Archive

Archive for March, 2015

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

Mar
28

Gravitationally frozen objects and relativistic explosion in general relativity: frozars, frozons and superbursts

 Zahid Zakir [1]

Abstract

 

In general relativity (GR) the worldline of a particle is unique and invariant, proper  time  and world time t are two parametrization of the same events on it only, that leads to a constraint for the proper time moments relating them by t. So, at contraction of a dust shell the proper times at finite t asymptotically freeze by no reaching a moment when the surface could cross the gravitational radius. Processes in entire volume of a star freeze at first at the center, then at higher layers, and at last the surface freezes outside the gravitational radius. Therefore in GR contraction leads to formation not black holes, but frozars (from “frozen star”) with the gravitationally frozen state of matter in entire volume, where the worldlines of particles are time-like everywhere, parallel to the t-axis and each other. Frozar formation in GR is shown for a thin dust shell, a dust ball, a star of uniform density and stars with ultrarelativistic matter. In real stars local temperatures in layers grow faster than temperature on the surface, and the last one grows on t exponentially fast. As high star’s mass, as high probability of that freezing occurs faster than warming up and the frozar will has time to be formed. But at lower masses, when the freezing does not enough fast, the warming up can stop contraction and can lead to explosion. During contraction a significant part of matter appear near the surface where in GR the physical volume sufficiently grows and energy of contraction is transformed to heat with transition of matter to the radiation dominated phase. If the star did not has time to be frozen, the part of ultrarelativistic matter and radiation leaves the star quickly, which appears as relativistic explosion, and the object will observed as relativistic supernova or hypernova. The observed lack of frozars of 2-4 solar mass and flat character of mass spectrum of more massive candidates to frozars confirm these predictions of the theory. the Big Bang and some explosions in astrophysics with large energy release probably are the cases of the relativistic explosion. In the frozar theory it appears a new GR phenomenon, the gravitational crystallization, defining structure of the most compact and massive objects in particle physics, astrophysics and cosmology. Gravitational radius of the system of few frozars sufficiently exceeds the radius of each of them and, therefore, at closing up they will not be able to merge and becomes frozen at distances larger their radii, forming a new state of matter – the gravitational crystal. Frozons, particles of the Planck energy, quantum fluctuations of which are frozen in their self gravitational field, also can not merge, i.e. for frozons there will be no interaction vertexes and they form only clusters and gravitational microcrystals. In astrophysics the supermassive frozen objects in the centers of star clusters, galaxies and quasars are probable gravitational supercrystals from frozars and ordinary matter. Relic frozons and frozar crystals could be the centers of inhomogeneities and also could be appear as a dark matter. If there is the backward contraction, the Universe as whole can be frozen also in the state of a global gravitational crystal which would stop the contraction.

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

Keywords: relativistic stars, gravitational collapse, black holes, quark stars

Vol. 10, No 1, p. 41 – 67, v1,     March 28, 2015
Electron.: TPAC: 5200-041 v1,    March 28, 2015 DOI: 10.9751/TPAC.5200-040