Aaron K. Grant

Classical orbits in power‐law potentials

The motion of bodies in power‐law potentials of the form V(r)=λrα has been of interest ever since the time of Newton and Hooke. Aspects of the relation between powers α and ᾱ, where (α+2)(ᾱ+2)=4, are derived for classical motion and the relation to the quantum‐mechanical problem is given. An improvement on a previous expression for the WKB quantization condition for nonzero orbital angular momenta is obtained. Relations with previous treatments, such as those of Newton, Bertrand, Bohlin, Faure, and Arnold, are noted, and a brief survey of the literature on the problem over more than three centuries is given.

Supersymmetric quantum mechanics and the Korteweg–de Vries hierarchy

The connection between supersymmetric quantum mechanics and the Korteweg–de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the τ function by means of supersymmetric quantum mechanics is discussed.

Choice of dispersion relation to calculate the QCD correction to {Gamma}({ital H}{r_arrow}{ital l}{sup +}{ital l}{sup {minus}})

We use the Operator Product Expansion (OPE) of quark vacuum polarization functions to show that the dispersion relation of Kniehl and Sirlin will yield the correct result to all orders in

Remarks on the dispersion relations used to calculate Delta rho.

\alpha_s

Implications of a heavy top quark for the two Higgs doublet model

when applied to the QCD correction to the leptonic decay width of the Higgs boson.

Updated description of quarkonium by power-law potentials.

We use the operator product expansion to show that nonperturbative QCD corrections to {Delta}{rho} can be calculated using unsubtracted dispersion relations for either the transverse or the longitudinal vacuum polarization functions. Recent calculations of the nonperturbative contribution to {Delta}{rho} based on a nonrelativistic calculation of corrections to the {ital t{bar t}} threshold are inconsistent with this result.