`BookProof.ChapterElectroweakFieldStrength.pauli_trace_orthonormal` (a b : Fin 3) : (pauliV a * pauliV b).trace = 2 * (if a = b then 1 else 0)

Proved

BookProof.ChapterElectroweakFieldStrength.pauli_trace_orthonormal

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterElectroweakFieldStrength.

BookProof.ChapterElectroweakFieldStrength.pauli_trace_orthonormal (a b : Fin 3) : (pauliV a * pauliV b).trace = 2 * (if a = b then 1 else 0)

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

Preamble

-- Generated from ChapterElectroweakFieldStrength.lean — theorem BookProof.ChapterElectroweakFieldStrength.pauli_trace_orthonormal
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_trace_orthonormal (a b : Fin 3) :
    (pauliV a * pauliV b).trace = 2 * (if a = b then 1 else 0) := by sorry

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