Algorithmic boundedness-from-below conditions for generic scalar potentials

Potentials Unbounded Below ?

Continuous interpolates are described for classical dynamical systems defined by discrete time-steps. Functional conjugation methods play a central role in obtaining the interpolations. The interpolates correspond to particle motion in an underlying potential, V . Typically, V has no lower bound and can exhibit switchbacks wherein V changes form when turning points are encountered by the partic...

Quintessentially Flat Scalar Potentials

Both inflationary and quintessence cosmologies require scalar fields which roll very slowly over cosmological time scales, and so typically demand extremely flat potentials. Sufficiently flat potentials are notoriously difficult to obtain from realistic theories of microscopic physics, and this poses a naturalness problem for both types of cosmologies. We propose a brane-world-based microscopic...

Boundedness of Solutions for Duffing’s Equations with Semilinear Potentials

Scalar mesons above and below 1 GeV

We show that two nonets and a glueball provide a consistent description of data on scalar mesons below 1.7 GeV. Above 1 GeV the states form a conventional qq̄ nonet mixed with the glueball of lattice QCD. Below 1 GeV the states also form a nonet, as implied by the attractive forces of QCD, but of more complicated nature. Near the center they are (qq)3̄(q̄q̄)3 in S-wave, with some qq̄ in P-wave, but ...

Gravitational Stabilization of Scalar Potentials *

Using the formalism of Boucher we derive the conditions under which gravity can stabilize otherwise metastable or unstable scalar field configurations. For the case of a double-welled potential we rederive the stability criteria first obtained by Coleman and DeLuccia. Our derivation does not require the assumption of 0(4) symmetry or the thin-walled approximation used in their work. We also giv...