International Journal of Geometric Methods in Modern Physics

We can find all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of variables in the Hamilton–Jacobi equation. Separation is carried out using the complete sets of mutually-commuting integrals of motion of type (2.1), whereby in a privileged coordinate system the Hamilton–Jacobi equation turns into a parabolic type equation.

In this paper, we investigate the effects of Type IV singularity through $f(T)$ gravity description of inflationary Universe, where $T$ denotes the torsion scalar. With the Friedmann equations of the theory, we reconstruct a $f(T)$ model according to a given Hubble rate susceptible to describe the inflationary era near the Type IV singularity. One obtains an interesting well-known $f(T)$ model but with additional constant parameter $c_0$ staying as the Type IV singularity contribution. Moreover, we calculate the Hubble flow parameters in order to determine the dynamical evolution of the cosmological system. The results show that some of the Hubble flow parameters are small near the Type IV singularity and become singular at Type IV singularity, indicating that a dynamical instability of the cosmological system occurs at that point. This means that the dynamical cosmological evolution up to that point ceases to be the final attractor since the system is abruptly interrupted. Furthermore, by considering the $f(T)$ trace anomaly equation, the previous result on the Type IV singularity is consolidated by the conditional instability coming from the de Sitter inflationary description of the reconstructed $f(T)$ model. The model leads to instability strongly governed by the Type IV singularity parameter $c_0$ is viewed as the graceful exit from inflation. Our theoretical $f(T)$ description based on slow-roll parameters not only confirms some observational data on spectral index and the scalar-to-tensor ratio from Planck data and BICEP$2$/Keck-Array data, but also shows the property of $f(T)$ gravity in describing the early and late-time evolution of our Universe.

In this paper, Jacobi stability of a segmented disc dynamo system is geometrically investigated from viewpoint of Kosambi–Cartan–Chern (KCC) theory in Finsler geometry. First, the geometric objects associated to the reformulated system are explicitly obtained. Second, the Jacobi stability of equilibria and a periodic orbit are discussed in the light of deviation curvature tensor. It is shown that all the equilibria are always Jacobi unstable for any parameters, a Lyapunov stable periodic orbit falls into both Jacobi stable regions and Jacobi unstable regions. The considered system is not robust to small perturbations of the equilibria, and some fragments of the periodic orbit are included in fragile region, indicating that the system is extremely sensitive to internal parameters and environment. Finally, the dynamics of the deviation vector and its curvature near all the equilibria are presented to interpret the onset of chaos in the dynamo system. In a physical sense, magnetic fluxes and angular velocity can show irregular oscillations under some certain cases, these oscillations may reveal the irregularity of magnetic field’s evolution and reversals.

In this work, we explore the structure of Clifford algebras and the representations of the algebraic spinors in quantum information theory. Initially, we present a general formulation through elements of minimal left ideals in tensor products of Clifford algebras. Posteriorly, we perform some applications in quantum computation: qubits, entangled states, quantum gates, representations of the braid group, quantum teleportation, Majorana operators and supersymmetry. Finally, we discuss advantages compared to standard Hilbert space formulation.

We test whether static charged dilaton black holes in $(2+1)$ dimensions can be turned into naked singularities by sending in test particles from infinity. We derive that overcharging is possible and generic for both extremal and nearly extremal black holes. Our analysis also implies that nearly extremal charged dilaton black holes can be continuously driven to extremality and beyond, unlike nearly extremal Ban̆ados–Teitelboim–Zanelli, Kerr and Reissner–Nordström black holes which are overspun or overcharged by a discrete jump. Thus, the weak form of the cosmic censorship conjecture and the third law of black hole thermodynamics are both violated in the interaction of charged dilaton black holes in $(2+1)$ dimensions, with test particles. We also derive that there exist no points, where the heat capacity vanishes or diverges in the transition from black holes to naked singularities. The phase transitions that could potentially prevent the formation of naked singularities do not occur.

In this paper, first, we will try to introduce the gravitational domain wall as a physical system. In the second step, we also introduce the Hun differential equation as a mathematical tools. We factorize the known Heun’s equation as form of operators $P^{+}$, $P^{-}$ and $P^0$. Then we compare the differential equation of gravitational domain wall with corresponding Hun equation. In that case the above-mentioned operators can be obtained for the gravitational system by the comparing process. Finally, we employ such operators and achieve the corresponding symmetry algebra with the usual commutation relation of operators to each other. Here, by having such operators, we investigate the stability of system.

The main aim of this work is to build unitary phase operators and the corresponding temporally stable phase states for the $su(n+1)$ Lie algebra. We first introduce an irreducible finite-dimensional Hilbertian representation of the $su(n+1)$ Lie algebra which is suitable for our purpose. The phase operators obtained from the $su(n+1)$ generators are defined and the phase states are derived as eigenstates associated to these unitary phase operators. The special cases of $su(3)$ and $su(2)$ Lie algebras are also explicitly investigated.

The aim of this paper is to establish a generalization of the Born geometry to $\rho$-commutative algebras. We introduce the notion of Born $\rho$-commutative algebras and study the existence and uniqueness of a torsion connection which preserves the Born structure. Also, an analogue of the fundamental theorem of Riemannian geometry will be proved for these algebras.

In this paper, we establish two kinds of Kastler-Kalau-Walze type theorems for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection on six-dimensional manifolds with boundary.

The aim of this paper is to investigate Killing magnetic trajectories of varying electrically charged particles in a three-dimensional warped product $I{\times }_f{𝔼}^2$ with positive warping function $f$, where $I$ is an open interval in $ℝ$ equipped with an induced semi-Euclidean metric on $ℝ$. First, Killing vector fields on $I{\times }_f{𝔼}^2$ are characterized and it is observed that lifts to $I{\times }_f{𝔼}^2$ of Killing vector fields tangent to ${𝔼}^2$ are also Killing on $I{\times }_f{𝔼}^2$. Now, any Killing vector field on $I{\times }_f{𝔼}^2$ corresponds to a Killing magnetic field on $I{\times }_f{𝔼}^2$. Magnetic trajectories (also known as magnetic curves) of charged particles which move under the influence of Lorentz force generated by Killing magnetic fields on $I{\times }_f{𝔼}^2$ are obtained in both Riemannian and Lorentzian cases. Moreover, some examples are exhibited with pictures determining Killing magnetic trajectories in hyperbolic $3$-space ${ℍ}^3(-1)$ modeled by the Riemannian warped product $𝔼{\times }_{exp(z)}{𝔼}^2$. Furthermore, some examples of spacelike, timelike and lightlike Killing magnetic trajectories are given with their possible graphs in the Lorentzian warped product ${𝔼}_1^1{\times }_{exp(-z)}{𝔼}^2$.

Stability, dark energy (DE) parameterization and swampland aspects for the Bianchi form-$V{I}_h$ universe have been formulated in an extended gravity hypothesis. Here, we have assumed a minimally coupled geometry field with a rescaled function of $f(R,T)$ replaced in the geometric action by the Ricci scalar $R$. Exact solutions are sought under certain basic conditions for the related field equations. For the following theoretically valid premises, the field equations in this scalar-tensor theory have been solved. It is observed under appropriate conditions that our model shows a decelerating to accelerating phase transition property. Results are observed to be coherent with recent observations. Here, our models predict that the universe’s rate of expansion will increase with the passage of time. The physical and geometric aspects of the models are discussed in detail. In this model, we also analyze the parameterizations of DE by fitting the EoS parameter $\omega (z)$ with redshift. The results obtained would be useful in clarifying the relationship between DE parameters. In this, we also explore the correspondence of quintessence DE with swampland criteria. The swampland criteria have been also shown the nature of the scalar field and the potential of the scalar field.

Our aim is to discuss spherically symmetric static wormholes with the Lorentzian signature in the Einsteinian cubic gravity for two different models of pressure sources. First, we calculate the modified fields equations for the Einsteinian cubic gravity for the wormhole geometry under the anisotropic matter. Then we investigate the shape-function for two different models, which can be taken as a part of the general relation, namely, $p_t=\sum n_i{p}_r^i$. We further study the energy conditions for both the models in the background of the Einsteinian cubic gravity. We show that our obtained shape-functions satisfy all the necessary conditions for the existence of wormhole solutions in the Einsteinian cubic gravity for some particular values of the different involved parameters. We also discuss the behavior of the energy conditions especially the null and the weak energy conditions for the wormhole models in the Einsteinian cubic gravity.

The Noether–Bessel-Hagen theorem can be considered a natural extension of Noether Theorem to search for symmetries. Here, we develop the approach for dynamical systems introducing the basic foundations of the method. Specifically, we establish the Noether–Bessel-Hagen analysis of mechanical systems where external forces are present. In the second part of the paper, the approach is adopted to select symmetries for a given systems. In particular, we focus on the case of harmonic oscillator as a testbed for the theory, and on a cosmological system derived from scalar–tensor gravity with unknown scalar-field potential $V(\phi )$. We show that the shape of potential is selected by the presence of symmetries. The approach results particularly useful as soon as the Lagrangian of a given system is not immediately identifiable or it is not a Lagrangian system.

This paper is devoted to formulate a new model of quintessence anisotropic compact stars in the modified $f(R,G)$ gravity. Dynamical equations in modified theory consisting of anisotropic fluid along with quintessence field have been evaluated by adopting analytical solution of Krori–Barua. In order to determine the unknown constraints of Krori–Barua metric observational data of different stars, $4U1820$-$30$, $HerX-1$, $SAXJ1808$-$3658$ has been taken into account. To solve the dynamical equations Starobinsky-like model, $f(R,G)=R+\lambda R^2+G$ of modified gravity has been used. The outcome of the results depicts that all the examined celestial bodies are free from central singularity and are physically stable. Different physical parameters, such as energy density, energy conditions, evolution of quintessence and compactness factor, have been reviewed in detail.

The tomographic representation of quantum fields within the deformation quantization formalism is constructed. By employing the Wigner functional we obtain the symplectic tomogram associated with quantum fields. In addition, the tomographic version of the Wigner map allows us to compute the symbols corresponding to field operators. Finally, the functional integral representation of the tomographic star product is determined. Some possible applications of the formalism to loop quantum cosmology and loop quantum gravity are briefly discussed.

The aim of this paper is to classify non-conformally flat static plane symmetric (SPS) perfect fluid solutions via proper conformal vector fields (CVFs) in $f(T)$ gravity. For this purpose, first we explore some SPS perfect fluid solutions of the Einstein field equations (EFEs) in $f(T)$ gravity. Second, we utilize these solutions to find proper CVFs. In this study, we found 16 cases. A detailed study of each case reveals that in three of these cases, the space-times admit proper CVFs whereas in the rest of the cases, either the space-times become conformally flat or they admit proper homothetic vector fields (HVFs) or Killing vector fields (KVFs). The dimension of CVFs for non-conformally flat space-times in $f(T)$ gravity is four, five or six.