Supersymmetry and Solution of Dirac Equation with Vector and Scalar Potentials

The Dirac equations with vector and scalar potentials of the Coulomb types in two and three dimensions are solved using the supersymmetric quantum mechanics method. For the system of such potentials, the analytical expressions of the matrix dements for both position and momentum operators are obtained.

Chaplygin gas inspired warm inflation and swampland conjectures through various scalar potentials

In this paper,we analyze inflationary parameters and swampland conjectures in the presence of a scalar field and Chaplygin models.We examine inflationary parameters,such as slow-roll parameters,scalar and tensor power spectra,spectral index,and tensor-to-scalar ratio,in the presence of a scalar field and Chaplygin gas models.We also discuss recently proposed swampland conjectures.We assume that the inflationary expansion is driven by a standard scalar field with a decay ratioΓthat has a generic power-law dependence on the scalar field 0 and that the temperature of the thermal bath T is given byΓ(φ,T)=C_(φ)T^(a)/φ^(a-1),where C_(φ)is a dimensionless parameter and a is the inflation decay rate.In a scenario where our model operates within a robust dissipative environment(R>>1),we analyze both fundamental and perturbative dynamics to extract key inflationary parameters.These include the scalar power spectrum P_(R),dissipative ratio R,scalar spectral index n_(s),tensor-to-scalar ratio r,running of the scalar spectral index dn_s/dlnk,and generalized ratio of the swampland de-Sitter conjecture T'V/V'T for three different potentials.

Re-study of the contribution of scalar potential and spectra of c, b and b(c) families

We indicated in our previous work that for QED the role of the scalar potential which appears at the loop level is much smaller than that of the vector potential and is in fact negligible. But the situation is different for QCD, one reason is that the loop effects are more significant because as is much larger than a, and second the non-perturbative QCD effects may induce a sizable scalar potential. In this work, we study phenomenologically the contribution of the scalar potential to the spectra of charmonia, bottomonia and bC（bc） families. Taking into account both vector and scalar potentials, by fitting the well measured charmonia and bottomonia spectra, we re-fix the relevant parameters and test them by calculating other states of not only the eharmonia and bottomonia families, but also the bc family. We also consider the Lamb shift of the spectra.

Phenomenological study on the significance of the scalar potential and Lamb shift

We indicated in our previous work that for QED the contributions of the scalar potential, which appears at the loop level, is much smaller than that of the vector potential, and in fact negligible. But the situation may be different for QCD, the reason being that the loop effects are more significant because α s is much larger than α, and secondly the non-perturbative QCD effects may induce the scalar potential. In this work, we phenomenologically study the contribution of the scalar potential to the spectra of charmonia. Taking into account both vector and scalar potentials, by fitting the well measured charmonia spectra, we re-fix the relevant parameters and test them by calculating other states of the charmonia family. We also consider the role of the Lamb shift and present the numerical results with and without involving the Lamb shift.

Semi-Relativistic Two-Body States of Spinless Particles with a Scalar-Type Interaction Potential

A semi-relativistic quantum approximation for mutual scalar interaction potentials is outlined and discussed.Equations are consistent with two-body Dirac equations for bound states of zero total angular momentum. Two-body effects near the non-relativistic limit for a linear scalar potential is studied in some detail.

Novel Rotating Hairy Black Hole in (2 + 1) Dimensions

We present some novel rotating hairy black hole metric in （2 ＋ 1） dimensions, which is an exact solution to the field equations of the Einstein-scalar-AdS theory with a non-minimal coupling. The scalar potential is determined by the metric ansatz and consistency of the field equations and cannot be prescribed arbitrarily. In the simplified, critical ease, the scalar potential contains two independent constant parameters, which are respectively related to the mass and angular momentum of the black hole in a particular way. As long as the angular momentum does not vanish, the metric can have zero, one or two horizons. The case with no horizon is physically uninteresting because of the curvature singularity lying at the origin. We identify the necessary conditions for at least one horizon to be present in the solution, which imposes some bound on the mass-angular momentum ratio. For some particular choice of pararneters our solution degenerates into some previously known black hole solutions.

Lepton and quark mixing patterns with generalized CP transformations

In this study,we modify a scenario,originally proposed by Grimus and Lavoura,in order to obtain maximal values for the atmospheric mixing angle and CP,violating the Dirac phase of the lepton sector.To achieve this,we employ CP and some discrete symmetries in a type Ⅱ seesaw model.To make predictions about the neutrino mass ordering and smallness of the reactor angle,we establish some conditions on the elements of the neutrino mass matrix of our model.Finally,we study the quark masses and mixing pattern within the framework of our model.

The Quasi-Exactly Solvable Problems in Relativistic Quantum Mechanics

We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein–Gordon and Dirac equations with equal vector and scalar potentials, and try to find the general form of the quasi-exactly solvable potential. After obtaining the general form of the potential, we present several examples to give the specific forms. In the examples, we show for special parameters the harmonic potential plus Coulomb potential, Killingbeck potential and a quartic potential plus Cornell potential are quasi-exactly solvable potentials.