International Journal of Modern Physics A

Feigin–Semikhatov conjecture, now established, states algebraic isomorphisms between the cosets of the subregular ${𝒲}$-algebras and the principal ${𝒲}$-superalgebras of type A by their full Heisenberg subalgebras. It can be seen as a variant of Feigin–Frenkel duality between the ${{𝒲}}_n$-algebras and also as a generalization of the connection between the ${𝒩}=2$ superconformal algebra and the affine algebra ${\widehat{𝔰𝔩}}_{2,k}$.

We review the recent developments on the correspondence of the subregular ${𝒲}$-algebras and the principal ${𝒲}$-superalgebras of type A at the level of algebras, modules and intertwining operators, including fusion rules.

The Dirac equation (DE) plays an essential role in the relativistic quantum systems, which is reduced to a form similar to Schrödinger equation when a certain potential’s type is selected as the Cornell potential. By choosing the generalized fractional derivative, the fractional Nikiforov–Uvarov method is applied as a good efficient tool. The energy eigenvalues and corresponding wave functions are obtained in the sense of fractional forms by solving DE analytically. The special case is obtained, which is compatible with the classical model. In addition, we applied the present results on the light mesons such as $D,Ds$ and $Bs$. Solving the fractional DE will open a new path to solve and improve results in the classical relativistic quantum systems.

This paper delves into the intriguing topic of the thermal stability of black holes (BHs) in the unique framework of bumblebee gravity. Our analysis primarily focuses on thermodynamic stability by examining the event horizon, black hole mass, thermal temperature and heat capacity. Additionally, we explore the intricacies of thermodynamic geometries such as Ruppeiner and Weinhold formulations and calculate their respective scalar curvatures in the context of bumblebee gravity. In our investigation, we also delve into the concept of phase transition through Gibbs free energy and the fascinating phenomenon of BH evaporation by energy emission. This research provides valuable insights into the complex thermodynamic properties of BHs and enhances our understanding of bumblebee gravity. We study the bosonic tunneling with spin-1 tunneling radiation in BHs. Initially, the generalized uncertainty principle (GUP) was used to correct the field equation (FE) for vector particles with spin-1 and demonstrate that the Hawking temperature rises with an improvement in the GUP and the radial component of the vector field but is unaffected by the radial components.

In the medium of relativistic heavy-ion collisions, dissociation of the quarkonium and its survival have been studied to understand the properties of Quark Gluon Plasma (QGP). The coupled rates of dissociation and recombination reactions in QGP are commonly solved with the Boltzmann transport equation in which the formation and dissociation reactions compete with each other. Since the dissociation of newly formed bound-states is not accounted in the Boltzmann equation, a framework of decoupled rates is developed to assess the combined effect of gluon-induced dissociation and recombination (though it is small for $\mathrm{\Upsilon }$) together with color screening on bottomonium production in heavy-ion collisions at center of mass energy $(\sqrt{s_{\mathrm{\text{NN}}}})=5.02$TeV. To calculate the recombination rates, we have employed an effective method of Bateman solution which ensures the correlated effect between the recombination and the dissociation of the newly combined bottomonium in the QGP medium. The modifications of bottomonium have been estimated in an inflating QGP with the constraints matching with the dynamics of $\mathrm{\text{Pb}}+\mathrm{\text{Pb}}$ collision events at LHC.

In this paper, we consider the Schrödinger equation with a generalized form of uncertainty principle and solve the problem up to a third-order correction to the arising equation. The particle in box and harmonic oscillator cases is considered in this formulation and various thermodynamic properties are reported including entropy, internal energy, chemical potential, specific heat, etc. Various consequences of the GUP are commented.

This research paper delves into the study of a nonrelativistic quantum system, considering the interplay of noninertial effects induced by a rotating frame and confinement by the Aharonov–Bohm (AB) flux field with potential in the backdrop of topological defects, specifically a screw dislocation. We first focus on the harmonic oscillator problem, incorporating an inverse-square repulsive potential. Notably, it becomes evident that the energy eigenvalues and wave functions are intricately influenced by multiple factors: the topological defect parameter $\beta$ (representing the screw dislocation), the presence of a rotating frame engaged in constant angular motion with speed $\mathrm{\Omega }$ and the external potential. Then we study the quantum behavior of nonrelativistic particles, engaging in interactions governed by an inverse-square potential, all while taking into account the effects of the rotating frame. In both scenarios, a significant observation is made: the quantum flux field’s existence brings about a shift in the energy spectrum. This phenomenon bears a resemblance to the electromagnetic Aharonov–Bohm effect.

The axial-vector form factor of the nucleons is studied at a finite temperature using the holographic soft-wall model with the thermal dilaton field. We use the bulk interaction action known from the zero temperature case and apply the profile functions of fields thermalized by the interaction with the thermal dilaton field. The dependence of the axial form factor on the square of the transferred momentum and the temperature is plotted for the ground and excited states of the nucleons.

The paper discusses the classical and quantum aspects of the dynamics of the flat Friedmann model of the universe in the late phase of its evolution, predominantly determined by the cosmological constant $\mathrm{\Lambda }$. In the classical part, the Lagrangian of the model is expressed in the Minkowski space and in the Euclidean space in the form of the Lagrangian of the inverted oscillator and the Lagrangian of the standard linear harmonic oscillator, respectively. The classic actions and Feynman propagators were determined as well as the dependence of the scale factor on time in the case of the Minkowski-type metric. Within the quantum part, the asymptotic form of the Wheeler–DeWitt wave function of the model in the considered expanding phase was first determined, and then the vacuum $p$-adic states with the specific conditions of their existence. In the generalized adelic approach, a vacuum adelic wave function is constructed, whose form implies minisuperspace discretization.

In this paper, we apply the scale-covariant formalism established by Canuto et al. in order to connect different eras of fluid-driven universes. This technique depends on a scale function that can be adjusted by imposing different physical restrictions. In a previous work, Chaplygin fluid was considered as cosmological source; now a van der Waals constituent shows to be a consistent source to establish a mapping between an old decelerated-to-accelerated universe, ruled by Einstein equations, and an early universe, controlled by a modified gravitational theory. A similar situation emerges when a generalized Chaplygin fluid is considered. These cosmological properties are shown to be a direct consequence of an appropriate use of the scale-covariant technique, and can be seen as extensions of the original barotropic and plain Chaplygin cases.