*22.07.1999*__arXiv:physics/9907037v2__Accelerated motion and special relativity transformations- Transformation rules for coordinates, velocities and accelerations in accelerated reference frames
are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional
space including projections of velocity vector as three additional coordinates to time and geometric
coordinates is studied. Turns in pseudoplane (
*dt*,*dv*) of 7-space describe accelerated motion of frame. In addition to the light velocity, the transformation formulas contain a fundamental constant which has a meaning of maximal acceleration. It is demonstrated if a source of light moves with acceleration with respect to some reference frame, the light velocity in this frame is less than the constant*c*and depends on acceleration. The special relativity relation between energy, impulse, and mass gets changed for particle in accelerated motion. A generalized wave operator being invariant to the above transformations is introduced. The components of tensor and of potential of electromagnetic field get intermixing in transformation relations for accelerated frame.

*15.09.1999*__arXiv:physics/9909026v1__Turns and special relativity transformations- We advance an universal approach to the construction of kinematics in non-inertial and, in
particular, rotating reference frames. On its basis a 10-dimensional space including three
projections of velocity vector and three turn angles in geometric space as additional coordinates to
time and geometric coordinates is introduced. In a specific case, the turns in 10-space describe the
uniform rotation of reference frame as well as its accelerated motion. Transformations for
coordinates and angular velocities are derived. Definitions of dynamic quantities contain a
fundamental constant
*Ω*with dimensionality of angular velocity and the maximal acceleration in addition to the velocity of light. The special relativity relation between energy, impulse, and mass gets changed for particles with moment of inertia. A wave equation obtained describes the rotary and accelerated motions of light wave. A relation between particle moment and the Planck constant representing Bohr's postulate is added to de Broglie's relations. A generalized space-time which allows to consider kinematics for derivations of arbitrary order is studied. Differential relations between velocity of arbitrary order and turn angles in the generalized space-time are obtained.

*16.09.1999*__arXiv:quant-ph/9909053v1__Generalized equation of relativistic quantum mechanics- We develop a new concept of quantum mechanics which is based on a generalized space-time and on an action vector space similar to it. Both spaces are provided by algebraic properties. This allows to calculate the Dirac matrixes and to derive quantum mechanics equations from structure equations of the specified algebras. A new interpretation of the wave function is given as differential of the action vector. A generalization of the Dirac equation for 8-component wave function is derived. It is interpreted as the equation for two leptons of the same generation. A procedure of the approximate description of free leptons is formulated. The generalized equation of quantum mechanics is reduced to the Dirac, Pauli and Schrödinger equations by the sequential use of this procedure. We explain the existence of three lepton generations.

*28.09.1999*__arXiv:quant-ph/9909087v1__Generalized equation of relativistic quantum mechanics in a gauge field- We develop an unified algebraic approach to the description of gauge interactions within the
framework of a new concept of quantum mechanics. The next step in generalizing the space-time and
the action vector space is made. The gauge field is defined through linear mappings in the
generalized space-time and the action space. Relativistic quantum mechanics equations for particles
in a gauge field are derived from the structure equations for the action space expanded in the
linear mappings of action vectors. In a special case, these equations are reduced to the
relativistic equations for the leptons in the electroweak field. As against the standard Glashow-
Weinberg-Salam model, the set of equations includes the equation for the right neutrino interacting
only with the weak
*Z*-field.

*17.09.2012*Unified Theory of Interactions. Theses- In this article we will bring together the results of a set of lectures and put them together as a short introduction to the Unified Theory of Interactions. Our approach is based on an algebraic generalization of two spaces: the spacetime and the action space, which is similar to the spacetime. Both the spacetime and the action space are provided properties of the tensor algebra. This allows us to explain a hierarchy of fundamental elementary particles and to make generalizations for them. The Clifford algebra as a special case of the tensor algebra is associated with leptons. Linear and bilinear transformations of the tensor algebra are associated with intermediate particles. These transformations also describe interaction between fundamental and intermediate particles.

(It is English translation of Lecture 24).