`BookProof.ChapterWignerOrbitClassification.exists_boost_spacelike_of_pos` {m : ℝ} (hm : 0 < m) (p : Fin 4 → ℝ) (hshell : minkSq p = -m ^ 2) (hpos : 0 < p 0 + p 3) : ∃ A : Matrix (

Proved

BookProof.ChapterWignerOrbitClassification.exists_boost_spacelike_of_pos

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWignerOrbitClassification.

BookProof.ChapterWignerOrbitClassification.exists_boost_spacelike_of_pos {m : ℝ} (hm : 0 < m) (p : Fin 4 → ℝ) (hshell : minkSq p = -m ^ 2) (hpos : 0 < p 0 + p 3) : ∃ A : Matrix (Fin 2) (Fin 2) ℂ, A.det = 1 ∧ act A (hermOfMom (spaceRefMom m)) = hermOfMom p

Formalization note: Lean 4 identifier BookProof.ChapterWignerOrbitClassification.exists_boost_spacelike_of_pos.

Preamble

-- Generated from ChapterWignerOrbitClassification.lean — theorem BookProof.ChapterWignerOrbitClassification.exists_boost_spacelike_of_pos
import Definitions.Def_ChapterWignerLittleGroupOrbits
import Mathlib
import Definitions.Def_ChapterWignerOrbitClassification
import Definitions.Def_ChapterGravityProjector
import Definitions.Def_ChapterWignerLittleGroup
open BookProof.ChapterGravityProjector
open BookProof.ChapterWignerLittleGroup
open BookProof.ChapterWignerOrbitClassification


open Matrix Complex


open BookProof.ChapterWignerLittleGroup BookProof.ChapterWignerLittleGroupOrbits

Formal statement

theorem BookProof.ChapterWignerOrbitClassification.exists_boost_spacelike_of_pos {m : ℝ} (hm : 0 < m) (p : Fin 4 → ℝ)
    (hshell : minkSq p = -m ^ 2) (hpos : 0 < p 0 + p 3) :
    ∃ A : Matrix (Fin 2) (Fin 2) ℂ, A.det = 1 ∧
      act A (hermOfMom (spaceRefMom m)) = hermOfMom p := by sorry

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