destructive fields. -/
+noncomputable def contract (q : index S → Fin 2) : FieldAlgebra S →ₗ[ℂ] ConstDestAlgebra S :=
+  ConstDestAlgebra.contract (fun i => q i.2) ∘ₗ toConstDestAlgebra.toLinearMap
+
 end FieldAlgebra
 
 end Species