Searcharxiv⌕ Search

arXiv subjects

Michael A. Ivanov

Publications and source records attributed to Michael A. Ivanov.

31 records · Page 2Linked to original sources
arXiv2004

The Diophantine equations $ x^{n}_{1} +x^{n}_{2} +...+x^{n}_{r_{1}}= y ^{n}_{1} +y^{n}_{2} +...+y^{n}_{r_{2}} $

The aim of this paper is to prove the possibility of linearization of such equations by means of introduction of new variables. For $n=2$ such a procedure is well known, when new variables are components of spinors and they are widely used in mathematical physics. For example, parametrization of Pythagoras threes $a^{2} +b^{2}$, $a^{2} -b^{2}$, $2ab$ may be cited as an example in number theory where two independent variables form a spinor which can be obtained by solution of a system of two linear equations. We also investigate the combinatorial estimate for the smallest sum $r(n)=r _{1}+r_{2} -1 $ for solvable equations of such a type as $r(n) \leq 2n+1$ (recently the better one with $r(n) \leq2n-1$ was received by L. Habsieger (J. of Number Theory 45 (1993) 92)). Apart from that we consider two conjectures about $r(n)$ and particular solutions for $n \leq11$ which were found with the help of the algorithm that is not connected with linearization.

math.NT↗
arXiv2004

May gravitons be super-strong interacting particles?

A scheme, in which gravitons are super-strong interacting, is described. The graviton background with the Planckian spectrum and a small effective temperature is considered as a reservoir of gravitons. A cross-section of interaction of a graviton with any particle is assumed to be a bilinear function of its energies. Any pair of bodies are attracting not due to an exchange with its own gravitons, but due to a pressure of external gravitons of this background. A graviton pairing is necessary to obtain classical gravity. Any divergencies are not possible in such the model because of natural smooth cut-offs of the graviton spectrum from both sides. Some cosmological consequences of this scheme are discussed, too. Also it is shown here that the main conjecture of this approach may be verified at present on the Earth.

gr-qc↗
arXiv2004

A quantum gravitational model of redshifts

The main features of an alternative model of redshifts are described here. The model is based on conjectures about an existence of the graviton background with the Planckian spectrum and a super-strong character of quantum gravitational interaction. This model is connected with the assumed quantum mechanism of gravity. A behavior of two theoretical functions of a redshift $z$ in this model - the geometrical distance $r(z)$ and the luminosity distance $D_{L}(z)$ - and an existence of two different cosmological horizons for any observer are discussed.

astro-ph↗
arXiv2004

Another origin of cosmological redshifts

If gravitons are super-strong interacting particles which fulfill a flat non-expanding universe, we would have another possibility to explain cosmological redshifts - in a frame of non-kinematic model. It is shown by the author that in this case SNe 1a data may be understood without any dark energy and dark matter. A value of relaxation factor is found in this paper. In this approach, we have Newton's law of gravity as a simplest consequence, and the connection between Newton's and Hubble's constants. A value of the latter may be theoretically predicted.

astro-ph↗
arXiv2004

Another possible interpretation of SN 1a data - without kinematics: Comments on the paper astro-ph/0402512 by A. Riess et al

It is shown here that for redshifts $z < 0.5$ the luminosity distance, which is predicted in author's model astro-ph/0005084 v2, fits well supernova observational data of astro-ph/0402512 by A.Riess et al. Discrepancies for higher $z$ would be explained in the model as a result of specific deformation of SN spectra due to a discrete character of photon energy losses. The model does not require any dark energy; it is based on the conjecture that gravitons are super-strong interacting particles fulfilling a flat non-expanding universe.

astro-ph↗
arXiv2003

Restrictions on a geometrical language in gravity

It was shown by the author (gr-qc/0207006) that screening the background of super-strong interacting gravitons creates Newtonian attraction if single gravitons are pairing and graviton pairs are destructed by collisions with a body. In such the model, Newton's constant is connected with Hubble's constant, for which the estimate is obtained: $94.576 km \cdot s^{-1} \cdot Mpc^{-1}.$ It is necessary to assume an atomic structure of any body to have the working model. Because of it, an existence of black holes contradicts to the equivalence principle in a frame of the model. For usual matter, the equivalence principle should be broken at distances $\sim 10^{-11} m,$ if the model is true.

astro-ph↗
arXiv2003

A fine quantum mechanism of classical gravity

It is shown that screening the background of super-strong interacting gravitons ensures the Newtonian attraction, if a part of single gravitons is pairing and graviton pairs are destructed by collisions with a body. If the considered quantum mechanism of classical gravity is realized in the nature, than an existence of black holes contradicts to the equivalence principle. In such the model, Newton's constant is proportional to $H^{2}/T^{4},$ where $H$ is the Hubble constant, $T$ is an equivalent temperature of the graviton background. The estimate of the Hubble constant is obtained for the Newtonian limit: $H=3.026 \cdot 10^{-18} s^{-1}$ (or $94.576 km \cdot s^{-1} \cdot Mpc^{-1}$).

gr-qc↗
arXiv2003

Discrete Symmetries Underlying Some Continuous Ones: Two Examples From Gravity And Particle Physics

Two examples, not connected at present, from author's papers (Nuovo Cim., 1992, v.105A, p.77 [hep-th/0207210] and GRG, 1999, v.31, p.1431 [gr-qc/0207017]) are considered here in which a physical model has discrete symmetries and additional non-observable coordinates or parameters. Then it is possible to introduce some apparent continuous symmetries of the model for an observer which cannot know values of these additional quantities.

math-ph↗
arXiv2002

Model of graviton-dusty universe

Primary features of a new cosmological model, which is based on conjectures about an existence of the graviton background and superstrong gravitational quantum interaction, are considered. An expansion of the universe is impossible in such the model because of deceleration of massive objects by the graviton background, which is similar to the one for the NASA deep space probes Pioneer 10, 11. Redshifts of remote objects are caused in the model by interaction of photons with the graviton background, and the Hubble constant depends on an intensity of interaction and an equivalent temperature of the graviton background. Virtual massive gravitons would be dark matter particles. They transfer energy, lost by luminous matter radiation, which in a final stage may be collected with black holes and other massive objects.

gr-qc↗
arXiv2002

Primary Postulates of the Standard Model as Consequences of the Composite Nature of the Fundamental Fermions

A field model of two-component fermions is described, the consequences of which coincide in the main with primary postulates of the standard model. Such a model can be constructed for 4 generations at the minimum. Peculiarities of the relative coordinate space, determining in general an internal symmetry group, are considered. Analogues of the Higgs fields appear in the model naturally after transition to the Grassmannian extra coordinates.

hep-th↗
arXiv2002

A model of gravitation with global U(1)-symmetry

It is shown that an embedding of the general relativity $4-$space into a flat $12-$space gives a model of gravitation with the global $U(1)-$symmetry and the discrete $D_{1}-$one. The last one may be transformed into the $SU(2)-$symmetry of the unified model, and the demand of independence of $U(1)-$ and $SU(2)-$transformations leads to the estimate $\sin^{2}θ_{min}=0,20$ where $θ_{min}$ is an analog of the Weinberg angle of the standard model.

gr-qc↗
arXiv2002

Possible manifestations of the graviton background

Possible effects are considered which would be caused by a hypothetical superstrong interaction of photons or massive bodies with single gravitons of the graviton background. If full cosmological redshift magnitudes are caused by the interaction, then the luminosity distance in a flat non-expanding universe as a function of redshift is very similar to the specific function which fits supernova cosmology data by Riess et al. From another side, in this case every massive body, slowly moving relatively to the background, would experience a constant acceleration, proportional to the Hubble constant, of the same order as a small additional acceleration of Pioneer 10, 11.

astro-ph↗