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Wolfgang Lucha

Publications and source records attributed to Wolfgang Lucha.

188 records · Page 11Linked to original sources
arXiv1996

Relativistic Coulomb Problem: Analytic Upper Bounds on Energy Levels

The spinless relativistic Coulomb problem is the bound-state problem for the spinless Salpeter equation (a standard approximation to the Bethe--Salpeter formalism as well as the most simple generalization of the nonrelativistic Schrödinger formalism towards incorporation of relativistic effects) with the Coulomb interaction potential (the static limit of the exchange of some massless bosons, as present in unbroken gauge theories). The nonlocal nature of the Hamiltonian encountered here, however, renders extremely difficult to obtain rigorous analytic statements on the corresponding solutions. In view of this rather unsatisfactory state of affairs, we derive (sets of) analytic upper bounds on the involved energy eigenvalues.

hep-ph↗
arXiv1996

Effective Potential Models for Hadrons

The aim of these lectures is to give a self-contained introduction to nonrelativistic potential models, to their formulation as well as to their possible applications. At the price of some lack of (in a mathematical sense) rigorous derivations, we try to give a feeling and understanding for the simplest conceivable method to extract the explicit form of the forces acting between quarks from the interplay between experimental observations and theoretical considerations. According to this spirit, we demonstrate, in detail, how to obtain the underlying Hamiltonian and how to determine the Lorentz structure of the quark--(anti-)quark interaction potential from well-established experimental facts.

hep-ph↗
arXiv1994

All Around the Spinless Salpeter Equation

We review some important topics related to the semirelativistic description of bound states by the spinless Salpeter equation: the special case of the Coulomb interaction, numerical approximation methods, and a way to avoid the problematic square-root operator of the relativistic kinetic energy.

hep-ph↗
arXiv1994

A Particular Class of GUTs with Vanishing One-Loop Beta Functions

By explicit solution of the one-loop finiteness conditions for gauge and quartic scalar-boson self-interaction coupling constants, a particular class of grand unified theories with vanishing Yukawa couplings as well as vanishing one-loop renormalization-group beta functions is constructed.

hep-ph↗
arXiv1994

Effectively Semi-Relativistic Hamiltonians of Nonrelativistic Form

We construct effective Hamiltonians which despite their apparently nonrelativistic form incorporate relativistic effects by involving parameters which depend on the relevant momentum. For some potentials the corresponding energy eigenvalues may be determined analytically. Applied to two-particle bound states, it turns out that in this way a nonrelativistic treatment may indeed be able to simulate relativistic effects. Within the framework of hadron spectroscopy, this lucky circumstance may be an explanation for the sometimes extremely good predictions of nonrelativistic potential models even in relativistic regions.

hep-ph↗
arXiv1993

Complete Classes of GUTs with Vanishing One-Loop Beta Functions

By explicit solution of the one-loop finiteness conditions for all dimensionless coupling constants (i.~e., gauge coupling constant as well as Yukawa and quartic scalar-boson self-interaction coupling constants), two classes of grand unified theories characterized by renormalization-group beta functions which all vanish at least at the one-loop level are constructed and analyzed with respect to the (suspected) appearance of quadratic divergences, with the result that without exception in all of these models the masses of both vector and scalar bosons receive quadratically divergent one-loop contributions.

hep-ph↗