Reexamining the Yang–Mills Mass Gap Problem: A Constructive Approach via Open Quantum Systems and Quantum Corral Confinement

We present a comprehensive reassessment of the Yang–Mills mass gap problem, challenging the traditional axiomatic foundations that assume an isolated quantum system with a unique vacuum state. By reformulating Yang–Mills theory as an open quantum system coupled to environmental degrees of freedom, we demonstrate that the mass gap emerges naturally as a collective property of dissipative dynamics. Our framework employs local C∗-algebras, the Gelfand–Naimark–Segal (GNS) construction, and the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equation to preserve unitarity at the total-system level while generating effective dissipation in the gauge sector.A central new element is the quantum corral: a geometric confinement mechanism in which local spacetime curvature R(r) acts as a potential wall. Within a corral ofradius R corr, the Yang–Mills eigenvalue problem reduces to a dissipative Schrödinger equation with Dirichlet boundary conditions. The allowed modes are characterized by the zeros ξ0n of the Bessel function J0, yielding a quantized fundamental mass gap mg,corr = ℏc ξ01 Rcorr, ξ01 = 2.4048. For mg,corr ≈ 1.06 GeV this gives Rcorr ≈ 0.47 fm, consistent with the established QCD confinement scale.We provide extended numerical evidence from a systematic lattice scaling study over β ∈ 5.7, 7.0 (seven values) and L ∈ 8, 48 (seven volumes), yielding the1continuum mass gap mcont g = 0.465 ± 0.002 (lattice units, χ2/dof = 0.87), corresponding to mphys g = 1.61 ± 0.01 GeV, consistent with independent lattice QCDdeterminations of the lightest 0++ glueball. Our framework satisfies a modified set of Osterwalder–Schrader axioms for open quantum field theories, to which we add a new Axiom 7 (Geometric Closure): the quantum corral exhibits a subregion where the unmodified Clay axioms hold with the mass gap determined by Rcorr. We prove uniqueness and global stability of the Lindblad steady state (Theorem 2.3) and verify that the corral boundary conditions are compatible with microcausality (Proposition 3.4). GPU acceleration via QUDA enabled ∼ 18× CPU speedup.