Asymptotically Universal Crossover in Perturbation Theory with a Field Cutoff

Abstract

We discuss the crossover between the small and large field cutoff (denoted x_{max}) limits of the perturbative coefficients for a simple integral and the anharmonic oscillator. We show that in the limit where the order k of the perturbative coefficient a_k(x_{max}) becomes large and for x_{max} in the crossover region, a_k(x_{max}) is proportional to the integral from -infinity to x_{max} of e^{-A(x-x_0(k))^2}dx. The constant A and the function x_0(k) are determined empirically and compared with exact (for the integral) and approximate (for the anharmonic oscillator) calculations. We discuss how this approach could be relevant for the question of interpolation between renormalization group fixed points.

15 pages, 11 figs., improved and expanded version of hep-th/0503047

References in corpus (4)

• New Optimization Methods for Converging Perturbative Series with a Field Cutoff
• An example of optimal field cut in lattice gauge perturbation theory
• A Tractable Example of Perturbation Theory with a Field Cutoff: the Anharmonic Oscillator
• Asymptotic Freedom of Elastic Strings and Barriers

Cited by in corpus (1)

• Nonlinear Aspects of the Renormalization Group Flows of Dyson's Hierarchical Model