Abstract: In this paper, making use of the global one-dimensionality conjecture, we discuss the reduction of the Wheeler–DeWitt quantum geometrodynamics to the Klein–Gordon equation describing the scalar bosonic particle. The method of second quantization in the appropriate Fock space is applied, and, employing both the Bogoliubov transformation as well as Heisenberg equations of motion, the quantum gravity is expressed as evolution of the creators and annihilators related to the initial data. It is shown that this procedure leads to the understanding of the boson mass, through the one-point two-boson quantum correlations, as a scaled initial data mass.

Abstract: The canonically quantized 3+1 General Relativity with the global one dimensionality conjecture defines the model, which dimensionally reduced and secondary quantized yields the one-dimensional quantum field theory wherein the generic one-point correlations create a boson mass responsible for quantum gravity. In this paper, this simple model is developed in a wider sense. We propose to consider the thermodynamics of space quanta, constructed ab initio from the entropic formalism, as the quantum gravity phenomenology.

Abstract: Taking into account the global one-dimensionality conjecture recently proposed by the author, the Cauchy-like analytical wave functional of the Wheeler-DeWitt theory is derived. The crucial point of the integration strategy is canceling of the singular behavior of the effective potential, which is performed through the suitable change of variables introducing the invariant global dimension. In addition, the conjecture is extended onto the wave functionals dependent on both Matter felids as well as the invariant global dimension. Through application of the reduction within the quantum gravity model, the appropriate Dirac equation is obtained and than solved. The case of superposition is also briey discussed.

Abstract: In this paper the model of quantum gravity for the higher dimensional Lorentzian space-times, in the sense of the analogy with the Arnowitt–Deser–Misner decomposition well-known from General Relativity, is presented. The model is constructed through making use of the quantum geometrodynamics supplemented by the global onedimensionality conjecture, and considers the objective wave functionals. The framework of quantum field theory is applied in order to establish the phenomenological efficiency in accordance with high energy physics. The empirical deductions on the spatial dimensionality are presented as the relationship between the model and gauge theories, especially string theory.

Abstract: Throughout the violation of momentum-velocity parallelism and deformation of the Einstein equivalence principle, the model of faster- than-light motion, wherein both the Minkowski energy-momentum space and the Lorentz invariance, laying the foundations of Special Relativity and Standard Model, is constructed. Recently announced and denounced CERN's superluminal neutrinos are confronted.

Abstract: A massless photon, originated already through the Maxwell theory of electromagnetism, is one of the basic paradigms of modern physics, ideally supported throughout both the quantum electrodynamics and the Higgs mechanism of spontaneous symmetry breaking which lays the foundations of the Standard Model of elementary particles and fundamental interactions. Nevertheless, the physical interpretation of the optical experimental data, such like observations of total internal reflection of the beam shift in the Goos–H¨anchen effect, concludes a photon mass. Is, therefore, light diversified onto two independent species - gauge photons and optical photons? Can such a state of affairs be consistently described through a unique theoretical model? In this paper, two models of a photon mass, arising from the scalar quantum electrodynamics with the Higgs potential, are discussed. The first scenario leads to a neutral scalar mass estimable throughout the experimental limits on a photon mass. In the modified mechanism, a neutral scalar mass in not affected throughout a photon mass and is determinable through the experimental data, while a massless dilaton is present and a non-kinetic massive vector field effectively results in the string theory of non-interacting invariant both a free photon and a neutral scalar, and the Aharonov–Bohm effect is considered. The Markov hypothesis on maximality of the Planck mass is applied.

Abstract: In this paper, an effcient combination of the diverse theoretical approaches, such like the Einstein gravitational waves, the Lifshitz cosmological perturbation theory, the Veltman perturbative quantum gravity, and the Maxwell electrodynamics, leads to an essentially new discussion of either massless and massive gravitons. The new force law of gravitation is established. The case of the Planckian particle is considered in the context of the Markov hypothesis.

Abstract: In this paper, making use of the’tHooft–Polyakov–Julia–Zeeansatz for the SU(2) Yang–Mills–Higgs gauge field theory, we present the straightforward generalization of the Bogomoln’yi equations and its several consequences. Particularly, this is shown that this idea is able to generate new types of non-abelian both dyons and magnetic monopoles and, moreover, that within the new model the scalar field can be described through the Coulomb potential, whereas, upto aconstant, the non-abelian gauge field becomes the Wu–Yang monopole.

Abstract: In this article, we present two numerical methods to solve the second order multi-pantograph equation with boundary conditions. The multi-pantograph equation is converted to an integral equation then the integral equation is solved by two projective methods. Some properties of Chebyshev polynomials are employed to prove the convergence analysis of the two proposed methods. Finally, numerical examples also are given to illustrate the efficiency and validity of the two proposed methods.

Abstract: On the example of a complex of 10 pulsars shows a method to identify the statistical models and the analysis of the model amplitude of gravitational waves, depending on the rotation periods of pulsars. Hilbert applied invariants. Shows the levels of adequacy asymmetric wavelet signals detected by statistical data. Proved insufficient deterministic models for the Laplace-Mandelbrot law. For 10 pulsars obtained statistical model pulsating universe. The model contains two modified 's law and two asymmetric wavelets oscillatory perturbation of gravitational waves in overcoming the energy crisis. Interpretation of the resulting statistical model is given based on the relativistic theory of gravitation. To do this, four components of the statistical model are divided into two cones of causality.