Physical model of Dirac electron. Calculation of its mass at rest and own electric and magnetic intensities on its moment location

The physical model (PhsMdl) of the relativistic quantized Dirac's electron (DrEl) is proposed. The DrEl is regarded as a point-like (PntLk) elementary electric charge (ElmElcChrg), taking simultaneously part in following four disconnected different motions: a/ in Einstein's random trembling harmonic shudders as a result of momentum recoils (impulse kicks), forcing the DrEl's PntLk ElmElcChrg at its continuous emission and absorption of high energy stochastic virtual photons (StchVrtPhtns) by its PntLk ElmElcChrg ; b/ in Schrodinger's fermion vortical harmonic oscillations of DrEl's fine spread (FnSpr) ElmElcChrg, who minimizes the self-energy at a rest of is an electromagnetic self-action between its continuously moving FnSpr ElmElcChrg and proper magnetic dipole moment (MgnDplMmn) and the corresponding potential and vector-potential; All the relativistic dynamical properties of the DrEl are results of the participate of its FnSpr ElmElcChrg in the Schrodinger's fermion vortical harmonic oscillations. c/ in Furthian quantized stochastic boson circular harmonic oscillations as a result of the permanent electric or magnetic interaction of its well spread (WllSpr) ElmElcChrg or proper MgnDplMmn with the electric intensity (ElcInt) or the magnetic intensity (MgnInt) of the resultant quantized electromagnetic field (QntElcMgnFld) of all the StchVrtPhtns within the fluctuating vacuum (FlcVcm); All the quantized dualistic dynamical properties of the SchEl are results of the participate of its WllSpr ElmElcChrg in the Furth's stochastic boson circular harmonic oscillations. d/ in Nweton's classical motion along a clear-cut smooth thin line as a result of some interaction of its over spread (OvrSpr) ElmElcChrg, MgnDplMmn or bare mass with the intensities of some classical fields.Comment: LaTeX, 13 pages, no figure

The Physical Model of Schrodinger Electron. Schrodinger Convenient Way for Description of its Quantum Behaviour

The physical model (PhsMdl) of a Schrodinger nonrelativistic quantized electron (ShEl) is built by means of a transition of the quadratic differential particle equation of Hamilton-Jacoby into the quadratic differential wave equation of Schrodinger in this work, which interprets the physical reason of its quantum (wave and stochastic) behaviour by explanation of the physical reason, which forces the classical Lorentz electron (LrEl) to participate in Furthian quantized stochastic oscillation motion, which turn it into quantum ShEl. It is performed that this transition is realized by my consideration the Bohm's quantum potential as a kinetic energy of the forced Furthian quantized stochastic oscillation motion of the ShEl's well spread elementary electric charge close to a smooth thin trajectory of a classical LrEl. There exist as an essential analogy between the Furthian quantum stochastic trembling oscillation motion and the Brownian classical stochastic trembling motion so and between the description of their behaviours.Comment: Latex, 9 pajes, no figure

Physical Model of the Fluctuating Vacuum and Photon as its Elementary Excitation

A physical model of the fluctuating vacuum (FlcVcm) and the photon as an elementary collective excitation in a solitary needle cylindrical form are offered. We assume that the FlcVcm is consistent by neutral dynamides, which are streamlined in a close-packed crystalline lattice. Every dynamide is a neutral pair, consistent by massless opposite point-like elementary electric charges (ElmElcChrgs): electrino (-) and positrino (+). In an equilibrium position two contrary Pnt-Lk ElmElcChrgs within every one dynamide are very closely installed one to another and therefore its aggregate polarization and its ElcFld also have zero values. However the absence of a mass in a rest of an electrino and positrino makes possible they to display an infinitesimal inertness of their own QntElcMgnFlds and a big mobility, what permits them to be found a bigger time in an unequilibrium distorted position. The aggregate ElcFld of dynamide reminds us that it could be considered as the QntElcFld of an electric quasi-dipole because both massless electrino and positrino have the same inertness. The aggregate ElcFld of every dynamide polarizes nearest neighbour dynamides in an account of which they interact between them-self, on account of which their photons display a wave character and behaviour. In order to obtain a clear physical evidence and true physical explanation of an emission and absorption of RlPhtns, I use Fermi method for the determination of the time dependence of expansion coefficients of wave function of SchEl in a hybrid state, using the solution of the Schrodinger quadratic differential wave equation in partial derivatives with the potentials of Coulomb and of Lorentz friction force.Comment: LaTeX, 17 pages, without picture

Physical model of Schrodinger's electron. Heisenberg convenient way for description of its quantum behaviour

The object of this paper is to discuss the physical interpretation of quantum behaviour of Schrodinger electron (SchEl) and bring to light on the cause for the Heisenberg convenient operator way of its describing, using the nonrelativistic quantum mechanics laws and its mathematical results. We describe the forced stochastically diverse circular oscillation motion, created by force of the electrical interaction of the SchEl's elementary electric charge with the electric intensity of the resultant quantum electromagnetic field of the existing StchVrtPhtns, as a solution of Abraham-Lorentz equation. By dint of this equation we obtain that the smooth thin line of a classical macro particle is rapidly broken of many short and disorderly orientated lines, owing the continuous dispersion of the quantum micro particle (QntMicrPrt) on the StchVrtPhtns. Between two successive scattering the centers of diverse circular oscillations with stochastically various radii are moving along this short disordered line. These circular oscillations lie within the flats, perpendicular to same disordered short line, along which are moving its centers. In a result of same forced circular oscillation motion the smooth thin line of the LrEl is roughly spread and turned out into some cylindrically wide path of the SchEl. Hence the dispersions of different dynamical parameters, determining the state of the SchEl, which are results of its continuously interaction with the resultant quantum electromagnetic field of the StchVrtPhtns. The absence of the smooth thin line trajectory at the circular oscilation moving of the QntMicrPrt forces us to use the matrix elements (Fourier components) of its roughly spread wide cylindrical path for its description.Comment: Latex, 13 pages, no figure

Physical Interpretation of the Mathematical Consequence of Lorentz' Transformations

A physical interpretation of the mathematical consequence of Lorentz transformation within spatial relativity theory is presented as a result of my new physical model of existent fluctuating vacuum (FlcVcm). It is assumed that the FlcVcm is considered as a molecular dielectric, which consists from neutral dynamides, streamlined in a close-packed crystalline lattice. Every dynamide is a neutral pair, consistent by two massless opposite point-like elementary electric charges (ElmElcChrgs): electrino (-) and positrino (+). In a frozen equilibrium position two contrary pont-like ElmElcChrgs within every one dynamide are very closely installed one to another and therefore the aggregate polarization of every dynamide and its electric field also have zero values. The aggregate electric field of every dynamide polarizes nearest neighbors dynamides in an account of which nearest dynamides interact between them-self, because of which their elementary excitations, phonons and photons, have a wave character and behaviors. We suppose that the photon is an polarization result of the phonon within the fluctuating vacuum considered as an ideal dielectric and therefore the photon could be considered as an elementary collective excitation of the FlcVcm in the form of a solitary needle cylindrical harmonic oscillation. Hence the light, which is a packet of the photons, must move within FlcVcm with constant velocity and Dopler effect must be observed in both cases, for the light and sound. Then all mathematical results of Lorentz transformation could be considered as results of a demand of an independence of the observation results from the reactive velocity of the observation frame.Comment: Latex, 10 pages, no figure

Physical model of Schrodinger electron. Feynman convenient way in mathematical description of its quantum behaviour

The physical model of a nonrelativistic quantized Schrodinger's electron (SE) is offered. The behaviour of the SE well spread elementary electric charge had been understood by means of two independent and different in a frequency and size motions. The description of this resultant motion may be done by substitution of the classical Wiener continuous integral with the quantized Feynmam continuous integral. There are possibility to show by means of the existent not only formal but substantial analogy between the quadratic differential wave equation in partial derivatives of Schrodinger and quadratic differential particle equation in partial derivatives of Hamilton-Jacoby that the addition of a kinetic energy of the stochastic harmonic oscillation of some quantized micro particles to the kinetic energy of classical motion of the same micro particles formally determines their wave behaviour.It turns out the stochastic motion of the quantized micro particles powerfully to break up the smooth thin line of the classical motion of the same micro particle in many broad cylindrically spread path. The SE participate in stochastically roughly determined circumferences within different flats and with different radii, with centres which are successively arranjed over short and very disorderly orientated lines. Therefore the quantized motion of some micro particle cannot be descripted by smooth thin well contured (focused) line, describing the classical motion of the macro particle.Comment: Latex, 12 pages, no figure

Physical model of Hadrons : Barions and mesons. Physical essence of quarks and gluons and physical interpretation of their parameters

The physical model (PhsMdl) of the hadrons is offered by means of the obvious analogy with the transparent surveyed PhsMdls of the vacuum and leptons in our recent works. It is assumed that the vacuum is consistent by dynamides, streamlined in junctions of some tight crystalline lattice. Every dynamide contains a neutral pair of massless contrary point-like (PntLk) elementary electric charges (ElmElc Chrgs): electrino $(-)$ and positrino $(+)$. By means of the existent fundamental analogy between their properties and behaviour we can understand the similarity and difference between them and assume that the quark parameter aroma is determined by the value of its size of its circular two-dimensional motion, while the quark parameter colour is determined by orientation of the flat of the same circular two-dimensional motion in the space. The colorless of the barions is explained by distribution of the same circular two-dimensional motion of its elementary electric charge within three mutually perpendicular flats. Then the exchange of the colors between two quarks with different colors within some hadron can be interpretated as some twisting of same hadron in the space. We give a new obvious physical interpretation of the charge values of quarks, which gives some explanation of angles of Cabibo and Weynberg. By some physical supposition about the structure of charged intermediate vector bozon $W$ and uncharged intermediate vector bozon $Z$ we have possibility to explain as the physical essence of the strong, weak and electromagnetic interactions, so the outline of all births, transformations and decays of the ElmPrts.Comment: Latex, 10 pages, no figure

A strong laser impact on spin precession of a charged particle in the semi-relativistic interaction regime

In the present note new effects concerned the dynamics of a charged spin-1/2 particle in a strong monochromatic plane wave background are discussed beyond the conventional dipole approximation. Namely using the semiclassical approach in the semi-relativistic regime it is shown that the magnetic forces associated with the laser field have been retained and alter the spin evolution appreciably.Comment: 2 pages, no figure

Lifted Convex Quadratic Programming

Symmetry is the essential element of lifted inference that has recently demon- strated the possibility to perform very efficient inference in highly-connected, but symmetric probabilistic models models. This raises the question, whether this holds for optimisation problems in general. Here we show that for a large class of optimisation methods this is actually the case. More precisely, we introduce the concept of fractional symmetries of convex quadratic programs (QPs), which lie at the heart of many machine learning approaches, and exploit it to lift, i.e., to compress QPs. These lifted QPs can then be tackled with the usual optimization toolbox (off-the-shelf solvers, cutting plane algorithms, stochastic gradients etc.). If the original QP exhibits symmetry, then the lifted one will generally be more compact, and hence their optimization is likely to be more efficient

Bianchi type I cosmology and the Euler-Calogero-Sutherland model

The Bianchi type I cosmological model is brought into a form where the evolution of observables is governed by the unconstrained Hamiltonian that coincides with the Hamiltonian describing the relative motion of particles in the integrable three-body hyperbolic Euler-Calogero-Sutherland system.Comment: 13 pages, LaTeX, no figures. V2: Title and abstract slightly changed, typos corrected. V3: Minor changes, version to appear in Physical Review