refactor: Rename CrAnAlgebra

HepLean/PerturbationTheory/Algebras/FieldOpFreeAlgebra/NormTimeOrder.lean

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+/-
+Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Joseph Tooby-Smith
+-/
+import HepLean.PerturbationTheory.FieldSpecification.TimeOrder
+import HepLean.PerturbationTheory.Algebras.FieldOpFreeAlgebra.SuperCommute
+import HepLean.PerturbationTheory.Koszul.KoszulSign
+/-!
+
+# Norm-time Ordering in the FieldOpFreeAlgebra
+
+-/
+
+namespace FieldSpecification
+variable {𝓕 : FieldSpecification}
+open FieldStatistic
+
+namespace FieldOpFreeAlgebra
+
+noncomputable section
+open HepLean.List
+
+/-!
+
+## Norm-time order
+
+-/
+
+/-- The normal-time ordering on `FieldOpFreeAlgebra`. -/
+def normTimeOrder : FieldOpFreeAlgebra 𝓕 →ₗ[ℂ] FieldOpFreeAlgebra 𝓕 :=
+  Basis.constr ofCrAnListBasis ℂ fun φs =>
+  normTimeOrderSign φs • ofCrAnList (normTimeOrderList φs)
+
+@[inherit_doc normTimeOrder]
+scoped[FieldSpecification.FieldOpFreeAlgebra] notation "𝓣𝓝ᶠ(" a ")" => normTimeOrder a
+
+lemma normTimeOrder_ofCrAnList (φs : List 𝓕.CrAnStates) :
+    𝓣𝓝ᶠ(ofCrAnList φs) = normTimeOrderSign φs • ofCrAnList (normTimeOrderList φs) := by
+  rw [← ofListBasis_eq_ofList]
+  simp only [normTimeOrder, Basis.constr_basis]
+
+end
+
+end FieldOpFreeAlgebra
+
+end FieldSpecification