The Spinless Relativistic Hulth\'en Problem

The spinless Salpeter equation can be regarded as the eigenvalue equation of a Hamiltonian that involves the relativistic kinetic energy and therefore is, in general, a nonlocal operator. Accordingly, it is hard to find solutions of this bound-state equation by exclusively analytic means. Nevertheless, a lot of tools enables us to constrain the resulting bound-state spectra rigorously. We illustrate some of these techniques for the example of the Hulth\'en potential.Comment: 8 page

Semirelativistic Bound-State Equations: Trivial Considerations

Observing renewed interest in long-standing (semi-) relativistic descriptions of bound states, we would like to make a few comments on the eigenvalue problem posed by the spinless Salpeter equation and, illustrated by the examples of the nonsingular Woods-Saxon potential and the singular Hulth\'en potential, recall elementary tools that practitioners looking for analytic albeit approximate solutions might find useful in their quest.Comment: 5 pages, contributed to "QCD@Work 2014 - International Workshop on Quantum Chromodynamics: Theory and Experiment" (16 - 19 June 2014, Giovinazzo, Bari, Italy

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.Comment: 26 pages, HEPHY-PUB 593/9