Archive

Archive for the ‘2006 Volume 1’ Category

Nov
28

Quantum field theory and experiments about vanishing of the zero-point vacuum energy

Zahid Zakir [1]

Abstract

     At quantization of relativistic fields the Hamiltonians symmetrized under the complex conjugate field operators lead to a zero-point vacuum energy. The standard recipe, introducing the operators of antiparticles, breaks the charge conjugation (C) symmetry. For the Hamiltonians unsymmetrical under the field operators at exact C-symmetry requirement the vacuum does not contain a zero-point energy and zero-point charge. The observable effects are described or as fluctuations of the physical vacuum with loop diagrams (Lamb shift), or as fluctuations of fields of real sources (Casimir effect). Both kind of vacuum fluctuations are created by the interaction Hamiltonians and they have no any relation to the zero-point fluctuations of (external) vacuum fields creating the zero-point vacuum energy in the free Hamiltonians. Therefore, in fact the known experiments exclude the existence of the zero-point fluctuations of the pure vacuum fields and the zero-point vacuum energy and for the relativistic fields allow one to use only Hamiltonians unsymmetrized under the complex conjugate field operators with unbroken C-symmetry.

PACS: 03.70. + k; 11.10.-z; 11.30. Er

Key wordsvacuum energy, vacuum fluctuations, Lamb shift, Casimir effect, time reversal, charge conjugation, cosmological constant

Vol. 1, No 4,  p. 61 – 72, v1,   28 November 2006

Online: TPAC: 2158-005 v2,  28 September 2012; DOI: 10.9751/TPAC.2158-005


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

      zahidzakir@theor-phys.org

Oct
20

On the theory of gravitationally-frozen superdense and supermassive objects

Zahid Zakir [1]

Abstract

     The black hole paradigm (BHP) is based on an implicit assumption that the collapse occurs quickly not only on proper times of falling particles, but on world time also, and that information about that is retarded only. According to general relativity (GR) in a static field there is a global simultaneity of events, the proper times are slowed down with respect to world time absolutely and these facts are confirmed experimentally by clocks long-term located at different heights. Therefore, the basic assumption of BHP is incompatible with GR, the collapse occurs not quickly, but it needs in really infinity world time. For a falling particle at any finite world time moment its corresponding proper time moment is insufficient for reaching the gravitational radius of the source. As the result, in GR real horizons and physical singularities do not exist, the black holes never be formed. Instead of the black holes GR predicts the gravitationally-frozen states of matter in superdense and supermassive objects. Particles inside of any compact object are frozen by the strong gravitational field so that the time dilation is finite, but maximal at the center and minimal on the surface. In cosmology this fact solves the problem of an initial singularity, in astrophysics allows one to construct a theory of superdense stars, quasars and AGN, in particle physics leads to the ultraviolet finiteness of quantum fields, including quantum gravity.

  PACS:  95.30.Sf, 97.60.Lf, 98.35.Jk, 98.54.-h, 98.80.-k, 04.60.-m

  Key words: black holes, horizon, collapse, singularities, quark stars, quasars, active galactic nuclei, cosmology, quantum gravity

Vol. 1, No 3,  p. 42 – 60, v1,       20 October 2006

Online: TPAC: 2119-004 v2,  28 September 2012; DOI: 10.9751/TPAC.2119-004


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

      zahidzakir@theor-phys.org

Sep
29

Quantum field theory without divergences at a correct temporal integration

Zahid Zakir [1]

Abstract

      Quantum mechanical trajectories for particles or fields, especially in path integrals, have not temporal differentials and the path integrals are defined only on a finite slice time lattice. Therefore, in QFT all integrals on energy should be taken before turning to the limit of very small times when they are finite. The renormalizable theories are invariant under the dilatations of the time lattice slice. It is a new space-time symmetry extending the Poincaré group and it has been discovered earlier in the momentum representation as the renormgroup. Thus, quantum mechanics requires turning to small times only after summation over all alternatives, i.e. energy integrations in loops, and this fact leads to natural regularization of loop integrals without additional hypotheses. These justify all effective methods of regularization as various realizations of the natural temporal regularization following from the fractal nature of paths. The covariant Planck time appears as a smallest time interval due to the gravitational proper time dilation and redshift of proper frequencies near the Planck energy source. Therefore, the standard QFT with such covariant and finite regularization becomes mathematically rigorous and physically consistent.

PACS: 11.10.Gh, 11.10.Hi, 11.15.Ha, 11.10.Ly, 12.20.-m

 Key words: quantum mechanics, path integral, quantization, renormalization, lattice regularization, symmetries, vacuum energy, cosmological constant

Vol. 1, No 2,  p. 28 – 41, v1,   29 September 2006

Online: TPAC: 2098-003 v2,  28 September 2012; DOI: 10.9751/TPAC.2098-003


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

      zahidzakir@theor-phys.org

Sep
22

Tи CPsymmetric quantization of fields without zero-point energy

Zahid Zakir [1]

Abstract

The standard replacement of negatively-frequency operators of relativistic fields to operators of antiparticles leads to incomplete time-reversal in field’s observables. In fact, a correct transition to the operators of antiparticles occurs only at a full T- or CP-transformation of matrix elements. Then the operators of observables of T – or CP-symmetric fields with standard Lagrangians appear as normal-ordered and the zero-point energy and the zero-point charge do not arise. The rules for the CP-symmetric quantization of fields are formulated and also the theorem about vanishing of the zero-point energy is proved. The theorem is in agreement with all known experiments since in fact the contributions of real sources are observed only. The divergent zero-point energy and zero-point charge appear only at using of the Lagrangians symmetrized under the complex-conjugate field operators, while the standard Lagrangians without such symmetrization lead to the required vanishing vacuum energy. At spontaneous symmetry breaking the vacuum zero-point energy and zero-point charge do not appear only if the remained scalar field is complex one and in this case the Standard Model predicts a pair boson-antiboson with hypercharge.

PACS:   03.70.+k;  11.10.-z;  11.30.Er

Key wordsvacuum energy, vacuum fluctuations, Casimir effect, time reversal,  charge conjugation, cosmological constant

Vol. 1, No 1 ,  p. 11 – 27, v1,   22 September 2006

Online: TPAC: 2091-002 v2,   28 September 2012; DOI: 10.9751/TPAC.2091-002


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

      zahidzakir@theor-phys.org

Sep
22

Symmetries of harmonic oscillator generating the zero-point and negative energies

Zahid Zakir [1]

Abstract

       The Hamiltonian of harmonic oscillator is symmetric under the replacement of canonically conjugate variables and a canonical transformation to ladder operators maintains this symmetry. The Hamiltonian is expressed through a symmetrized product of the ladder operators and, as a result, at quantization there arise a zero-point energy. Therefore, for quantized fields, canonically conjugate variables of which enter into the Hamiltonian unsymmetrically, the zero-point energy could not arise. A new symmetry of harmonic oscillator is found: a wave equation and its solutions do not vary at a joint changing of signs of frequency, energy and mass of a particle. It is shown that the problem of the negative norm for negative-frequency states appears at taking positive mass at negative energy and, contrary, the problem disappears at taking the same sign of mass and energy as it is required by relativistic kinematics. In the nonrelativistic theory, considered as a limiting case of relativistic theory, the states of a particle with negative frequency, energy and mass are described consistently as evolving only backward in time and representing the states of its antiparticle with positive frequency, energy and mass evolving forward in time. For such charge-conjugation symmetric system of oscillators an extended space of states with generalized operators is constructed.

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

  Key words: Hamiltonian dynamics, discrete symmetries, time reversal, quantization

Vol. 1, No 1 ,  p. 1 – 10, v1,    22 September 2006

Online: TPAC: 2091-001 v2,  28 September 2012; DOI: 10.9751/TPAC.2091-001


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

      zahidzakir@theor-phys.org