## Applied Theory of the Spinor Field

#B-914

Mathematical Modeling the Momentum Continuum Media and the Spinor Field Flux Optimal Control

**Tech Area / Field**

- PHY-PFA/Particles, Fields and Accelerator Physics/Physics
- PHY-OPL/Optics and Lasers/Physics
- PHY-SSP/Solid State Physics/Physics

**Status****3** Approved without Funding

**Registration date****06.08.2002**

**Leading Institute**

Belorussian National Technical University, Belarus, Minsk

**Project summary**

*The Project prime objective.*

To develop a concept, theory, and methods of new, so called relativistic-synergetic approach to formulating universal laws.

Concept: Creating of mathematical models of various objects using an analogy with the physical vacuum.

Theory: mathematical theory of spinor field organization and control.

Method: Submerging nongradient dynamical systems into the gradient continuum media.

*The problem statement. *

Currently existing three approaches to formulating universal laws, known as thermodynamic, statistical and synergetic, had been being developed by Nobel Prize Winner I. Prigozhin, Prof. L. Landau with his fellows and Stuttgart group headed by Prof. G. Hagen, respectively. Within the Project we are going to develop new, called relativistic – synergetic approach that integrates the above three approaches and provides substantially new possibilities. The following three Project components will be developed:

– the spinor field theory at the turn of the theory of Physical Vacuum, ideas of the Synergy, applied theory of catastrophe and the qualitative theory of differential equations;

– algorithms for calculating spinor field dynamic flux control, fluxes interaction, algorithms for optimal control of dynamic systems, submerged into the spinor field;

– approaches to and methods of application problem solving on the basis of the spinor field formalism.

*The Project impact on the progress in science and technology. *

The contemporary theory of the Physical Vacuum, which is based on postulates of relativity principles, contains results, which are of a great importance for further progress of science and technology. However, these results have not yet been used due to the great complexity of the object in question as well as mathematical tools applied. We intend to overcome this problem situation by means of using analogy with parameters of the Physical Vacuum and subsequent substitution of the abstract 4-dimentional space R^{4} by real observed 3-dimentional one R^{3}.

This idea made it possible to create a mathematical model of the spin employing the formalism of ordinary differential equations. Then this model was used for developing the mathematical model of the spinor field. Eventually we found out seven analogies between parameters of caliber model of the physical vacuum and those of the spinor model of the last.

*Project participants. *

The project Leader and principal executors are Doctors of science with many years experience in carrying out defense R&D in the following areas:

– nuclear power engineering;

– deterministic and chaos continuum media;

– systems stability and optimal control

– applied theory of catastrophe;

– synergy;

– physical vacuum;

– spin effects;

– generating the laser radiation;

– linear and circular lasers in navigation and control systems;

– gravity measuring systems;

– oscillation processes in complex dynamic systems.

A major part of participants’ scientific publications are classified or have districted dissemination. Some other publications are given in the last part – Supporting information.

Other specialists in the field of system programming, computer graphics, software development and other related fields (group of administrative support) are also planning to be employed in frame of the project.

*Expected results of the research. *

The Projects relates to both basic and applied research. It is planned that in the course of the Project development theoretical problems will be substantiated and solved. This will constitute a backbone of a spinor field theory, which further will be used for solving a number of application problems.

Methods and algorithms which will be elaborated and tested in the frame of the theory can be applied in research of continuum media, various dynamic systems, structures, field formations, mathematical models, stabilization modes as well as for solving a number of classical and principally new problems in basic sciences.

The capability of the new approach was demonstrated when two classical problems were solved:

– all the types of limiting cycles were found and their parameters were determined, without Liapunov’s values being calculated;

– the problem of a particular “center” type point existence in nonlinear dynamic systems of N-order was solved, without special functions being employed.

*Meeting ISTC goals and objectives. *

The Project fully meets ISTC goals and objectives in the following respects:

– weapon scientists are provided with opportunities to implement their knowledge, ideas, research reserves in civil oriented applications;

– the Project stimulates integration of Belorussian scientists and specialists into the international scientific community;

– the Project supports and further develops basic and applied research with a purpose of the peaceful application;

– the Project contributes to national and international technological problem solving, such as new non-traditional energy sources, new materials and technologies, systems and mechanisms.

*The Scope of Activities. *

The total scientific and technical manpower involved in the Project is planned to be 219 man/months. It will be used to realize the concept, create the theory, develop methods and after all – to employ all these to solving a number of applied problems.

Major Project stages:

1. Mathematical modeling the momentum continuum media and constructive generalization of Liapunov’s direct method.

2. Classification and geometrical interpretation of dynamic system stability matrix expressed in a spin form.

3. Ascertaining, organization and study of vector flux structures in continuum media.

4. Spinor field flux control and optimal control in dynamic systems, submerged into gradient media.

5. Employing spinor field theory formalisms for applied problem solving.

*The Role of Foreign Collaborators. *

In the frame of the Project submitted the cooperation with foreign collaborators is assumed to be realized along the following directions, possibilities and understanding of potential partners are being taken into account:

– information exchange in a course of the Project realization;

– reviewing and commenting Project scientific and technical reports and survey;

– participating in ISTC technical revisions of the activity carried out by the Project team;

– financial support to Project participants for attending International scientific events;

– holding joint symposia and seminars;

– joint patent application.

*Technical Approach and Methodology**.** *

It is for the first time that we propose to develop the novel, so called relativistic-synergetic approach to formulating universal laws, which is based on using a new object – spinor field.

Definition. The spinor field is an organized vector field of dynamic system rotation moments and spin moments of elementary particles.

A mathematical model of the spinor field is defined by means of analogy between a “spin” moment, generated by dynamic system phase plane rotating around one of its coordinate axis, on one hand, and objects and postulates of the physical vacuum caliber theory, on the other hand.

A research methodology makes the Project to go through the following stages:

– a mechanics of “vacuum” perturbations is introduced into a dynamic chaos of the continuum media;

– a potential function is built up in accordance with the algorithm developed;

– media vector characteristics are calculated and interactions of the media and a dynamic system submerged into the media are considered (a potential of interaction);

– properties of both self-action and interaction potentials leading to the Liapunov’s function are investigated when the phase plane is revolved around its axis.

As the further development of the geometrical interpretation of roots of dynamic system stability matrix characteristic equation, introduced by R. Gilmor, we propose a new method of separatrix ascertaining. In this method the strait line of own value real parts is directly coupled with cones generated by negative, zero and positive values of real parts. It makes it possible to interpret the 4-dimentional space of spin coefficients as three circle cones in contrast to common used representation on the torus.

Also the proposed method can be used for ascertaining and classification of new structures emerged under phase transitions in the I. Prigozhin’s thermodynamics.

Phase plane revolutions are in fact the analogy of phase transitions (an organization), whereas the vector flux generation in a cone of revolving is the analogy of a laser beam generation (a self-organization) which is studied in statistical physics.

It is planned that in the frame of the Project the following applied problems will be solved:

– the development of girotropic media models and thermodynamics;

– increasing laser measuring system accuracy by means of employing both a white noise mode and organized controlled chaos study;

– improving a sensitivity of gravitation measuring systems by means of mathematical modeling the gravitation media and development of the algorithm for signal detection and processing under presence of the gravitation media white noise;

– the study of complex oscillating dynamic systems employing spinor field and catastrophe theory formalisms.

The spinor approach integrates all three currently known approaches, i.e. thermodynamic, statistical and synergetic. It provides substantially new possibilities: it describes the physical vacuum, ascertains both structural and dynamical stability and instability, classifies new structures emerged and their parameters.

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