2014/07/01 by Alexander Dynin · 1 citation
Mathematics · #Spectral Theory in Mathematical Physics #Advanced Operator Algebra Research #Advanced Algebra and Geometry #Eigenvalues and eigenvectors #Yang–Mills existence and mass gap #Operator (biology) #Mathematical physics #Mathematics #Coupling constant #Inverse #Quantum #Mass gap #Schrödinger's cat #Quantum mechanics #Physics #Gauge theory
paper · doi:10.1134/s1061920814030042
openalex publication_date 2014/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Theorem 4.1 of the author’s paper “Quantum Yang-Mills-Weyl dynamics in the Schroedinger paradigm”, RJMP 21 (2), 169–188 (2014) claims the relative ellipticity of cutoff Yang-Mills quantum energy-mass operators in von Neumann algebras with regular traces. This implies that the spectra of cutoff self-adjoint Yang-Mills energy-mass operators in a nonperturbative quantum Yang-Mills theory (with an arbitrary compact simple gauge group) are nonnegative sequences of the eigenvalues converging to +∞. The spectra are self-similar in the inverse proportion to the running coupling constant. In particular, they have self-similar positive spectral mass gaps. Presumably, this is a solution of the Yang-Mills Millennium problem. The present note shows that the fundamental spectral value of a cutoff quantum Yang-Mills energy-mass operator is the simple zero eigenvalue with the vacuum eigenvector. The direct proof (without von Neumann algebras) is based on the domination over the number operator (with simple fundamental eigenvalue) and the standard spectral variational principle.