Maxwell’s equations and the mechanical balance equations for a deformable electromagnetic solid are obtained via a strictly variational approach. The Lagrangian (density) is taken as the sum of the electromagnetic field Lagrangian, the matter Lagrangian, and the interaction Lagrangian. The construction of the interaction Lagrangian is performed by modeling the solid as a set of charged particles and by defining the macroscopic quantities through a suitable average procedure: the interaction Lagrangian then takes the form of a multipole expansion. The Euler–Lagrange equations provide directly Maxwell’s equations, the equations of motion, and the constitutive equations. The calculations are made explicitly up to the quadrupole approximation; the agreement with existing theories makes the approach applicable to multipole expansions of any order.

Lagrangian and equations of \(N = 1\) supergravity are obtained in terms of universal matrix nonlinear first-order equations with quadratic nonlinearities, which have a number of advantages. The quadratic and cubic matrices are derived and their properties are investigated. It is shown that tetrad-formalism matrices have much simpler minimum polynomial compared with metric one. The field function structure is obtained containing tetrads, Ricci coefficients and Riemann tensor and also both spin-vector and components lowering non-linearities.

It is shown that the only Kasner-like solution of the GET field equations with a nonzero electromagnetic field corresponds to an empty field geometry of the space-time. In this case, the electromagnetic field tensors of the theory coincide as could be expected from general. considerations.

In this work both the radial and angular parts of the relativistic fermion–antifermion equation with the Coulomb-like scalar potential are investigated. The formula is obtained determining a discrete energy mass spectrum of the composite quark–antiquark systems. The performed analysis of the angular part of the equations leads to the two series of solutions corresponding to the \(P\)-parity values \(P=(-1)^J\) and \(P=(-1)^{J+1}\), respectively. By using weak coupling approximation the satisfactory agreement between particle mass values calculated on this basis and experimental data for several families of the real mesons is obtained.

Using the group-theoretical methods and the geometrical picture of pure spinors due to E. Cartan we give the explicit construction of the manifold of such spinors for the group SO\((\nu \), \(\nu )\). We apply this construction to solve the Dirac equation for pure spinors in the momentum space.

Realistic momentum distribution in nuclear matter is used in calculating the absorptive potential \(W\) and the nucleon mean free path \(\lambda \) for nucleon energies \(e \lesssim 200\) MeV. \(W\) is calculated with a simple expression in terms of free NN cross section, which takes care of Pauli blocking and binding effects. Whereas previous calculations suggested a sharp increase in \(\lambda \) as \(e \to 0\), present results show a much smoother dependence of \(\lambda \) on \(e\), with \(\lambda = 5 \pm 1\) fm in the whole energy range \(0 \lesssim e \lesssim 200\) MeV.