Secular Terms in Dyson Series to All-Orders of Perturbation
arXiv:1712.00943 · doi:10.1093/ptep/pty079
Abstract
In classical and quantum systems, perturbation of an evolution equation is often invalidated by secular terms which diverge at late times. The diverging behavior of evolution can be remedied by various techniques of resumma- tion such as renormalization group or multi-scale analysis. In this paper, we prove that, in a generic quantum mechanical system, secular terms can be systematically removed to all orders in the Dyson series by the method of improved (renormalized) perturbation. A recurrence relation to provide an explicit method to remove the secular terms is given. As a byproduct, we give a simple method to obtain energy eigenvalues and decay rates to all orders of perturbation.
arXiv comment28 pages
References in corpus (8)
- The Renormalization Group and Singular Perturbations: Multiple-Scales, Boundary Layers and Reductive Perturbation Theory
- Introduction to Nonequilibrium Quantum Field Theory
- Super-Hubble de Sitter Fluctuations and the Dynamical RG
- A Geometrical Formulation of the Renormalization Group Method for Global Analysis
- Dynamical renormalization group approach to relaxation in quantum field theory
- Multiple-Scale Analysis of the Quantum Anharmonic Oscillator
- Multiple-Scale Analysis of Quantum Systems
- Time Dependent Couplings as Observables in de Sitter Space