Mass gap in quantum energy-mass spectrum of relativistic Yang-Mills fields
Abstract
A non-perturbative relativistic quantum Yang-Mills theory with a semisimple compact gauge Lie group on the four-dimensional Minkowski spacetime is set up in a Schroedinger representation with infinite-dim ensional differential operators in the framework of sesqui-holomorphic nuclear Kree-Gelfand triples. The linear quantum Yang-Mills energy-mass operator H is defined as the anti-normal quantization of the non-linear Yang-Mills energy-mass functional of Cauchy data supported by a ball B(R) with the center at the origin of R 3 and the variable radius R > 0. The general global solution of the non-linear YangMills system of partial differential equations (with no res trictions at infinity) is reduced to the solution of the initial value problems in the t emporal gauge with the Cauchy data supported by the balls B(R). It is shown that H dominates the number operator N. Since 0 is the spectral infimum of H and, simultaneously, the simple fundamental eigenvalue of N, variational spectral principles imply that 0 is the simple fundamental eigenvalue of N as well. Thus H has a positive mass gap. The domination proof depends crucially on the magic of the Killing quadratic form that reveals a mass quadratic form in the Weyl symbol of H. With a dimensional transmutation of the coupling constant, the mass gap is proportional to 1/R and the running coupling constant is proportional to √ R. The inverse dependence demonstrates an asymptotic freedom for quantum Yang-Mills self-interaction at…
Read the paper
Related studies
- Chaos and quantum thermalization
- The Dalton quantum chemistry program system
- Cord Blood Leptin and Adiponectin as Predictors of Adiposity in Children at 3 Years of Age: A Prospective Cohort Study
- Quantitative metabolomics by H-NMR and LC-MS/MS confirms altered metabolic pathways in diabetes
- Stable adiabatic quantum batteries
- A novel self-lipid antigen targets human T cells against CD1c(+) leukemias
Go deeper in Evidence Hub
Evidence Hub adds a study data sheet (design, sample size, evidence level, key numbers), an AI summary and a chat grounded in the paper's text.