80 research outputs found
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
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
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
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