M. Kirchbach

Romanovski polynomials in selected physics problems

We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.

Trigonometric quark confinement potential of QCD traits

Abstract.We make the case that the Coulomb- plus linear quark confinement potential predicted by lattice QCD is an approximation to the exactly solvable trigonometric Rosen-Morse potential that has the property to interpolate between the Coulomb- and the infinite wells. We test the predictive power of this potential in the description of the nucleon (considered as a quark-diquark system) and provide analytic expressions for its mass spectrum and the proton electric form factor. We compare the results obtained in this fashion to data and find quite good agreement. We obtain an effective gluon propagator in closed form as the Fourier transform of the potential under investigation.

Spin-

Abstract.We employ the two independent Casimir operators of the Poincaré group, the squared four-momentum, p2, and the squared Pauli-Lubanski vector, W2, in the construction of a covariant mass m, and spin-

{\frac{{3}}{{2}}}

{\frac{{3}}{{2}}}

beyond the Rarita-Schwinger framework

projector in the four-vector spinor, ψμ. This projector provides the basis for the construction of an interacting Lagrangian that describes a causally propagating spin-

The Trigonometric Rosen‐Morse Potential as a Prime Candidate for an Effective QCD Potential

{\frac{{3}}{{2}}}

Rotational symmetry and degeneracy: a cotangent-perturbed rigid rotator of unperturbed level multiplicity

particle coupled to the electromagnetic field by a gyromagnetic ratio of

Proton Spin in Chiral Quark Models

g_{\ensuremath \frac{3}{2}}=2

Bosonic and fermionic Weinberg-Joos (j,0) ⊕ (0,j) states of arbitrary spins as Lorentz tensors or tensor-spinors and second-order theory

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Modelling duality between bound and resonant meson spectra by means of free quantum motions on the de Sitter space-time dS4

We make the point that the trigonometric Rosen‐Morse (tRM) potential is of possible interest to quark physics in so far as it captures the essentials of the QCD quark‐gluon dynamics. This potential (i) interpolates between a Coulomb‐like potential (associated with one‐gluon exchange) and the infinite wall potential (associated with asymptotic freedom), (ii) reproduces in the intermediary region the linear confinement potential (associated with multi‐gluon self‐interactions) as established by lattice QCD calculations of hadron properties. Moreover, its exact real solutions given here display a new class of real orthogonal polynomials and thereby interesting mathematical entities in their own.