`BookProof.BookBrstYangMills.bookCCR_poly` (μ ν : Fin 4) (a b : Fin N) : AfieldPoly μ a * momPoly ν b - momPoly ν b * AfieldPoly μ a = if (μ, a) = (ν, b) then (Complex.I • 1 : Modu

Proved

BookProof.BookBrstYangMills.bookCCR_poly

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBookBrstYangMills.

BookProof.BookBrstYangMills.bookCCR_poly (μ ν : Fin 4) (a b : Fin N) : AfieldPoly μ a * momPoly ν b - momPoly ν b * AfieldPoly μ a = if (μ, a) = (ν, b) then (Complex.I • 1 : Module.End ℂ (FieldPoly N)) else 0

Formalization note: Lean 4 identifier BookProof.BookBrstYangMills.bookCCR_poly.

Preamble

-- Generated from ChapterBookBrstYangMills.lean — theorem BookProof.BookBrstYangMills.bookCCR_poly
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterQuantumGravityBrstCharge
import Mathlib
import Definitions.Def_ChapterBookBrstYangMills
import Definitions.Def_ChapterNavierStokesDifferentialL2
open BookProof.NavierStokesFlow.DifferentialL2
open BookProof.BookBrstYangMills



open MvPolynomial BookProof.BRSTNilpotent BookProof.QuantumGravityBrstCharge

noncomputable section

variable {N : ℕ} (G : GaugeAlgebra N)

Formal statement

theorem BookProof.BookBrstYangMills.bookCCR_poly (μ ν : Fin 4) (a b : Fin N) :
    AfieldPoly μ a * momPoly ν b - momPoly ν b * AfieldPoly μ a
      = if (μ, a) = (ν, b) then (Complex.I • 1 : Module.End ℂ (FieldPoly N)) else 0 := by sorry

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