We show from the action integral that in the special environment of a flux tube, QCD4 in (3+1) dimensional space-time can be approximately compactified into QCD2 in (1+1) dimensional spacetime. In such a process, we find out how the coupling constant g2D in QCD2 is related to the coupling constant g4D in QCD4. We show how the quark and the gluon in QCD2 acquire contributions to their masses arising from their confinement within the tube, and how all these quantities depend on the excitation of the partons in the transverse degree of freedom. The compactification facilitates the investigation of some dynamical problems in QCD4 in the simpler dynamics of QCD2 where the variation of the gluon fields leads to a bound state.
The dynamics of quarks and gauge fields in the lowest energy states in QCD and QED interactions is studied by compactifying the (3+1)D space-time to the (1+1)D space-time with cylindrical symmetry and by combining Schwinger's longitudinal confinement in (1+1)D with Polyakov's transverse confinement in (2+1)D. Using the action integral, we separate out the transverse and longitudinal degrees of freedom. By solving the derived transverse and longitudinal equations, we study the QCD and QED collective excitations. In addition to the well known QCD low-energy states, we find stable collective QED excitations showing up as massive QED-confined mesons, in support of previous studies. In particular, the masses of the recently observed X17 particle at about 17 MeV and the E38 particle at about 38 MeV are calculated in the developed approach, in good agreement with experimental results.
Impact of scattering in matter on particle decays at high energy is studied. The consistent method of the calculation of the decay probability of the particles scattered multiply elastically in an equilibrium medium is developed. The decay probability of such particles is obtained. The Dalitz decay of a pion in the matter is studied.
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