The available theory of the electron conduction in dielectrics and semiconductors assumes that the conduction electron moves within one of the “allowed” energy bands of a crystal, and the electron ш-function is a wave, whose amplitude is constant over the whole crystal bulk. The presence of forbidden gaps in crystals is experimentally confirmed: this is testified by the fact of the dielectric existence itself, data on the temperature dependence of the electric conduction, data on the internal photoeffect and the photoeffect from a metal into a dielectric, etc. Other features of the theory mentioned above did not find any direct confirmation, and they even contradict sometimes the experimental facts. But first of all (at least in the case of ionic crystals), it is worth to indicate that the available theory includes an internal contradiction, namely: while considering the quantum states of conduction electrons, it is assumed, as usual, that ions are fixed at lattice sites; in this case, an electron appears to be in a periodic field. However, in reality, ions are moving, and the electron state adiabatically follows the ion motion. S.I. Pekar already considered this motion [1] and showed that the conduction electron polarizes dielectrically the ionic crystal with the own electric field. It turns out that, already at the very beginning of the process of polarization, the polarized crystal represents a potential well with discrete spectrum for the electron. The electron having spent a part of its energy to polarize the crystal goes to a discrete level into the local state; then the crystal polarization increases, and the electron level and the energy of the whole system are lowered. The equilibrium will be reached when the energy of the system reaches its minimum. In this case, the polaron is created, as was considered by one of the authors in the previous works [2, 3] in detail. Thus, the band state of a conduction electron does not correspond to an extremum of the system energy, i.e. it is unstable. Slow conduction electrons should constantly transfer into the polaron state. The decay time of a band state for the slow electron should be of the order of 10−13 s; hence, it is necessary to revise the foundations of the available conduction theory. S.I. Pekar [1, 4] offered a new point of view concerning the electron conduction of ionic crystals. According to it, the current carrier is just a polaron, rather than a free electron in the conduction band. In an external electric field, the polaron should move like a negative charge. In this case, the local state should shift as a whole along the field direction (the inertial polarization of the crystal should follow the polaron movement). The calculated polaron mobility [4] is in good agreement, by the order of magnitude, with the mobility of a current carrier determined experimentally as a product of the electric conduction and the Hall constant. In the present paper, we will calculate the effective mass of a polaron.

The distribution of magnetic moments in a ferromagnetic crystal is investigated. It is found that such a crystal consists of elementary layers magnetized to saturation. The width of these layers is determined. In an external magnetic field, the boundaries between these layers move; the velocity of this propagation is determined. The magnetic permeability in a periodical field parallel and perpendicular to the axis of easiest magnetization is found.

A b s t r a c t : A var ian t of the theory is proposed in which non-conservat ion of par i ty can be in t roduced wi thout assuming a s y m m e t r y of space with respect to inversion. Various possible consequences of non-conservat ion o~ par i ty are considered which per ta in to the properties of the neutr ino and in this connection some processes involving neut r inos are examined on the assumpt ion t h a t the neutr ino mass is exact ly zero.

The production of an electron and positron by a collision of two particles, moving with a velocity near to the velocity of light, is investigated. The cross-section of this effect is obtained; it increases with the cube of the logarithm of the energy of the colliding nuclei.