Experimental-Numerical Exploration of Mass-Gap-Like Behaviour in Yang-Mills-Inspired Stochastic Dynamics
Ywo Josue BAZIE *
Departement de Mathematiques, Universite Joseph KI-ZERBO, 03 BP 7021, Ouagadougou, Burkina Faso.
R. Frank E. 1er J.KABORE
Departement de Mathematiques, Universite Joseph KI-ZERBO, 03 BP 7021, Ouagadougou, Burkina Faso.
Abel ZONGO
Departement de Mathematiques, Universite Joseph KI-ZERBO, 03 BP 7021, Ouagadougou, Burkina Faso.
Pierre Clovis NITIEMA
Departement de Mathematiques de Decision, Universite Thomas Sankara, 12 BP 417, Ouagadougou, Burkina Faso.
*Author to whom correspondence should be addressed.
Abstract
The Yang–Mills mass gap problem remains one of the deepest unsolved challenges in modern mathematical physics. In this work, we propose an experimental mathematical approach to explore the emergence of the mass gap through stochastic particle dynamics inspired by particle swarm optimization (PSO) and stochastic approximation theory. By modeling the evolution of gauge field energy configurations as interacting stochastic particles, we perform large-scale simulations to investigate how energy fluctuations stabilize toward nonzero vacuum expectation values, suggesting a natural gap in the spectrum. The resulting trajectories reveal self-organizing patterns analogous to confinement phenomena in non-Abelian gauge theories. Based on the empirical evidence, we formulate conjectures on the probabilistic structure of energy minima and derive semi-analytical approximations linking stochastic stability and spectral gaps. As limitations, our results claim to be empirical, numerical and intuitive in nature, and thereby are not a mathematical proof of the mass gap.
Keywords: Yang–Mills theory, mass gap, stochastic processes, particle swarm optimization, experimental mathematics, gauge field dynamics