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refactor: move algebra files

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jstoobysmith 2025-02-03 12:12:36 +00:00
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commit ea6e128293
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47
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.Basic
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 ofCrAnListFBasis ℂ fun φs =>
normTimeOrderSign φs • ofCrAnListF (normTimeOrderList φs)
@[inherit_doc normTimeOrder]
scoped[FieldSpecification.FieldOpFreeAlgebra] notation "𝓣𝓝ᶠ(" a ")" => normTimeOrder a
lemma normTimeOrder_ofCrAnListF (φs : List 𝓕.CrAnFieldOp) :
𝓣𝓝ᶠ(ofCrAnListF φs) = normTimeOrderSign φs • ofCrAnListF (normTimeOrderList φs) := by
rw [← ofListBasis_eq_ofList]
simp only [normTimeOrder, Basis.constr_basis]
end
end FieldOpFreeAlgebra
end FieldSpecification