О ПРОБЛЕМЕ КВАНТОВАНИЯ В ТЕОРИИ ГРАВИТАЦИИ

A perturbativ equantization proves to be possible in the framework of the field-theoretic paradigm only for weak gravitational fields. The geometric approach admits a nonperturbative quantization of both geometry as a whole and space-time. Quantum mechanics and quantum field theory may be considered in a given space-time.В рамках теоретико-полевой парадигмы пертурбативное квантование оказывается возможным только для слабых гравитационных полей. Геометрический подход допускает непертурбативное квантование как геометрии в целом, так и пространства-времени. Квантовая механика и квантовая теория поля могут рассматриваться в заданном искривлённом пространстве-времен

МАТЕМАТИЧЕСКИЕ МОДЕЛИ В ТЕОРЕТИЧЕСКОЙ ФИЗИКЕ

Quantum theory and relativity theory as well as possible reconciliation have been analyzed from the viewpoint of mathematical models being used in them, experimental affirmation, interpretations and their association with dualistic paradigms.Проанализированы квантовая теория и теория относительности, а также их возможные согласования, с точки зрения используемых в них математических моделей, экс-периментального подтверждения, интерпретаций и отнесения их к дуалистическим парадиг-мам

Об интерпретациях общей теории относительности

The article considers the assumptions of A. Eddington on the possibility to interpret gravitation outside the framework of a geometric paradigm. The results obtained are consistent with astronomic observations.Обсуждаются предположения А. Эддингтона o возможности интерпретации гравитации вне рамок геометрической парадигмы. Полученные результаты согласуются с астрономическими наблюдениями

Band-gap solitons in nonlinear optically-induced lattices

We introduce novel optical solitons that consist of a periodic and a spatially localized components coupled nonlinearly via cross-phase modulation. The spatially localized optical field can be treated as a gap soliton supported by the optically-induced nonlinear grating. We find different types of these band-gap composite solitons and demonstrate their dynamical stability.Comment: 4 pages, 5 figure

Quantum Cosmology and Open Universes

Quantum creation of Universes with compact spacelike sections that have curvature $k$ either closed, flat or open, i.e. $k=\pm1,0$ are studied. In the flat and open cases, the superpotential of the Wheeler De Witt equation is significantly modified, and as a result the qualitative behaviour of a typical wavefunction differs from the traditional closed case. Using regularity arguments, it is shown that the only consistent state for the wavefunction is the Tunneling one. By computing the quantum probabilities for the curvature of the sections, it is shown that quantum cosmology actually favours that the Universe be open, $k=-1$. In all cases sufficient inflation $\sim 60$ e-foldings is predicted: this is an improvement over classical measures that generally are ambiguous as to whether inflation is certain to occur.Comment: 11 pages, Revtex, 7 figures. Accepted for publication in PRD. New material and important corrections added in response to referee's repor

Quantum creation and inflationary universes: a critical appraisal

We contrast the possibility of inflation starting a) from the universe's inception or b) from an earlier non-inflationary state. Neither case is ideal since a) assumes quantum mechanical reasoning is straightforwardly applicable to the early universe; while case b) requires that a singularity still be present. Further, in agreement with Vachaspati and Trodden [1] case b) can only solve the horizon problem if the non-inflationary phase has equation of state $\gamma<4/3$.Comment: 21 pages Late

Stable multicolor periodic-wave arrays

We study the existence and stability of cnoidal periodic wave arrays propagating in uniform quadratic nonlinear media and discover that they become completely stable above a threshold light intensity. To the best of our knowledge, this is the first example in physics of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons.Comment: 12 pages, 3 figure

Dynamics of the Universe with global rotation

We analyze dynamics of the FRW models with global rotation in terms of dynamical system methods. We reduce dynamics of these models to the FRW models with some fictitious fluid which scales like radiation matter. This fluid mimics dynamically effects of global rotation. The significance of the global rotation of the Universe for the resolution of the acceleration and horizon problems in cosmology is investigated. It is found that dynamics of the Universe can be reduced to the two-dimensional Hamiltonian dynamical system. Then the construction of the Hamiltonian allows for full classification of evolution paths. On the phase portraits we find the domains of cosmic acceleration for the globally rotating universe as well as the trajectories for which the horizon problem is solved. We show that the FRW models with global rotation are structurally stable. This proves that the universe acceleration is due to the global rotation. It is also shown how global rotation gives a natural explanation of the empirical relation between angular momentum for clusters and superclusters of galaxies. The relation $J \sim M^2$ is obtained as a consequence of self similarity invariance of the dynamics of the FRW model with global rotation. In derivation of this relation we use the Lie group of symmetry analysis of differential equation.Comment: Revtex4, 22 pages, 5 figure