A generic approach in tackling the Yang-Mills Theory’s existence and mass gap problem – Conditions found for which the mass gap do not exist in different gauge theories

The Yang-Mills Theory’s existence and mass gap problem is one of the unsolved problems in mathematics and mathematical physics. It is proposed by the physicists Chen Ning Yang and Robert Mills in 1953. Although the academical literature expects the mass gap to exist in non-abelian gauge theories (e.g.quantum chromodynamics resp. QCD) in any dimensions less or equal than 4, until this day, no unconditional and generic proof valid for all dimensions, circumstances and use cases could be delivered for the mass gap existence even in non-abelian gauge theories like quantum chromodynamics resp. QCD. In our work, we firstly build our main particle model for both abelian gauge theories (e.g. QED) and especially non-abelian gauge theories like QCD (non-pure QCD with matter fields & quarks and pure QCD without quark particles). Then we apply the energy-momentum relation to our main particle models and finally we are able to disprove the existence of mass gap in both abelian and non-abelian gauge theories like QED and non-pure & pure QCD through discovering a set of counter examples and conditions for which the mass gap existence is not feasible, because the relationship between mass of the massive particle in non-vacuum state and the minimum decrease of initial momentum of the original particle in vacuum derived from the energy-momentum relation formula would always be violated under these conditions and circumstances.