Regular Series

Vol. 43 (2012), No. 9, pp. 1791 – 1911

Supersymmetry Approach and Shape Invariance for Pseudo-harmonic Potential


In this paper, we have considered supersymmetry algebra for pseudo-harmonic potentials with an arbitrary radial angular momentum. We have obtained the bound states and wave functions by the associated Laguerre differential equation. We have factorized Schrödinger equation for pseudo-harmonic potential in terms of first order differential equations, where these operators can make corresponding partner Hamiltonian. Therefore, by introducing superpotential, we obtained the pseudo-harmonic potential which gives rise to existence of shape invariance condition. In that case, we have calculated supercharge algebras. Finally, we have computed energy eigenvalues for several diatomic molecules.

Bose–Einstein Condensation in Arbitrary Dimensions


The density of bosonic states is calculated for spinless free massive bosons in generalised d dimensions. The number of bosons is calculated in the lowest energy state. The Bose–Einstein condensation was found in generalised \(d\) dimensions (at and above \(d = 3\)) and the condensation temperature is calculated. It is observed to drop abruptly above three dimensions and decreases monotonically as the dimensionalities of the system increase. The rate of fall of the condensation temperature decreases as the dimensionality increases. Interestingly, in the limit \(d \to \,\infty \), the condensation temperature is observed to approach a nonzero finite value.

A Note on Angular Momentum Commutators in Light-cone Formulation of Open Bosonic String Theory


We recalculate, in a systematic and pedagogical way, one of the most important results of Bosonic open string theory in the light-cone formulation, namely the \([J^{-i},J^{-j}]\) commutators, which together with Lorentz covariance, famously yield the critical dimension \(D=26\) and the normal order constant \(a=1\). We use traditional transverse oscillator mode expansions (avoiding the elegant but more advanced language of operator product expansions). We streamline the proof by introducing a novel bookkeeping/regularization parameter \(\kappa \) to avoid splitting into creation and annihilation parts, and to avoid sandwiching between bras and kets.

Energy Loss and Jet Quenching Parameter in a Thermal Non-relativistic Non-commutative Yang–Mills Plasma


In this paper, we consider the problem of a moving heavy quark through a hot non-relativistic, non-commutative Yang–Mills plasma. We discuss the configuration of the static and dynamic quarks, and also obtain the quasi-normal modes. The main goal of this study is calculating the jet-quenching parameter for the non-relativistic, non-commutative theory and comparing it with drag forces which were recently obtained in an independent work, K.L. Panigrahi, S. Roy, J. High Energy Phys. 04, 003 (2010).

Perturbative Formulae for Relativistic Interactions of Effective Particles


The concept of effective particles as degrees of freedom in a relativistic quantum field theory is defined using a non-perturbative renormalization group procedure for Hamiltonians. However, every candidate for a basic physical theory appears to require an initial perturbative search for the set of interaction terms that may provide a basis with which the full effective theory Hamiltonian could be constructed in a series of successive approximations. This article describes the required perturbative expansion and illustrates it with a set of general 4th-order formulae.

Higgs-mass Predictions


A compilation of Higgs-mass predictions is proposed.

Remark on In-medium Masses of Hadrons with One Heavy Quark


In this short note we derive a formula which describes the dependence of the mass of a hadron which contains a single heavy quark at the temperature of the heat bath. It takes a simple scaling form with the exponent which is different than in the case of the light hadrons. The derivation is based on dimensional arguments within the framework of the bag model paradigm. The simple realization of this scenario is presented for the MIT bag model. The mass splitting between pseudoscalar and vector mesons (\(D, D^\ast \) or \(B, B^\ast \)) as a function of temperature is presented.

Two-component Perfect Fluid in the FRW Universe


We consider the cosmological model which allows to describe on equal footing the evolution of matter in the universe in the time interval from the inflation till the domination of dark energy. The matter has a form of a two-component perfect fluid imitated by homogeneous scalar fields between which there is energy exchange. Dark energy is represented by the cosmological constant, which is supposed invariable during the whole evolution of the universe. The matter changes its Equation of State with time, so that the era of radiation domination in the early universe smoothly passes into the era of a pressureless gas, which then passes into the late-time epoch, when the matter is represented by a gas of low-velocity cosmic strings. The inflationary phase is described as an analytic continuation of the energy density in the very early universe into the region of small negative values of the parameter which characterizes typical time of energy transfer from one matter component to another. The Hubble expansion rate, energy density of the matter, energy density parameter, and deceleration parameter as functions of time are found.

ERRATUM for Acta Phys. Pol. B 43, 1509 (2012)

Pulse Shape Discrimination in Liquid Argon and Its Implications for Dark Matter Searches Using Depleted Argon


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