Some consequences of a non-commutative space-time structure

The existence of a fundamental length (or fundamental time) has been conjectured in many contexts. Here we discuss some consequences of a fundamental constant of this type, which emerges as a consequence of deformation-stability considerations leading to a non-commutative space-time structure. This mathematically well defined structure is sufficiently constrained to allow for unambiguous experimental predictions. In particular we discuss the phase-space volume modifications and their relevance for the calculation of the Greisen-Zatsepin-Kuz’min sphere. The (small) corrections to the spectrum of the Coulomb problem are also computed.Received: 23 December 2004, Revised: 18 April 2005, Published online: 8 July 2005PACS: 13.60.-r; 03.65.Bz; 98.70.Sa     

Some consequences of the Finslerian structure of the space-time with the absolute parallelism

In the present paper the correspondence between the Reimannian and the Finslerian metric structures of the space-time with the absolute parallelism is considered. The statistical characteristics of the gravitational field, defined by the Finslerian metrization, are investigated. Some basic principles of the development of the theory of physical fields, depending on the line support elements, are discussed.     

Quantum space-time and gravitational consequences

Relativistic particle dynamics and basic physical quantities for the general theory of gravity are reconstructed from a quantum space-time point of view. An additional force caused by quantum space-time appears in the equation of particle motion, giving rise to a reformulation of the equivalence principle up to values ofO(L ²), whereL is the fundamental length. It turns out that quantum space-time leads to quantization of gravity, i.e., the metric tensorg _v () becomes operator-valued and is not commutative at different pointsx andy in usual space-time on a large scale, and its commutator depending on the vielbein field (gaugelike graviton field) is proportional toL ² multiplied by a translation-invariant wave function propagated between pointsx andy . In the given scheme, there appears to be an antigravitational effect in the motion of a particle in the gravitational force. This effect depends on the value of particle mass; when a particle is heavy its free-fall time is long compared to that for a light-weight particle. The problem of the change of time scale and the anisotropy of inertia are discussed. From experimental data from testing of the latter effect it follows thatL10^–22cm.     

Some developments in twistors and space-time

On twistors, strings, and the cosmological constant.     

Some astrophysical consequences of the Jordan-Brans-Dicke theory

It is shown that the appearance of a new dimensional constant — the speed of light — in the field equations of the Jordan-Brans-Dicke theory (JBD) makes it possible to construct from the set of constant constructions appearing in the system two with the dimension of energy. This is an indication of the existence of two branches of equilibrium configurations in the JBD theory, which was discovered from numerical calculations by Saakyan and Mnatsakanyan. The problem of the gravitational stability of the cosmological model of the JBD theory is considered. It is shown that the two modes of perturbation evolution obtained differ little from the perturbation modes in the Friedmann model.This article is the result of work performed under the direction of Candidate of Physical and Mathematical Sciences V. I. Bashkov.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 24–27, February, 1982.     

Some exact solutions of the Dirac equation in the Kasner space-time

The exact solutions of the covariant generalization of the Dirac equation are obtained in the Kasner space-time for two types of coordinates, cartesian coordinates and cylindrical ones. The tetrads for both cases are constructed on the basis of a global quasicartesian coordinate systems that allows one to get rid of coordinate effects connected with the rotation of the local frame under transition of the triad from one space-time point to another. The possibility of plane and cylindrical spinor waves in the Kasner space-time is proved.     

Some consequences of the vanishing of the triple-pomeronchukon-vertex

Starting with the assumption that the triple-pomeronchukon-vertex vanishes when all three pomeronchukons have zero mass, we show that in the absence of pionization, total cross sections would fall at least logarithmically with energy, while the mean multiplicity would approach a constant. Several reasons are presented to suggest that some pionization must occur and that, otherwise, limiting fragmentation itself would vanish. A secondary result, that the P-P-P′ coupling will also vanish in certain regions, is also proved.     

Some remarks on the dynamical origin of charge and space-time quantisation

It is argued here that the concept of dynamical origin of charge as formulated in a previous paper requires the quantisation of space-time. Indeed, in this scheme, it is pointed out that the quantisation of electric charge in unit ofe is a direct consequence of this space-time quantisation.     

Some phenomenological consequences of the super higgs effect

To the combined system of supergravity ofN=1 and the Higgs multiplet (a scalar multiplet) is coupled a complex scalar multiplet as a simplified representative of the matter. An order-of-magnitude estimate is attempted on the masses and the couplings of the gravitino and other fields.     

Some consequences of exchange degeneracy and the triple-Regge-hypothesis

We extract the proton-Reggeised rho total cross-section from inclusive data for K⁺ + p → K⁰ + (anything) in the triple-Regge domain and find that it is of the same order as physical meson-proton cross-sections for a range of Reggeon mass. We also relate other processes such as pp→pX and K⁺p→K⁺X to K⁺p→K⁰X, and get good agreement with data. We suggest methods for calculating baryon exchange processes as well.     

Some consequences of neutral current systematics

Two kinds of general consequences of the ΔS=0 weak hadron neutral current independent of a gauge model are presented. Firstly are results which depend on the quark parton model. These involve bounds among neutrino inclusive cross-section and a bound onQ(Z, N) in terms of these inclusive cross-sections. Secondly are results which are independent of the quark-parton model and depend only on the SU(3) structure of the most general ΔS=0 neutral current. These tests of isopin and speciallyU-spin properties of the current are given forv+N→v+hadron+anything,v+N→v+baryon+meson ande ⁺ e ⁻→baryon+anti-baryon. In addition some conjectures are made with regard to the semi-inclusive neutrino-reactions using the quark parton model.     

Some consequences of global horizontal symmetry

It is pointed out that the present SU(3) _c ×SU(2) _L ×U(1) gauge interactions with three families have a global horizontal symmetry (denoted hereby SU(3) _H ) which is broken only by the weak charged hadron currentJ _h. Also, with (u, c), (d, s), (v _e, {ie437-1}) and (e ⁻,μ ⁻) as doublets of SU(2) _H (subgroup of SU(3) _H ),J _h has simple transformation properties under this subgroup. Amplitude relations, using SU(2) _H symmetry, for hadronic leptonic and semileptonic decays are given.     

Some consequences of infinite mass renormalization

Using a finite form of local field equations some consequences of infinite mass renormalization are studied in a rigorous manner. The method is applied to various models. For pseudoscalar meson-nucleon interaction sufficient conditions are given for the equivalence to a direct Fermi coupling. Confirming a recent result byKroll, Lee, andZumino it is shown that a vector meson field should be proportional to the corresponding current if the bare meson mass is infinite. In the conventional treatment of neutral vector meson theories this causes certain difficulties which are analyzed in detail. In case of two vector fields coupled to the same current it is found that the fields must be proportional provided the bare masses are both infinite. In the Appendix finite local field equations are discussed for the coupling of a neutral vector meson field to the current of a spin 1/2 field.     

The total space-time of a point charge and its consequences for black holes

Singularities associated with an incomplete space-timeS are not uniquely defined until a boundaryB is attached to it. [The resulting space-time-with-boundary, ¯S S B, will be termed a total space-time (TST).] Since an incomplete spacetime is compatible with a variety of boundaries, it follows thatS does not represent a unique universe, but instead corresponds to a family of universes, one for each of its distinct TSTs. It is shown here that the boundary attached to the Reissner-Nordström space-time for a point charge is invalid forq ²<m ². When the correct boundary is used, the resulting TST is inextendible. This implies that the Graves-Brill black hole cannot be produced by gravitational collapse. The same is true of the Kruskal-Fronsdal black hole for the point mass, and for those black holes which reduce to the latter for special values of their parameters.     

Some remarks on nonlocal field theory and space-time quantization

From the point of view that the charge and mass of an electron is of dynamical origin and quantization of charge in units ofe is related to the space-time quantization as developed in an earlier paper, we here show that it is possible to consider that the internal space within the elementary domain of the quantized space-time world is not governed by Lorentz invariance. This helps us to develop a consistent theory of nonlocal fields for extended particles where the infinite mass degeneracy is avoided. Moreover, this ensures the convergence of nonlocal field theories and suggests that massless particles like photons and neutrinos, though they may be taken to be of extended structure, will appear only as point particles in the physical world. In this picture, Lorentz invariance appears to be a consequence of the distribution of matter and energy in the Universe, and this may be taken to be another interpretation of Mach's principle.     

Some exact solutions of string cosmology in Bianchi III space-time

Following the techniques used by Letelier and Stachel some exact Bianchi III cosmological solutions of massive strings in the presence of magnetic field are obtained and their physical features are discussed. Some string solutions in which magnetic fields are absent are also discussed.     

Some interesting consequences of the maximum entropy production principle

Two nonequilibrium phase transitions (morphological and hydrodynamic) are analyzed by applying the maximum entropy production principle. Quantitative analysis is for the first time compared with experiment. Nonequilibrium crystallization of ice and laminar-turbulent flow transition in a circular pipe are examined as examples of morphological and hydrodynamic transitions, respectively. For the latter transition, a minimum critical Reynolds number of 1200 is predicted. A discussion of this important and interesting result is presented.     

Some consequences of exchangeability in random-matrix theory

Properties of infinite sequences of exchangeable random variables result directly in explicit expressions for calculating asymptotic densities of eigenvalues rho(infinity)(lambda) of any ensemble of random matrices H whose distribution depends only on tr(H+H), where H+ is the Hermitian conjugate of H. For real symmetric matrices and for Hermitian matrices, the densities rho(infinity)(lambda) are constructed by summing up Wigner semicircles with varying radii and weights as confirmed by Monte Carlo simulations. Extensions to more general matrix ensembles are also considered.     

Group analysis of masses and spins in curved space-time: Cosmological and experimental consequences

Recent developments in spontaneously broken gauge theories as well as in group analysis of masses and spins in curved space-time indicate that rest masses may change as a function of cosmic time. Such as effect is incompatible with standard cosmological models. A set of cosmological models that incorporate mass variation is introduced. These cosmological models are shown to be fully compatible with the group analysis, yielding exactly the same formula; they are used therefore as a theoretical testing ground for the hypothesis of mass variation. The following consequences of this hypothesis are obtained: (1) Cosmological red-shifts are shown to correspond to a contracting, rather than expanding, universe. (2) The effects of mass variation on planetary orbits are calculated; they are not precluded by the data. Conclusive experimental evidence is expected within a few years.