Quantum Dynamics of the Slow Rollover Transition in the Linear Delta Expansion

We apply the linear delta expansion to the quantum mechanical version of the slow rollover transition which is an important feature of inflationary models of the early universe. The method, which goes beyond the Gaussian approximation, gives results which stay close to the exact solution for longer than previous methods. It provides a promising basis for extension to a full field theoretic treatment.Comment: 12 pages, including 4 figure

Optimization of R(e+e-) and "Freezing" of the QCD Couplant at Low Energies

The new result for the third-order QCD corrections to R_{e^+e^-}, unlike the old, incorrect result, is nicely compatible with the principle-of-minimal-sensitivity optimization method. Moreover, it leads to infrared fixed-point behaviour: the optimized couplant, alpha_s/pi, for R(e+e-) does not diverge at low energies, but "freezes" to a value 0.26 below about 300 MeV. This provides some direct theoretical evidence, purely from perturbation theory, for the "freezing" of the couplant -- an idea that has long been a popular and successful phenomenological hypothesis. We use the "smearing" method of Poggio, Quinn, and Weinberg to compare the resulting theoretical prediction for R(e+e-) with experimental data down to the lowest energies, and find excellent agreement.Comment: 27 pages, LaTeX, 8 uuencoded figures, DE-FG05-92ER40717-