We consider non-Abelian Proca theories with extra fundamental fields included. In the case of SU(2) Proca theory with nonlinear scalar and spinor fields, we obtain spherically symmetric regular solutions describing particlelike configurations with finite energy. For such systems, we find the energy spectrum and show the presence of a mass gap. In the case of SU(3) Proca theory with a nonlinear scalar field, we obtain cylindrically symmetric solutions describing tubes either with the flux of a longitudinal electric field or with the energy flux or with both of them. It is shown that the tubes with the energy flux may contribute considerably to the Proca proton spin. Consistent with all of this, we have argued that non-Abelian Proca theories containing extra fields may approximately describe some phenomena in QCD.

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An approach for measuring energy of cosmic-ray particles with energies E > 1012 eV using an ultrathin calorimeter is presented. The method is based on the analysis of the correlation dependence of the cascade size on the rate of development of the cascade process. In order to determine the primary energy, measurements are made based on the number of secondary particles in the cascade, N e , at two observation levels Z 1 and Z 2, separated by an absorber layer. Based on the obtained measurements, a correlation analysis of the dependence of logN e (Z 1) on th e difference d N = logN e (Z 1) − logN e (Z 2) is carried out. The correlation curves (logN e from d N) in the negative part of the dN axis are almost parallel to each other and practically do not depend on the depth of the cascade development. It makes it possible to determine the primary energy using an ultrathin calorimeter. The best option for applying the method is a calorimeter, which has a unit with a heavy target, leading to the rapid development of the cascade, and a homogeneous measuring and absorption block.

We consider thermodynamic properties of a quark–gluon plasma related to quasiparticles having the internal structure. For this purpose, we employ a possible analogy between quantum chromodynamics and non-Abelian Proca-Dirac-Higgs theory. The influence of characteristic sizes of the quasiparticles on such thermodynamic properties of the quark–gluon plasma like the internal energy and pressure is studied. Sizes of the quasiparticles are taken into account in the spirit of the van der Waals equation but we take into consideration that the quasiparticles have different sizes, and the average value of these sizes depends on temperature. It is shown that this results in a change in the internal energy and pressure of the quark–gluon plasma. Also, we show that, when the temperature increases, the average value of characteristic sizes of the quasiparticles increases as well. This leads to the occurrence of a phase transition at the temperature at which the volume occupied by the quasiparticles is compared with the volume occupied by the plasma.