A non-conformal, type one solution of Einstein–Maxwell equations for a Static charged fluid sphere is obtained and joined smoothly to the Reissner–Nordstrom solution. The solution thus obtained is analysed numerically. The solution is reducible to Schwarzschild’s interior solution in the absence of charge.

The leptonic sector of an electroweak plasma in an external magnetic field is studied within the Weinberg–Salam model. Nonvanishing chemical potentials \(\mu _1\), \(\mu _2\) related to electric charge and leptonic number are introduced and used to establish the set of equations describing the chemical equilibrium of the system, which will be taken as electrically neutral. The partition functional is expressed in terms of an effective Lagrangian dependent on \(\mu _1\), \(\mu _2\) as background fields. Gauge conditions dependent on \(\mu _1\), \(\mu _2\) are imposed. By using them and expanding the charged fields in magnetic eigenfunctions, the functional integration is performed in the one-loop approximation. The thermodynamic potential is written in terms of the spectra of the physical particles, and the equilibrium conditions are discussed. No Bose condensation in the usual sense occurs at \(T \not = 0\) in the presence of the magnetic field, but it is produced in the \(T = 0\) case. By calculating the magnetization it is shown that an increase in the lepton density may provoke an increase in the effective magnetic field.

The nonminimal description (with the help of 3-rd and 4-th rank Lorentz tensor) of the spin 2, equivalent to the Pauli–Fierz theory, is given. The variational principle is formulated.

A review of the on-shell renormalization scheme is given. We stress the analogy of this renormalization procedure with the “usual” one used in QED and discuss the differences. The calculation of some important parameters in the GWS model is sketched.

The production of low-mass dileptons in ion–ion collisions is estimated under the assumption that this process is a “sum” of nucleon–nucleon collisions. The resulting estimate of dilepton production can be considered as a background for dileptons originated by a true quark–gluon plasma.

Following the general principles of both Newton’s mechanics and quantum mechanics a new formulation of wave mechanics is proposed. The new basic equations do not contain physical parameters and admit a different interpretation of the Planck constant.