Archive

Archive for the ‘1. Quantum mechanics’ Category

May
01

Diffusive mechanism for a small mass of composite particles and new perspectives for preon models 

 Zahid Zakir [1]

Abstract

   In the diffusion of cold light gas in warm heavy gas, initially and far before the relaxation, the thermal velocities of light and heavy atoms are the same order and the light gas remains cold, and mean energies of its particles are approximately conserved. The description of such conservative diffusion is analogous to the formalism of quantum mechanics, and quantum mechanics appears as a description of such diffusion of a particle in a physical vacuum, where the diffusion coefficient is proportional to the Planck constant inverse proportional to the mass. The growth of the diffusion flux in the localization of particles leads to an increase in the osmotic pressure, which reveals the “microscopic mechanism” of the uncertainty relations and allows us to identify cases where the prohibitions imposed by them can be circumvented, in particular, to solve the mass paradox for composite particles in the preon models. If two light particles (atoms) with different masses began to diffuse at distances much greater than the mean free path, then the diffusion mechanism prevents them from further joining and as more energy must be expended to form a composite particle, as smaller the final volume of localization. However, if these particles were initially located at a distance less than the mean free path and during a time shorter than the free pass time they formed a bound state (the atoms joined in the molecule), then this composite particle (molecule) diffuses as other light particles (atoms), but with a mass slightly less than the total mass of the initial particles.

PACS: 12.60.Rc, 12.60.Nz, 03.65.Ta, 05.30.Ch, 05.40.Jc

Keywords: composite models, technicolor, quantum mechanics, conservative diffusion

Vol. 11, No 1, p. 1 – 11, v1,     May 1, 2016
Electron.: TPAC: 5200-041 v1,    May 1, 2016    DOI: 10.9751/TPAC.5600-042

Mar
28

Finite quantum field theory with rotatory quantization and gravitational regularization

 Zahid Zakir [1]

Abstract

    At quantization of harmonic rotator, a rotational mode of planar oscillator, energy spectrum is linear on frequency and equidistant, but zero-point energy in ground state can not arise. This is in agreement with generalization of uncertainty relations to non-Hermitean canonical pairs. Quantization of waves at collective rotations of a chain of harmonic rotators allows one to model the fields with charge-conjugation and gauge symmetries. In quantum field theory (QFT) at quantization of rotational modes as harmonic rotators the observables of fields are normal ordered and zero-point energy and zero-point charge of vacuum do not arise. In this case frequencies of quanta are angular speeds of rotation of field vectors in real or field spaces and two signs of helicity correspond to a particle and an antiparticle. Photons with circular polarization and complex fields are examples of such fields, spin and isospins (charges) of particles can be related by their frequencies as angular momenta and helicities of the rotating field vectors. At rotational quantization of strings there are no zero-point energy of modes and here a conformal anomaly is absent, so spacetime dimensionality and gauge group are not fixed. In QFT the fields should be averaged in small cells of space and time, where distribution and evolution of fields are described classically, and field functions on borders of cells should be sewed. Then loop integrals are finite and the renormalized theories are invariant under reduction of the size of cells (a renormgroup with the cell regularization). The Planck scale cell is smallest because of freezing of proper times in a strong external gravitational field of the loop diagram with redshifting of frequencies up to zero. In the Standard Model and quantum gravity the loop contributions of fields, with exception of scalars, are small and the perturbation theory is convergent.

PACS: 03.65.Ge, 11.30.Er, 1130.Ly, 11.90. + t, 03.65.Ge, 03.70. + k, 11.10.Gh, 11.10.Hi, 11.15.Ha, 11.10.Ly, 12.20. – m, 11.25. – w, 12.10. – g,

Keywords: quantization, charge conjugation symmetry, harmonic rotator, quantum fields, vacuum energy, renormalization, regularization, strings, anomalies

Vol. 10, No 1, p. 1 – 40, v1,     March 28, 2015
Electron.: TPAC: 5200-040 v1,    March 28, 2015 DOI: 10.9751/TPAC.5200-040

Aug
01

Conservative Diffusion as a Physical Mechanism for Quantum Mechanics and Gravitation

 Zahid Zakir [1]

Abstract

     The theory of conservative diffusion and its main applications are reviewed. A basic model for the theory is diffusion of a cold light gas in a warm heavy gas before relaxation when light gas remains cold and mean energy of its particles conserves. Unlike the Lorentz gas, where thermal energies of light and heavy atoms are equal, here the same order are their thermal speeds.  Such conservative diffusion is described by two equations – the Hamilton-Jacobi and continuity equations, nonlinear under the probability density. They can be linearized by introduction of a complex probability amplitude, transforming them to the Schrödinger equation where one must add not probabilities, but probability amplitudes of alternatives. Mean free path and the corresponding momentum determine an elementary phase volume and a diffusion coefficient. The theory predicts a number of quasiquantum effects in classical systems. The formalism of quantum mechanics thus describes a classical conservative diffusion and quantum mechanics is only a special case of such diffusion in the vacuum, when the elementary phase volume is equal to the Planck constant. A conservative thermodiffusion at nonzero temperature gradient is studied also. Its properties, such as decreasing of intensity of fluctuations of particles (including redshift of frequencies), drift of particles to colder region and their thermodiffusive acceleration, not depending on the mass of particles, are similar to properties of gravitation. This allows us to identify gravitation by thermodiffusion in the physical vacuum. In the diffusive picture fluctuations of energy-momentum of classical particles due to interaction with vacuum lead to increasing of their mean energy, which appears as quantum phenomena, while corresponding local decreasing of vacuum energy density reveals as gravitation. The diffusive treatment of quantum theory thus leads to the thermodiffusive treatment of gravitation too with natural synthesis of theories of both phenomena. Observable effects following from the new theory are discussed.

PACS: 03.65.Ta, 04.20.Cv, 02.50.Ey, 05.40.Jc

Key words: quantum fluctuations, vacuum energy, thermodiffusion, metrics, curvature

Vol. 9, No 2, p. 54 –72, v1,         31 July 2014

Online: TPAC: 4960-038 v1,     31 July 2014;   DOI: 10.9751/TPAC. 4960-038


[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan  zahidzakir@theor-phys.org

May
06

Gravitation as a thermodiffusion in the physical vacuum

 Zahid Zakir [1]

Abstract

     An influence of matter on the vacuum energy density is considered and a treatment of gravitation as inhomogeneity of quantum diffusion is developed. A treatment of quantum theory as conservative diffusion [1] is briefly presented, where quantum fluctuations of energy and momentum of a classical particle occur because of interaction with physical vacuum. The increasing of particle’s mean energy at such fluctuations appears as quantum phenomena, while corresponding local decreasing of mean vacuum energy to the same value appears as gravitation. For one a particle the decreasing is extremaly small and in particle physics it can be neglected. However, when large number of particles are concentrated in a small volume, consequences of the vacuum energy decreasing become appreciable and they appear as gravitation. The diffusion treatment of quantum processes thus leads to the diffusion treatment of gravitation with natural synthesis of theories of both phenomena. New properties of inhomogeneous diffusion related by local decreasing of vacuum energy, such as slowering of fluctuations of particles with delay of intensity of processes (including redshift of frequencies), drift of particles toward slower fluctuations region and their diffusive acceleration, which is independent on mass of particles, are studied. Observable effects following from the new treatment are discussed.

PACS: 02.50.Ey, 03.65.Ta , 05.40.Jc  

Key words: quantum mechanics, diffusion, Brownian motion, kinetic theory of gases

Vol. 9, No 1, p. 33 –53, v1,      6 May 2014

Online: TPAC: 4874-037 v1,     6 May 2014;   DOI: 10.9751/TPAC.4874-037


[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org

May
06

Theory of conservative diffusion in classical and quantum systems

 Zahid Zakir [1]

Abstract

     In previous paper [1] conservative diffusion of light particles in a dilute medium of heavy particles was studied by analogue with Brownian motion. In the present paper the theory is formulated in more consistent “hydrodynamic” form by using a conservativity condition only, that mean energy of a light particle is conserved. As a model is taken diffusion of very cold light gas in warm heavy gas a time interval before relaxation when light gas remains cold. Unlike Lorentz’s gas, where thermal energies of light and heavy atoms are equal, here their thermal speeds are equal and this leads to the effects of conservativity similar to quantum effects. Such conservative diffusion is described by two equations – the continuity equation and the energy conservation condition, non-linear under the probability density. At introduction of a complex probability amplitude the equations linearized and turn to the Schrödinger equation. As a result, one must add not probability of alternatives, but probability amplitudes. A free pass length and corresponding momentum define an elementary phase volume and the diffusion coefficient. The predicting new quasi-quantum effects in classical systems are discussed. It is shown that the formalism of quantum mechanics describes the classical conservative diffusion with a constant diffusion coefficient and that quantum mechanics is a particular case of such diffusion in the vacuum where the elementary phase volume of free passage is equal to the Planck constant.

PACS: 02.50.Ey, 03.65.Ta , 05.40.Jc  

Key words: quantum mechanics, diffusion, Brownian motion, kinetic theory of gases

Vol. 9, No 1, p. 18 –32, v1,    6 May 2014

Online: TPAC: 4874-036 v1,   6 May 2014;   DOI: 10.9751/TPAC.4874-036


[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org

Sep
14

Rotatory quantization of charge-conjugation symmetric systems.

3. Relativistic fields.

Zahid Zakir [1]

Abstract    

Quantum theory of complex fields with rotational modes based on a harmonic rotator model is constructed. For purely rotational modes the energy spectrum is equidistant, observables are automatically normal-ordered and there is no zero-point vacuum energy and zero-point charge. Frequencies of quanta are angular speeds of rotating field vectors (in real or field spaces). States of two signs of the helicity (particle-antiparticle) are related through the crossing symmetry. The well-known examples are photon field with circular polarization and complex fields. The spin and isospins of particles appear as related to their frequencies, representing angular momenta of rotations of field vectors with these frequencies. It is shown that the standard covariant perturbation theory is constructed in fact for description on the basis of harmonic rotators, where the recipe of transition from oscillatory to the rotatory representations of modes earlier it has been found empirically as normal-ordering of operators. The vacuum energy vanishes for free Hamiltonians and C-symmetric interactions.

PACS: 03.70. +k, 11.30.Er

Key words: quantization of fields, charge conjugation, parity, vacuum energy

Vol. 6, No 3, p. 48 – 63, v1,  14 December 2011

Online: TPAC: 4000-023 v2,  28 September 2012; DOI: 10.9751/TPAC.4000-023


[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org

Sep
05

Rotatory quantization of charge-conjugation symmetric systems.

1. Harmonic oscillators

       Zahid Zakir [1]

Abstract    

In a system of a particle and antiparticle in the harmonic potential, represented as an oscillator with a complex generalized coordinate, there is a global U(1) symmetry and the charge conjugation (C) symmetry. It is shown that two pairs of ladder operators, introduced at the frequency decomposition of canonical variables, are not mutually charge-conjugate and that, therefore, their standard interpretation as operators of the charge-conjugate quanta breaks C-symmetry. Operator identities between bilinear products of the ladder operators are discovered, allowing expressing observables through charge-conjugate operators and it is correct to take into account C-symmetry. It is shown that these identities are maintained and at insert of the C-symmetric interactions. In a Lagrangian unsymmetrized and symmetrized orderings of complex conjugate operators of a momentum lead to different charge operators and are not equivalent at interaction with the gauge field. It is shown that due to C-symmetry conditions a zero-point charge does not arise in both orderings and in the first case a zero-point energy disappears also. The contribution of interaction with the gauge field and anharmonic potentials in higher orders of perturbation theory is considered. The same system also can be presented as a particle with positive and negative frequencies and, if to consider that a sign of mass of the particle coincides with a sign of its frequency, then the norm of negative frequency states remains positive.

PACS: 03.65.Ge, 11.30.Er, 1130.Ly, 11.90. +t

Key words: Hamiltonian dynamics, discrete symmetries, quantization

Vol. 6, No 2, p. 14 – 30, v1, 5 September 2011

Online: TPAC: 3900-021 v2, 28 September 2012; DOI: 10.9751/TPAC.3900-021

Download pdf 426 kb


[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org

Sep
05

Rotatory quantization of charge-conjugation symmetric systems.

2. Harmonic and magneto-harmonic rotators

Zahid Zakir [1]

Abstract

     For soft rotators the lack of a radial component of velocity is a defining property and it allows to simplify quantization of harmonic and magneto-harmonic rotators. Operators of observables of soft rotators are normal ordered due to symmetries of the system, energy spectrum is linear under frequency and equidistant, and in the ground state there is no zero-point energy from rotational modes. It coincides with a generalization of the uncertainty relations for systems with non-hermitian canonical variables where the restrictions on fluctuations depend on state’s charge. Applications of the new formalism to quantization of waves at collective rotations of one-dimensional chain of harmonic rotators allows to model fields with charge-conjugation and gauge symmetries. For the rotating modes there is a crossing symmetry between states with opposite rotation directions, and arising of negative-frequency modes are positive-frequency states of antiquanta with replaced initial and final states. The commutators and causal correlators (propagators) of generalized coordinates of the harmonic rotator are derived.

PACS: 03.65.Ge, 11.30.Er, 1130.Ly, 11.90. + t

Key words: discrete symmetries, rotations, charge-conjugation symmetry, Landau levels, chain of rotators, propagators

Vol. 6, No 2, p. 31 – 47, v1,      5 September 2011

Online: TPAC: 3900-022 v2,  28 September 2012; DOI: 10.9751/TPAC.3900-022


[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org

May
28

Models of soft rotators and the theory of a harmonic rotator

Zahid Zakir [1]

Abstract

    The states of a planar oscillator are separated to a vibrational mode, containing a zero-point energy, and a rotational mode without the zero-point energy, but having a conserved angular momentum. On the basis of the analysis of properties of models of rigid and semirigid rotators, the theory of soft rotators is formulated where the harmonic attractive force is balanced only by the centrifugal force. As examples a Coulomb rotator (the Bohr model) and a magneto-harmonic rotator (the Fock-Landau levels) are considered. Disappearance of the radial speed in the model of a magneto-harmonic rotator is taken as a defining property of a pure rotational motion in the harmonic potential. After the exception of energies of the magnetic and spin decompositions, specific to magnetic fields, one turns to a simple and general model of a plane harmonic rotator (circular oscillator without radial speed) where kinetic energy is reduced to the purely rotational energy. Energy levels of the harmonic rotator have the same frequency and are twice degenerate, the energy spectrum is equidistant. In the ground state there is no zero-point energy from rotational modes, and the zero-point energy of vibrational modes can be compensated by spin effects or symmetries of the system. In this case the operators of observables vanish the ground state, i.e. are “strongly” normally ordered. In a chain of harmonic rotators collective rotations around a common axis lead to transverse waves, at quantization of which there appear quasi-particles and holes carrying an angular momentum. In the chain SU (2) appears as a group of symmetry of a rotator.

PACS: 03.65.Ge, 11.30.Er, 1130.Ly, 11.90. + t

Key words: quantization, zero-point energy, vibrations, rotations, discrete symmetries

Vol. 6, No 1, p. 1 – 13, v1,        28 May 2011

Online: TPAC: 3800-020 v2, 18 September 2012; DOI: 10.9751/TPAC.3800-020

Download  pdf 320 kb


[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org

May
20

Are strings thermostrings? [1]

      Zahid Zakir [2]

Abstract

      In the method of thermostring quantization the time evolution of point particles at finite temperature kT is described in a geometric manner. The temperature paths of particles are represented as closed (thermo)strings, which are swept surfaces in a space-time-temperature manifold. The method makes it possible a new physical interpretation of superstrings IIA and heterotic strings as point particles in a thermal bath with Planck temperature.

PACS: 11.10.Wx, 11.10.Kk, 11.25.-w, 11.25.Uw, 11.25.Wx

Key words: quantization, finite temperature, extra dimensions, strings, branes

Vol. 5, No 1,  p. 8 – 13, v1,  20 May 2010

Online: TPAC: 3400-016 v2,  28 September 2012; DOI: 10.9751/TPAC.3400-016

Download  pdf 182 kb


[1] The preprint of the paper has been presented in 1998 (revised 2003): Zakir Z. arXiv:hep-th/9809247

[2] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org