Some structural considerations are made on the field equations in the theory of fields in Finsler spaces. In particular, much attention is paid to the Finslerian gravitational field equations proposed by Miron.

An interpretation is suggested that a spontaneous compactification of space-time can be regarded as a topological defect in a higher-dimensional Einstein–Yang–Mills (EYM) theory. We start with \(D\)-dimensional EYM theory in our present analysis. A compactification leads to a \(D\)-2 dimensional effective action of Abelian gauge-Higgs theory. We find a “vortex” solution in the effective theory. Our universe appears to be confined in a center of a “vortex”, which has \(D\)-4 large dimensions. In this paper we show an example with SU(2) symmetry in the original EYM theory, and the resulting solution is found to be equivalent to the “instanton-induced compactification”. The cosmological implication is also mentioned.

The alternative definition of the many-particle Wigner functions for real and complex scalar fields is proposed. It leads to the consistent quantum transport theory. We obtain the exact. hierarchy of the quantum transport equations. Its truncation in the kinetic case yields the relativistic Vlasov-type equation with the series of the quantum corrections. The hierarchy is truncated also beyond the kinetic case.

A model of two-component fermion field is constructed, solutions of the version of which set up 4 generations with SU(3)\(_{\rm c} \times \) SU(2)\(_{\rm L} \times \) U(1) as the symmetry group. An internal space is not the Minkovski one. A permissible multiplet of the model may contain two SU(2)\(_{\rm R}\)-singlets in the lepton sector.

The differential cross-section is calculated for the bremsstrahlung of photons from magnetic moments of protons or neutrons decelerated in an external static nuclear (vector) potential. The lowest-order perturbative approximation is used (both with respect to the magnetic moment and external potential). The recent hypothesis of a new magnetic-type interaction of nucleons is also considered in the context of possible bremsstrahlung of a new kind from the corresponding nucleon magnetic-type moments.

The EMC and SLAC data on momentum dependence of nuclear attenuation of fast hadrons produced by leptons from nuclear targets are interpreted in terms of the string model of particle production. It is shown that the colour string formed in a collision interacts strongly in nuclear matter before the final hadron is formed. A prediction for behaviour of nuclear attenuation in the region of large momentum of the hadron is given.

We formulate the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of kinetic equations for quark-less QCD plasma. Assuming Bose-Einstein distribution for the equilibrium distribution of hot gluons and ghosts, we solve those kinetic equations in the mean-field limit and obtain the dispersion relation in the order \(g^2\). Contrary to this above assumption, the state of noninteracting gluons is unstable, i.e. the damping constant of the colour oscillations is negative. We argue that the non-perturbative effects at the scale \(\sim gT\) make the perturbative approximation to the equilibrium distribution of hot gluons inconsistent with the kinetic equations already at the lowest, non-trivial order \(g^2\).

A discussion of the dispersive effects arising when scalar waves are coupled to plane electromagnetic waves is given. Higher powers of the electromagnetic invariants are included that may arise in strong fields and certain distinct signatures for the number of independent frequency components that occur for particular couplings are found.

Using the thermodynamic model at zero temperature and density-dependent quark mass approach to confinement, the possibilities of light quark liberation and strange quark formation near ground state nuclear matter have been investigated.