Poly-Hamiltonian Dynamic Systems and Turbulence

Proceeding from the general theory of poly-Hamiltonian dynamic systems, a model of multiflow motion is constructed in the phase space. The kinetic theory of poly-Hamiltonian systems is formulated. Hydrodynamic approximation is considered. In the context of this theory, a definition of turbulence is given and a scenario of its origin is described. As an example of systems creating turbulence, a gas of one-dimensional coupled oscillators is considered.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 23–32, March, 2005.     

Problem of Interactions: Electromagnetic Interactions of Particles

Proceeding from the dynamic theory of particles proposed in [1], electromagnetic interactions of charged particles are examined. The existence of interactions of this type is associated with the degeneracy of the ground state of a relativistic bi-Hamiltonian system U _e(1) underlying the given theory.     

Quantum Mechanics of Systems with a Nonenumerable Number of Degrees of Freedom

Is has been shown that the quantum theory of systems with an infinite nonenumerable number of degrees of freedom is incompatible with the assumption about the continuity of the space of indices of degrees of freedom: in this case, a discrete topology on the space of indices is required. This is illustrated by the example of field systems.     

Problem of Interactions: Gravitational Interactions

Within the framework of a new approach to the problem of particles [1], gravitational interactions are considered. Interactions of this type are associated with the degeneracy of states of a relativistic bi-Hamiltonian system T _3,1 underlying the given approach. Within the framework of this approach, there is a clearly defined difference between the gravitation and the metric theory of space-time.     

On the Physical Principles of Gravitation

As is well known, the general theory of relativity (GTR) proceeds from the so-called equivalence principle according to which the dynamic effects of gravitation are identified with the kinematic effects of accelerated motion. In this theory, gravitation is associated with the Riemannian structure of the pseudo-Euclidean space-time (described by the metric tensor and the Riemannian connectivity and the curvature related with this tensor) specified in the four-dimensional space-time continuum. In the present work, it is first demonstrated that on the level of elementary particles (within the framework of the theory of quantized fields), the equivalence principle is violated. It is established that elementary particles with different masses (for example, electron and proton) move in the external gravitational field with different accelerations. In this connection, a new approach to the problem of gravitational interactions is suggested based on deformations of a latent dynamic system conditionally called ether that underlies elementary particle theory [2].     

Theory of the sommerfeld fine-structure constant

The value of the “bare” fine-structure constant α₀ is calculated within the framework of a new approach to the problem of elementary particles. Khar'kov Physics and Technology Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10. pp. 60–63, October, 1997.     

Quantum Mechanics of an Oscillator with Infinitesimal Frequency

Russian Physics Journal -     

The Green's Causal Functions of Bilocal Fields

On concrete examples it is demonstrated that in quantum field theory with three universal constants c, h, and k suggested in [1], the limiting value k ^–1 = 0 corresponding to local theory is a bifurcation point: the Green's causal function for finite k bifurcates into . The natural carrier of the latter is the Euclidean space-time R ₄, and its continuation from R ₄ to R _3,1 is regular. The former is singular at zero point and on the light cone and hence is rejected.     

Lepton theory

Within the framework of the elementary-particle theory proposed in [1], the electron, muon, and τ-lepton masses are calculated. Khar’kov Physicotechnical Institute, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 29–37, July, 1997.     

Quantization of the dirac fiber and its application to the theory of elementary particles

A problem of ultraviolet divergences in the quantum field theory is analyzed. It is pointed out that this problem is associated with the use of improper functions in space-time. It is shown that a radically new method of quantization of matter based on the dynamical structure of a new type is possible in the context of fiber spaces. The carrier of this structure is a completely disconnected space. A concrete model of a dynamical system of this type and its application to the theory of elementary particles are considered. Khar'kov Physical-Technical Institute of the Academy of Sciences of Ukraine. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 52–61, November, 1999.