International Journal of Modern Physics A

We review (and extend) the analysis of general theories of all interactions (gravity included) where the mass scales are due to dimensional transmutation. Quantum consistency requires the presence of terms in the action with four derivatives of the metric. It is shown, nevertheless, how unitary is achieved and the classical Ostrogradsky instabilities can be avoided. The four-derivative terms also allow us to have a UV complete framework and a naturally small ratio between the Higgs mass and the Planck scale. Moreover, black holes of Einstein gravity with horizons smaller than a certain (microscopic) scale are replaced by horizonless ultracompact objects that are free from any singularity and have interesting phenomenological applications. We also discuss the predictions that can be compared with observations of the microwave background radiation anisotropies and find that this scenario is viable and can be tested with future data. Finally, how strong phase transitions can emerge in models of this type with approximate scale symmetry and how to test them with GW detectors is reviewed and explained.

Using the light-front holographic model, we study the transverse momentum-dependent parton distributions (TMDs) for the case of pion. At leading twist, the unpolarized parton distribution function $f_{1\pi }(x,k_{\perp }^2)$ and the Boer–Mulders function $h_{1\pi }^{\perp }(x,k_{\perp }^2)$ are obtained for pion. We calculate both the functions using the light-front holographic model with spin improved wave function and compare the predicted results with available results of other models. In order to provide inputs in predicting future experimental data, an LO evolution is performed from model scale to experimental scale for the case of unpolarized parton distribution function $f_{1\pi }(x,k_{\perp }^2)$.

We study a generalized KG-oscillator in the five-dimensional cosmic string geometry background with a magnetic field and quantum flux using Kaluza–Klein theory under the effects of a Cornell-type scalar potential, and observe the gravitational analogue of the Aharonov–Bohm effect. We see that the scalar potential allows the formation of bound states solution, and the energy eigenvalue depends on the global parameter characterizing the space–time. We also see that the magnetic field depends on quantum numbers of the relativistic system which shows a quantum effect.

We propose the description of superintegrable models with dynamical $so(1.2)$ symmetry, and of the generic superintegrable deformations of oscillator and Coulomb systems in terms of higher-dimensional Klein model (the noncompact analog of complex projective space) playing the role of phase space. We present the expressions of the constants of motion of these systems via Killing potentials defining the $su(N.1)$ isometries of the Kähler structure.

We study $d$-dimensional black holes surrounded by dark energy (DE), embedded in $D$-dimensional M-theory/superstring inspired models having ${\mathrm{\text{AdS}}}_d\times {𝕊}^{d+k}$ space–time where $D=2d+k$. We focus first on the thermodynamical Hawking–Page phase transitions, whose microscopical origin is linked to $N$ coincident $(d-2)$-branes supposed to live in such inspired models. Interpreting the cosmological constant as the number of colors, we compute various thermodynamical quantities in terms of the brane number, the entropy and the DE contribution. Calculating the ordinary chemical potential conjugated to the number of colors, we show that a generic black hole is more stable for a larger number of branes in lower dimensions. In the presence of DE, however, we find that the DE state parameter ${\omega }_q$ takes particular values, for $(D,d,k)$ models, providing nontrivial phase transitions. Then, we examine some optical properties. Concretely, we investigate shadow behaviors of quintessential black holes in terms of $(d-2)$-brane physics. In terms of certain ratios, we find similar behaviors for critical quantities and shadow radius.

The Snyder–de Sitter model is an extension of the Snyder model to a de Sitter background. It is called triply special relativity (TSR) because it is based on three fundamental parameters: speed of light, Planck mass and cosmological constant. In this paper, we study the three-dimensional DKP oscillator for spin-0 and spin-1 in the framework of Snyder–de Sitter algebra in momentum space. By using the technique of vector spherical harmonics the energy spectrum and the corresponding eigenfunctions are obtained for the both cases.

We study the problem of the instability of inhomogeneous radiation universes in quadratic Lagrangian theories of gravity written as a system of evolution equations with constraints. We construct formal series expansions and show that the resulting solutions have a smaller number of arbitrary functions than that required in a general solution. These results continue to hold for more general polynomial extensions of general relativity.

We analyze the Abraham–Minkowski problem known from classical electrodynamics from two different perspectives. First, we follow a formal approach, implying use of manifolds with curved space sections in accordance with Fermat’s principle, emphasizing that the resulting covariant and contravariant components of the photon four-momentum are a property linked to the Minkowski theory only. There is thus no link to the Abraham theory in that context. Next we turn to the experimental side, giving a brief account of older and newer radiation pressure experiments that clearly show how the Minkowski photon momentum is preferable under optical conditions. Under low-frequency conditions, where experimental detection of the individual oscillations predicted by the Abraham term are possible, the picture is however quite different.

It is shown that first-order Darboux transformations for the two-dimensional massless Dirac equation with scalar potential and for the Schrödinger equation are the same up to a change of coordinates. As a consequence, we obtain a closed-form representation of iterated, higher-order Darboux transformations for our Dirac equation. We use the formalism to generate several new exactly-solvable Dirac systems through higher-order Darboux transformations.

The effect of the geometry (deviation from the flat space) on the quantum evolution of the momentum and position of a free particle is discussed. It is shown that beginning with a wave-packet of minimum uncertainty (a Gaussian wave), there is a usual increase in the product of the volume uncertainties in the momentum and position space, as seen in the quantum mechanics on a flat spaces. But there is also a contribution from geometry. The leading order of this contribution is calculated.

We consider an elastic medium with the distortion of a circular curve into a vertical spiral. Then, we investigate the topological effects of a charged screw dislocation on the attractive inverse-square potential that stems from the interaction of the induced electric dipole moment of a neutral quasiparticle with an electric field. We show that an analogue of the Aharonov–Bohm effect for bound states can be obtained. In addition, we consider a rotating reference frame. Thus, we analyze an Aharonov–Bohm-type effect for bound states and the arising of a coupling between torsion and the angular velocity.

We analyze nonrelativistic quantum effects on a neutral particle due to the presence of an attractive inverse-square potential that stems from the effects of the Lorentz symmetry violation determined by the parity-even sector of the tensor ${(K_F)}_{\mu \nu \alpha \beta }$. We show that bound states solutions to the Schrödinger equation can be achieved. We go further by considering a repulsive inverse-square potential yielded by Lorentz symmetry breaking effects, which are also determined the parity-even sector of the tensor ${(K_F)}_{\mu \nu \alpha \beta }$. Then, we analyze the influence of this repulsive inverse-square potential on a neutral particle confined to two cylindrical surfaces and a cylindrical surface.