Renormalized Four Dimensional Quantum Yang-Mills Theory and Mass Gap

2014/06/16 by Simone Farinelli, Farinelli, Simone
Physics and Astronomy · #53Z05 #58Z05 #Black Holes and Theoretical Physics #FOS: Mathematics #General Mathematics (math.GM) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.1406.4177

openalex publication_date 2014/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A quantization procedure for the Yang-Mills equations for the Minkowski space R^1,3 is carried out in such a way that field maps satisfying Wightman axioms of Constructive Quantum Field Theory can be obtained. Moreover, by removing the infrared and ultraviolet cutoffs, the spectrum of the corresponding (non-local) QCD Hamilton operator is proven to be positive and bounded away from zero, except for the case of the vacuum state, which has vanishing energy level. The whole construction is invariant for all gauge transformations preserving the Coulomb gauge. As expected from QED, if the coupling constant converges to zero, then so does the mass gap. This is the case for the running coupling constant leading to asymptotic freedom.

Related

• A Constructive Proof of Existence and Mass Gap for Pure SU(3) Yang-Mills in Four-Dimensional Space-Time
• Positive mass gap of quantum Yang-Mills Fields
• Four Dimensional Quantum Yang-Mills Theory for Weak Coupling Strength: Mass Gap Implies Quark Confinement
• A Geometric Approach to the Yang-Mills Mass Gap
• Quantum energy-mass spectra of relativistic Yang-Mills fields in a\n functional paradigm