arXiv subjects

A. A. Ketsaris

Publications and source records attributed to A. A. Ketsaris.

4 recordsLinked to original sources

arXiv1999

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.

quant-ph↗

arXiv1999

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.

quant-ph↗

arXiv1999

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.

physics.gen-ph↗

arXiv1999

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 this 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 that 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.

physics.class-ph↗