arXiv subjects
Publications and source records attributed to Lowell S. Brown.
The threshold behavior of a theory with two coupled scalar fields $χ$ and $ϕ$ is investigated. We compute the amplitude for two on-mass-shell $χ$-particles to produce an arbitrary number of $ϕ$-particles at rest in the tree approximation.
The solution of the classical field equation generates the sum of all tree graphs. We show that the classical equation reduces to an easily solved ordinary differential equation for certain multiparticle threshold amplitudes and compute these amplitudes.
The constraints imposed by asymptotic freedom and analyticity on the large-order behavior of perturbation theory for the electromagnetic current-current correlation function are examined. By suitably applying the renormalization group, the coefficients of the asymptotic expansion in the deep Euclidean region may be expressed explicitly in terms of the perturbative coefficients of the Minkowski space discontinuity (the $R$-ratio in $e^+ e^-$ scattering). This relation yields a ``generic'' prediction for the large-order behavior of the Euclidean perturbation series and suggests the presence of non-perturbative $1/q^2$ correction in the Euclidian correlation function. No such ``generic'' prediction can be made for the physically measurable $R$-ratio. A novel functional method is developed to obtain these results.