`BookProof.ChapterElectroweakFieldStrength.pauli_commutator` (k l : Fin 3) : pauliV k * pauliV l - pauliV l * pauliV k = (2 * Complex.I) • ∑ m, eps k l m • pauliV m

Proved

BookProof.ChapterElectroweakFieldStrength.pauli_commutator

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterElectroweakFieldStrength.

BookProof.ChapterElectroweakFieldStrength.pauli_commutator (k l : Fin 3) : pauliV k * pauliV l - pauliV l * pauliV k = (2 * Complex.I) • ∑ m, eps k l m • pauliV m

Formalization note: Lean 4 identifier BookProof.ChapterElectroweakFieldStrength.pauli_commutator.

Preamble

-- Generated from ChapterElectroweakFieldStrength.lean — theorem BookProof.ChapterElectroweakFieldStrength.pauli_commutator
import Definitions.Def_ChapterParity
import Mathlib
import Definitions.Def_ChapterElectroweakFieldStrength
import Definitions.Def_ChapterParitySU2
open BookProof.ChapterParitySU2
open BookProof.ChapterElectroweakFieldStrength


open Matrix


open BookProof.ChapterParity BookProof.ChapterParitySU2

Formal statement

theorem BookProof.ChapterElectroweakFieldStrength.pauli_commutator (k l : Fin 3) :
    pauliV k * pauliV l - pauliV l * pauliV k = (2 * Complex.I) • ∑ m, eps k l m • pauliV m := by sorry

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