The coherence of the EEG and the coupling of the impulse activity of neurons of the visual and sensorimotor areas of the neocortex of rabbits, recorded simultaneously from the same electrodes, were compared under chronic experimental conditions. An association was found between the presence and properties of the conjugated functioning of neurons and the coherence of the EEG at various frequencies. Greater coherence of the EEG was observed during the correlated functioning of neurons at frequencies of 3–4.5 Hz than during independent functioning. The neurons discharged in pairs, with a smaller delay between them at the highest level of EEG coherence, and a common source participating more often in their synchronization than at the lowest level of EEG coherence.

A representation in the form of the Faddeev-Popov path integral is constructed for solving the equations of quantum geometrodynamics (QGD). It is shown that QGD is equivalent to canonical quantization of gravity in a unitary gauge. Given the state of the gravitational field on the initial Cauchy hypersurface, a wave function of closed universe is constructed so that it satisfies the QGD equations. Using the principles of canonical quantization, a probabilistic interpretation of this wave function is constructed in a fashion close to Everett's concepts of quantum mechanics.

A solution of the field equations in the Einstein-Cartan theory, describing a uniform isotropic distribution of spinning dust is obtained. Unlike the interpretations of previous authors, the resulting cosmological solution of this theory supports a chaotically disoriented distribution of particle spins. Further, nonzero square spin density terms remain after averaging (twisting). The analogy between the cosmological twisting of space-time and the Einstein Λ-term is discussed. The solution can be matched to an external metric of the Robertson-Walker type.

It is shown that for a definite value of the spin-spin interaction constant, which must be introduced from gauge considerations, the Einstein-Cartan equations without the Λ term admit a cosmological solution in the form of a steady-state de Sitter metric. It is asserted that such a solution can serve as a model of the pre-Friedmann stage of the expansion of the universe, when the spin-torsion interaction is comparable with the energy-momentum-curvature interaction. The value of the interaction constant is obtained (θ∼-10−20) under the condition that the de Sitter stage was realized at quantum densities (1094 g/cm3).

The effect of the creation of massless scalar particles by a cosmological torsion field is considered. It is shown that the particles produced make an initially isotropic universe anisotropic.

The quantization of a homogeneous isotropic closed Friedmann model filled with an ideal fluid is discussed within the framework of a geometrodynamical approach.

This article is the first of a series of studies devoted to several problems of quantum and classical cosmology as well as to the gravitational collapse of inhomogeneous configurations. In this article we consider the structure of the theory of gravitational collapse and we construct the Hamiltonian of an ideal liquid with an arbitrary equation of state.