International Journal of Modern Physics A

The analyticity properties of the scattering amplitude for a massive scalar field are reviewed in this paper where the space–time geometry is $R^{3,1}\otimes S^1$, i.e. one spatial dimension is compact. Khuri investigated the analyticity of scattering amplitude in a nonrelativistic potential model in three dimensions with an additional compact dimension. He showed that under certain circumstances, the forward amplitude is nonanalytic. He argued that in high energy scattering if such a behavior persists it would be in conflicts with the established results of quantum field theory and LHC might observe such behaviors. We envisage a real scalar massive field in flat Minkowski space–time in five dimensions. The Kaluza–Klein (KK) compactification is implemented on a circle. The resulting four-dimensional manifold is $R^{3,1}\otimes S^1$. The LSZ formalism is adopted to study the analyticity of the scattering amplitude. The nonforward dispersion relation is proved. In addition the Jin–Martin bound and an analog of the Froissart–Martin bound are proved. A novel proposal is presented to look for evidence of the large-radius-compactification scenario. A seemingly violation of Froissart–Martin bound at LHC energy might hint that an extra dimension might be decompactified. However, we find no evidence for violation of the bound in our analysis.

We present a Petrov type II general spacetime which violates causality in the sense that it allows for the formation of closed timelike curves that appear after a definite instant of time. The metric, which is axially symmetric, admits an expansion-free, twist-free and shear-free null geodesic congruence. From the general metric, we obtain two particular type II metrics. One is a vacuum solution while the other represents a Ricci flat solution with a negative cosmological constant.

The relativistic bound-state energy spectrum and the wave functions for the Coulomb potential are studied for de Sitter and anti-de Sitter spaces in the context of the extended uncertainty principle. Klein–Gordon and Dirac equations are solved analytically to obtain the results. The electron energies of hydrogen-like atoms are studied numerically.

In the Dirac theory of the quantum-mechanical interaction of a magnetic monopole and an electric charge, the vector potential is singular from the origin to infinity along a certain direction — the so-called Dirac string. Imposing the famous quantization condition, the singular string attached to the monopole can be rotated arbitrarily by a gauge transformation, and hence is not physically observable. By deriving its analytical expression and analyzing its properties, we show that the gauge function $\chi (r)$ which rotates the string to another one is a smooth function everywhere in space, except their respective strings. On the strings, $\chi (r)$ is a multi-valued function. Consequently, some misunderstandings in the literature are clarified.

In this work, the $q$-Schrödinger equations with symmetric polynomial potentials are considered. The spectrum of the model is obtained for several values of $q$, and the limiting case as $q\to 1$ is considered. The Rayleigh–Ritz variational method is adopted to the system. The discrete $q$-Hermite I polynomials are handled as basis in this method. Furthermore, the following potentials with numerous results are presented as applications: $q$-harmonic, purely $q$-quartic and $q$-quartic oscillators. It is also shown that the obtained results confirm the ones that exist in the literature for the continuous case.

The relativistic quantum dynamics of the generalized Klein–Gordon (KG) oscillator having position-dependent mass in the Gödel-type space–time is investigated. We have presented the generalized KG oscillator in this space–time, and discussed the effect of Cornell potential and linear potential for our considered system. The modification from the parameters of position-dependent mass and characterizing the space–time for the energy spectrums are presented.

In this paper, we analyze gauge groups in six-dimensional $N=1$ F-theory models. We construct elliptic Calabi–Yau 3-folds possessing various singularity types as double covers of “1/2 Calabi–Yau 3-folds,” a class of rational elliptic 3-folds, by applying the method discussed in a previous study to classify the singularity types of the 1/2 Calabi–Yau 3-folds. One to three U(1) factors are formed in six-dimensional F-theory on the constructed Calabi–Yau 3-folds. The singularity types of the constructed Calabi–Yau 3-folds corresponding to the non-Abelian gauge group factors in six-dimensional F-theory are deduced. The singularity types of the Calabi–Yau 3-folds constructed in this work consist of $A$- and $D$-type singularities.

In this paper we study through tunneling formalism, the effect of noncommutativity to Hawking radiation and the entropy of the noncommutative Schwarzschild black hole. In our model we have considered the noncommutativity implemented via the Lorentzian distribution. We obtain noncommutative corrections to the Hawking temperature using the Hamilton–Jacobi method and the Wentzel–Kramers–Brillouin (WKB) approximation. In addition, we found corrections of the logarithmic and other types due to noncommutativity and quantum corrections from the generalized uncertainty principle (GUP) for the entropy of the Schwarzschild black hole.

Two infinite sets of Galilean invariant equations are derived using the irreducible representations of the orthochronous extended Galilean group. It is shown that one set contains the Schrödinger equation, which is the fundamental equation for ordinary matter, and the other set has a new asymmetric equation, which is proposed to be the fundamental equation for dark matter. Using this new equation, a theory of dark matter is developed and its profound physical implications are discussed. This theory explains the currently known properties of dark matter and also predicts a detectable gravitational radiation.