`BookProof.ChapterElectroweakFieldStrength.connection_comm_trace` (Wμ Wν : Fin 3 → ℂ) (j : Fin 3) : ((connection Wμ * connection Wν - connection Wν * connection Wμ) * pauliV j).tra

Proved

BookProof.ChapterElectroweakFieldStrength.connection_comm_trace

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterElectroweakFieldStrength.

BookProof.ChapterElectroweakFieldStrength.connection_comm_trace (Wμ Wν : Fin 3 → ℂ) (j : Fin 3) : ((connection Wμ * connection Wν - connection Wν * connection Wμ) * pauliV j).trace = Complex.I * ∑ k, ∑ l, eps k l j * Wμ k * Wν l

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

Preamble

-- Generated from ChapterElectroweakFieldStrength.lean — theorem BookProof.ChapterElectroweakFieldStrength.connection_comm_trace
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.connection_comm_trace (Wμ Wν : Fin 3 → ℂ) (j : Fin 3) :
    ((connection Wμ * connection Wν - connection Wν * connection Wμ) * pauliV j).trace
      = Complex.I * ∑ k, ∑ l, eps k l j * Wμ k * Wν l := by sorry

View graph