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