Mathematical quantum Yang-Mills theory revisited II: Mass without mass

TL;DR

This paper revisits the mathematical formulation of quantum Yang-Mills theory, demonstrating that the spectrum of the interaction Hamiltonian exhibits a positive mass gap without explicitly introducing mass.

Contribution

It provides a rigorous mathematical analysis showing the emergence of a mass gap in massless Dirac coupled gauge theories without adding mass terms.

Findings

Positive mass gap in the spectrum of the second quantized Hamiltonian

Massless Dirac equations can produce massive spectra through gauge interactions

Revisits foundational aspects of quantum Yang-Mills theory with new insights

Abstract

Massless Dirac equation for spinor multiplets is minimally coupled with a unitary representation of an arbitrary compact semisimple gauge group. The spectrum of the second quantized interaction Hamiltonian has a positive mass gap running along the classical energy scale.