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The Yang-Mills theory is part of the Standard Model of particle physics. Thelack of the mathematical understanding of the theory stands out in theoreticalphysics. In order to address this problem we observe that a recently proposedgeneral model beyond the Standard Model resolves the energy scales of a latticeregularized Yang-Mills theory by means of an extra dimension. The extradimension ensures that all intermediate length scales of the physical systemare available by definition. In this paper we study the role of the extradimension also in the case of the free boson field. We find that if the extradimension size is large, the model describes the classical motion of thesystem. In the opposite limit we recover its standard quantum mechanical motionwithout loss of information. Therefore, the Hilbert space of states in thepresence of the extra dimension describes physical phenomena at all energyscales. This observation allows us to raise the description of length scales byan extra dimension at the level of a principle for the theories beyond theStandard Model, the only modeling constraint being the correspondenceprinciple. As it was shown recently, the fermion ground state energy of a gaugeinvariant Hamilton operator of Dirac fermions gives a particular latticeregularization of the Yang-Mills theory. Integration of gauge fields gives apure fermion theory of color singlet fermion-antifermion pairs at each latticesite evolving along the extra dimension. Color confinement follows directlyfrom this property. It allows for a saddle point solution in the limit of alarge number of colors. In this paper we find that the glueball spectrum of theYang-Mills regularized theory is of the Hagedron type and bounded below by apositive value. We show also that the color charge is screened and thequark-antiquark potential is constant.

Resolving the scales of the Yang-Mills theory by means of an extra dimension