Modern Physics Letters A

This paper presents a critical historical review of the two main approaches to providing an understanding of the nature of the weak nuclear force via the Standard Model and the Generation Model of particle physics. The Standard Model is generally considered to be incomplete in the sense that it provides little understanding of several empirical observations: the Generation Model was developed to overcome several dubious assumptions made during the development of the Standard Model. This paper indicates that the Generation Model provides a more consistent understanding of the weak nuclear force than the earlier Standard Model.

We argue in a quantitative way that the unitarity principle of quantum field theory together with the quantum information bound on correlation functions is in tension with a space which is made out of disconnected patches at microscopic scales.

In this paper, we show that the causally connected four-dimensional line element of the $\kappa$-deformed Minkowski spacetime induces an upper cut-off on the proper acceleration and derive this maximal acceleration, valid up to first order in the deformation parameter. We find a contribution to maximal acceleration which is independent of $\hslash$ and thus signals effect of the non-commutativity alone. We also construct the $\kappa$-deformed geodesic equation and obtain its $\kappa$-deformed Newtonian limit, valid up to first order in deformation parameter. Using this, we constrain non-commutative parameters present in the expression for maximal acceleration. We analyze different limits of the maximal acceleration and also discuss its implication to maximal temperature. We also obtain a bound on the deformation parameter.

In the description of neutron stars, it is very important to consider gravitational theories as general relativity, due to the determining influence on the behavior of the different types of stars, since some objects show densities even bigger than nuclear density. This paper starts with Einstein’s equations for a perfect fluid and then we present a uniparametric stellar model which allows to describe compact objects like neutron stars with compactness ratio $u\le 0.2533053$. The pressure and density are monotone decreasing regular functions, the speed of sound satisfies the causality condition, while the value for its adiabatic index $\gamma =4.9227102>4/3$ guarantees the stability. In addition, the graph of $P$ versus $\rho$ shows a quasi-linear relationship for the equation of state $P(\rho )=P_c(\rho -{\rho }_b)/({\rho }_c-{\rho }_b)$, which is similar to the so-called MIT Bag equation when we have the interaction between quarks. In our case it is due to the interaction of the different components found inside the star, such as electrons and neutrons. As an application of the model, we describe the star PSR J1614-2230 with a observed mass of $M=(1.97\pm 0.04)M_{\odot }$ and a radius $R=(13\pm 2)\mathrm{\text{km}}$, the model shows that the maximum central density occurs for a maximal compactness value ${\rho }_c=7.8065214\times 10^{17}{\mathrm{\text{kg/m}}}^3$.

A static anisotropic relativistic fluid sphere model with regular geometry and finite hydrostatic functions is presented. In the interior of the sphere, the density, radial pressure and tangential pressure are positives, monotonically decreasing with increasing radius and the radial pressure vanishes at the surface of the matter distribution and is joined continuously to the exterior Schwarzschild’s solution at this surface. The speeds of the radial and tangential sound are positive and lower than the speed of light, that is, the causal condition is not violated, and also the behavior of these guarantees that the model is potentially stable. Furthermore, the range of the compactness ratio is characteristic of compact stars and it is shown that the effect of the anisotropy generates that the speed of the radial sound can behave as a function monotonically increasing or monotonically decreasing.

We established the criteria for thermal stability of a most general black hole in the form of a series of inequalities connecting second-order derivatives of the black hole mass with respect to its parameters. The mass of a black hole depends solely on these parameters, e.g. horizon area and electric charge are these parameters for non-rotating charged black hole. We also introduced the notion of “Quasi stability”. It is known how to calculate the fluctuations of these parameters for both stable and quasi stable black holes. In this paper, we consider the simplest black hole having nontrivial parameter, i.e. electrically charged non-rotating asymptotically flat Reissner–Nordstrom black hole (AFRNBH). We will show here that this black hole is not stable anywhere in its parameter space, but it is actually quasi stable, having positive specific heat in some region, violating Hawking’s prediction. In fact, this black hole will be shown to exhibit phase transition which is structurally quite different from that in case of Schwarzschild black hole, as predicted first by Hawking. This black hole will also be shown to try to resist its decay under Hawking radiation, but ultimately remains unsuccessful.

The information theoretic concepts are crucial to study the quantum mechanical systems. In this paper, the information densities of ${𝒫}{𝒯}$-symmetric potential have been demonstrated and their properties deeply analyzed. The position space and momentum space information entropy is obtained and Bialynicki-Birula–Mycielski inequality is saturated for different parameters of the potential. Some interesting features of information entropy have been discussed. The variation in these entropies is described which gets saturated for specific values of the parameter. These have also been analyzed for the ${𝒫}{𝒯}$-symmetry breaking case. Further, the entropy squeezing phenomenon has been investigated in position space as well as momentum space. Interestingly, ${𝒫}{𝒯}$ phase transition conjectures the entropy squeezing in position space and momentum space.

In this paper, we study the (2 + 1)-dimensional Klein–Gordon oscillator coupled to an external magnetic field, in which we change the standard partial derivatives for the Dunkl derivatives. We find the energy spectrum (Landau levels) in an algebraic way, by introducing three operators that close the su(1, 1) Lie algebra and from the theory of unitary representations. Also, we find the energy spectrum and the eigenfunctions analytically, and we show that both solutions are consistent. Finally, we demonstrate that when the magnetic field vanishes or when the parameters of the Dunkl derivatives are set to zero, our results are adequately reduced to those reported in the literature.

Using a formulation of quantum mechanics based on orthogonal polynomials in the energy and physical parameters, we study quantum systems totally confined in space and with a linearly spaced energy spectrum. We present several examples of such systems, derive their corresponding potential functions, and plot some of their bound states.