What question did this study set out to answer?

To provide a complete proof of existence and mass gap for four-dimensional Yang–Mills theory with gauge group SU(3).

March 15, 2026Open Access

BCT Appendix JH4: Yang–Mills Existence and Mass Gap — Complete Proof from BCT D4 Superfluid Lattice Geometry

Key Points

To provide a complete proof of existence and mass gap for four-dimensional Yang–Mills theory with gauge group SU(3).
Proof structured in four steps: existence, continuum limit, mass gap determination, and uniqueness analysis.
Utilized Wilson lattice measure and D4 self-duality in the proof process.
Applied Jentzsch theorem and cluster expansion to establish the mass gap.
Confirmed existence of SU(3) Yang–Mills theory as a quantum field theory.
Established that the mass gap Δ is greater than 0, with a lower bound of Δ ≥ √(2π)·Λ_QCD ≈ 550 MeV.

Abstract

Complete proof that four-dimensional Yang–Mills theory with gauge group SU (3) exists as a quantum field theory and possesses a mass gap Δ > 0. Proof in four steps: (I) existence via Wilson lattice measure and D4 self-duality; (II) continuum limit with geometrically fixed coupling g2 = π5/24; (III) mass gap via Jentzsch theorem and cluster expansion; (IV) uniqueness of D4. Lower bound Δ ≥ √ (2π) ·ΛQCD ≈ 550 MeV. Companion technical appendix to Letter 38.

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