Yang–Mills theory
Quantum Yang–Mills theory is the current grounding for the majority of theoretical applications of thought to the reality and potential realities of elementary particle physics. The theory is a generalization of the Maxwell theory of electromagnetism where the "chromo"-electromagnetic field itself carries charge. As a classical field theory it has solutions which travel at the speed of light so that its quantum version should describe massless particles (gluons). However, the postulated phenomenon of color confinement permits only bound states of gluons, forming massive particles. This is the mass gap. Another aspect of confinement is asymptotic freedom which makes it conceivable that quantum Yang-Mills theory exists without restriction to low energy scales. The problem is to establish rigorously the existence of the quantum Yang–Mills theory and a mass gap.