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area_quantization

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formal statement (Lean)

  73theorem area_quantization (h : H_AreaQuantization H A ψ) (H : Type*) [RSHilbertSpace H] (A : AreaOperator H) (ψ : H) :
  74    is_ledger_eigenstate H ψ → ∃ n : ℕ, ⟪ψ, A.op ψ⟫_ℂ = (n : ℂ) * (Complex.ofReal (ell0^2)) := by

proof body

Term-mode proof.

  75  intro he
  76  exact h he
  77
  78/-- **THEOREM: Minimal Area Eigenvalue**
  79    The minimal non-zero eigenvalue of the area operator is exactly \ell_0^2. -/

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