With this work, we try to answer 3 fundamental questions that have plagued mathematicians and physicists for several decades. As known, the spontaneous symmetry breaking (SSB) and the Brout-Englert-Higgs Mechanism (BEH-M) solved the Yang-Mills Mass Gap Problem. However, various mathematicians, even prestigious ones, consider the basic assumptions of the gauge theories to be wrong, as well as in conflict with the experimental evidences and in clear disagreement with the facts, distorcing the physical reality itself. Likewise, the Quantum Fields Theory (QFT) is mathematically inconsistent, adopting a mathematical structure somewhat complicated and arbitrary, which does not satisfy the strong demands for coherence. The weakest point of the gauge theories, in our opinion, consists in imposing that all the particles must be free of an intrinsic mass (massless).
On the contrary, even for the particle considered universally massless, i.e. the photon (P), our calculations show a dynamic-mass, a push-momentum (p) of 1.325⋅10−22[g⋅cm/s]. That is, an optic P hits a particle with an energy-mass greater than 100 protons rest-mass’. It is clear that if we replaced this value with the full value of the P inserted in the equations of the Perturbation Theory, QFT and Yang-Mills theories, all divergences, that is all zeroes and infinities, would suddenly disappear.
Consequently, the limits imposed by the SSB disappear so that there is no longer any need to deny the mass to the Nuclear Forces bosons, including the Yang-Mills b quantum. Still, the photons (Ps) are the basis of the quantum vacuum energy, which is distributed ubiquitously, also within the intra-atomic spaces. It is likely that a lot of Ps were trapped in atomic nuclei (at the time of nucleosynthesis) and among quarks (Qs) at the time of primordial nucleonic synthesis. We believe that when Qs get too close to each other, till repelling each other (Asymptotic Freedom of Qs), this may depend on the presence of a multitude of Ps that, no further compressible, begin to exert an antigravity repulsive force, just as a Dark Energy. This limit to Compressibility (C) of the radiation is shown in equation: PV 4/3 = C, where V is the volume, and P is the Pressure of the photonic gas. Quantum Mechanics plays a crucial role, through the Uncertainty Principle, in the spatial Confinement of Qs, which have remained eternally confined in an extremely narrow space by the Strong Interaction, but in primis by the very short range (likely ≈8.44[±1.44]⋅10-16cm) and lifetime of gluon(G) which, from our calculations, is ≈2.73[±0.564]⋅10-26 sec. Therefore, a new parameter may be added to the Qs and G spatial Confinement: the b quantum or G Temporal Confinement (and of their Colours and anti-Colours).
Yang-Mills Mass Gap Clay Institute Problem Solution