Archive

Archive for November, 2007

Nov
30

Quantization of complex harmonic oscillator and the zero-point energy vanishing effect

Zahid Zakir [1]

Abstract

      The system of two harmonic oscillators with different sign frequencies is presented as a positive-frequency oscillator with a complex generalized coordinate where there are a global U(1) symmetry and a charge conjugation symmetry (C-symmetry). It is shown that two pairs of ladder operators, appearing at the frequency decomposition of canonical variables, are not mutually charge-conjugate and their standard interpretation as operators of charge-conjugate quanta breaks the C-symmetry. Bilinear operator identities for the ladder operators are found allowed the theory to obey the C-symmetry restrictions and to express observables through the mutually charge-conjugate operators. These identities hold for C-symmetric interactions also. It is shown that C-symmetry eliminates a ground state zero-point charge and a zero-point energy. The uncertainty relations are generalized for non-hermitian canonical variables and it is shown that the charge-conjugation symmetric ground states do not quantized. It is shown that the C-symmetric interactions do not contribute to the ground state energy in all orders of perturbation theory.

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

Key words: Hamiltonian dynamics, discrete symmetries, quantization, oscillator, uncertainty relations

Vol. 2, No 2,  p. 9 – 21, v1,   30 November 2007

Online: TPAC: 2525-007 v2,  18 September 2012; DOI: 10.9751/TPAC.2525-007


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

      zahidzakir@theor-phys.org

Nov
02

General relativity constrains proper times and predicts frozen stars instead of black holes

Zahid Zakir [1]

Abstract

     In a static gravitational field an intersection of a worldline by a global hypersurface of simultaneity t=const gives an invariant constraint relating the proper time of this event by t. Since at any finite t such constrained proper time intervals are less than required for crossing a horizon, general relativity predicts the gravitational freezing of proper times in stars with timelike or null geodesics everywhere. The time dilation stabilizes contracting massive stars by freezing, which is maximal but finite at the centre and the surface is frozen near the gravitational radius. The frozen stars (frozars) slowly defrost due to emissions and external interactions, the internal phase transitions can initiate refreezing with bursts and explosions.

PACS: 04.20.Dg;  04.70.-s;  97.60.-s,  98.54.-h

Key words: relativistic stars, black holes, quasars, active galactic nuclei, collapse, horizon, singularities

Vol. 2, No 1,  p. 1 – 8, v1,   2 November 2007

Online: TPAC: 2497-006 v2,  28 September 2012; DOI: 10.9751/TPAC.2497-006


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

      zahidzakir@theor-phys.org