Modern Physics Letters A

We review the development of the equations of gravitoelectromagnetism and summarize how the motion of the neutral masses in an accretion disk orbiting a black hole creates a general-relativistic magnetic-like (gravitomagnetic) field that vertically accelerates neutral particles near the accretion disk upward and then inward toward the axis of the accretion disk. Even though this gravitomagnetic field is not the only mechanism to produce collimated jets, it is a novel means to identify one general relativistic effect from a much more complicated problem. In addition, as the accelerated material above or below the accretion disk nears the axis with a nearly vertical direction, a frame-dragging effect twists the trajectories around the axis thus contributing to the collimation of the jet.

In this paper, we have developed a formalism to obtain the Schrödinger equation for a particle in a frame undergoing a uniform acceleration in an otherwise flat Minkowski spacetime geometry. We have presented an exact solution of the equation and obtained the eigenfunctions and the corresponding eigenvalues. It has been observed that the Schrödinger equation can be reduced to a one-dimensional hydrogen atom problem. Whereas, the quantized energy levels are exactly identical with that of a one-dimensional quantum harmonic oscillator. Hence, considering transitions, we have predicted the existence of a new kind of quanta, which will either be emitted or absorbed if the particles get excited or de-excited, respectively.

Two models with linear and nonlinear second class constraints are considered and gauged by embedding in an extended phase space. These models are studied by considering a free non-relativistic particle on the hyperplane and hypersphere in the configuration space. The gauged theory of the first model is obtained by converting the very second class system to the first class one directly. In contrast, the first class system related to the free particle on the hypersphere is derived with the help of the infinite Batalin–Fradkin–Tyutin (BFT) embedding procedure. We propose a practical formula, based on the simplified BFT method, which is practical in gauging linear and some nonlinear second class systems. As a result of gauging these two models, we show that in the conversion of second class constraints to the first class ones, the minimum number of phase space degrees of freedom for both systems is a pair of phase space coordinates. This pair is made up of a coordinate and its conjugate momentum for the first model, but the corresponding Poisson structure of the embedded non-relativistic particle on hypersphere is a nontrivial one. We derive infinite correction terms for the Hamiltonian of the nonlinear constraints and an interacting gauged Hamiltonian is constructed by summing over them. At the end, we find an open algebra for three first class objects of the embedded nonlinear system.

We compare the Parton distributions deduced in the framework of a quantum statistical approach for both the longitudinal and transverse degrees of freedom with the unpolarized distributions measured at HERA and with the polarized ones proposed in a previous paper, which have been shown to be in very good agreement also with the results of experiments performed after that proposal. The agreement with HERA data in correspondence to very similar values for the “temperature” and the “potentials” found in the previous work gives a robust confirm of the statistical model. The unpolarized distributions are compared also with the result of NNPDF. The free parameters are fixed mainly by data in the range (0.1, 0.5) for the x variable, where the valence Partons dominate, and in the small x region for the diffractive contribution. This feature makes the parametrization proposed here very attractive.

We argue that our recent success in using our resummed quantum gravity (RQG) approach to Einstein’s general theory of relativity, in the context of the Planck scale cosmology formulation of Bonanno and Reuter, to estimate the value of the cosmological constant $\mathrm{\Lambda }$ supports the use of quantum mechanical consistency requirements to constrain the main uncertainty in that very promising result. This main uncertainty, which is due to the uncertainty in the value of the time $t_{\text{tr}}$ at which the transition from the Planck scale cosmology to the FRW model occurs, is shown to be reduced, by requiring consistency between the Heisenberg uncertainty principle and the known properties of the solutions of Einstein’s equations, from four orders of magnitude to the level of a factor of ${𝒪}(10)$. This lends more credibility to the overall RQG approach itself, in general, and to our estimate of $\mathrm{\Lambda }$ in particular.

In this paper, it is shown that the covariant representation (CR) transforming the Dirac field under de Sitter isometries is equivalent to a direct sum of two unitary irreducible representations (UIRs) of the Sp(2, 2) group transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down for the first time finding that these representations are equivalent to an UIR from the principal series whose canonical labels are determined by the fermion mass and spin. The properties of the conserved observables (i.e. one-particle operators) associated to the de Sitter isometries via Noether theorem and of the corresponding Pauli–Lubanski type operator are also pointed out.

In the present study, we mainly investigate the nature of entropy function in non-flat Kaluza–Klein universe. We prove that the first and generalized second laws of gravitational thermodynamics are valid on the dynamical apparent horizon.

We consider the interplay of the pentaquark states and strange tetraquark states in the decay ${\Lambda }_b^0\to K^{-}J/\psi p$. Possible existence of ($cs\bar{c}ū$)-states is taken up and their manifestation in the $K^{-}J/\psi$-channel is discussed. It is emphasized that these exotic mesons can imitate broad bumps in the $pJ/\psi$-channel.