`BookProof.SmDiracYukawa.diagOp_quadForm_eq` (d : Finset (Fin n) → ℝ) (ψ : FermiFock n) : (inner ℂ ψ (diagOp d ψ) : ℂ).re = ∑ S : Finset (Fin n), d S * ‖ψ S‖ ^ 2

Proved

BookProof.SmDiracYukawa.diagOp_quadForm_eq

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmDiracYukawa.

BookProof.SmDiracYukawa.diagOp_quadForm_eq (d : Finset (Fin n) → ℝ) (ψ : FermiFock n) : (inner ℂ ψ (diagOp d ψ) : ℂ).re = ∑ S : Finset (Fin n), d S * ‖ψ S‖ ^ 2

Formalization note: Lean 4 identifier BookProof.SmDiracYukawa.diagOp_quadForm_eq.

Preamble

-- Generated from ChapterSmDiracYukawa.lean — theorem BookProof.SmDiracYukawa.diagOp_quadForm_eq
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterSmDiracYukawa
import Definitions.Def_ChapterAbelianDiagonalCountable
import Definitions.Def_ChapterSmCarAlgebra
open BookProof.ChapterAbelianDiagonalCountable
open BookProof.SmCar
open BookProof.SmDiracYukawa



open Finset Matrix
open BookProof.SmCar BookProof.FarisLavine

variable {n : ℕ}

noncomputable section

Formal statement

theorem BookProof.SmDiracYukawa.diagOp_quadForm_eq (d : Finset (Fin n) → ℝ) (ψ : FermiFock n) :
    (inner ℂ ψ (diagOp d ψ) : ℂ).re = ∑ S : Finset (Fin n), d S * ‖ψ S‖ ^ 2 := by sorry

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