MultipleScale Analysis of the Quantum Anharmonic Oscillator
Abstract
Conventional weakcoupling perturbation theory suffers from problems that arise from the resonant coupling of successive orders in the perturbation series. Multiplescale perturbation theory avoids such problems by implicitly performing an infinite reordering and resummation of the conventional perturbation series. Multiplescale analysis provides a good description of the classical anharmonic oscillator. Here, it is extended to study the Heisenberg operator equations of motion for the quantum anharmonic oscillator. The analysis yields a system of nonlinear operator differential equations, which is solved exactly. The solution provides an operator mass renormalization of the theory.
 Publication:

Physical Review Letters
 Pub Date:
 November 1996
 DOI:
 10.1103/PhysRevLett.77.4114
 arXiv:
 arXiv:hepth/9605181
 Bibcode:
 1996PhRvL..77.4114B
 Keywords:

 High Energy Physics  Theory;
 High Energy Physics  Phenomenology;
 Quantum Physics
 EPrint:
 12 pages, Revtex, no figures, available through anonymous ftp from ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at http://euclid.tp.ph.ic.ac.uk/Papers/papers_956_.html