Project-declaredLean 4.32.0 · mathlib@81a5d257c8e4

Of Field Op mul normal Order of Field Op List eq super Commute

FieldSpecification.WickAlgebra.ofFieldOp_mul_normalOrder_ofFieldOpList_eq_superCommute

physics quantum field theory relativity lemmas

Plain-language statement

Within a proto-operator algebra we have that φ * 𝓝ᶠ(φ₀φ₁…φₙ) = 𝓝ᶠ(φφ₀φ₁…φₙ) + [anpart φ, 𝓝ᶠ(φ₀φ₁…φₙ)]ₛF.

Exact Lean statement

lemma ofFieldOp_mul_normalOrder_ofFieldOpList_eq_superCommute (φ : 𝓕.FieldOp)
    (φs : List 𝓕.FieldOp) : ofFieldOp φ * 𝓝(ofFieldOpList φs) =
    𝓝(ofFieldOp φ * ofFieldOpList φs) + [anPart φ, 𝓝(ofFieldOpList φs)]ₛ

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

lemma ofFieldOp_mul_normalOrder_ofFieldOpList_eq_superCommute (φ : 𝓕.FieldOp)    (φs : List 𝓕.FieldOp) : ofFieldOp φ * 𝓝(ofFieldOpList φs) =    𝓝(ofFieldOp φ * ofFieldOpList φs) + [anPart φ, 𝓝(ofFieldOpList φs)]ₛ := by  conv_lhs => rw [ofFieldOp_eq_crPart_add_anPart]  rw [add_mul, anPart_mul_normalOrder_ofFieldOpList_eq_superCommute_reorder, ← add_assoc,    ← crPart_mul_normalOrder, ← map_add]  conv_lhs =>    lhs    rw [← add_mul, ← ofFieldOp_eq_crPart_add_anPart]

Project: Physlib
License: Apache-2.0
Commit: dd43e9e65791
Source: Physlib/QFT/PerturbationTheory/WickAlgebra/NormalOrder/Lemmas.lean:341-349

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