Experimental Exploration of the Yang–Mills Mass Gap through Stochastic Particle Dynamics

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. From the empirical evidence, we formulate conjectures on the probabilistic structure of energy minima and derive semi-analytical approximations linking stochastic stability and spectral gaps. This work illustrates how stochastic dynamical systems can serve as an experimental framework for probing nonperturbative aspects of the Yang–Mills theory, bridging computational experimentation and mathematical insight.