When is a semiclassical approximation self-consistent?

Suzhou Huang
Phys. Rev. D 54, 5280 – Published 15 October 1996
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Abstract

A general condition for the self-consistency of a semiclassical approximation to a given system is suggested. It is based on the eigenvalue distribution of the relevant Hessian evaluated at the streamline configurations (configurations that almost satisfy the classical equations of motion). The semiclassical approximation is consistent when there exists a gap that separates small and large eigenvalues and the spreading among the small eigenvalues is much smaller than the gap. The idea is illustrated in the case of the double-well potential problem in quantum mechanics. The feasibility of the present idea to test instanton models of QCD vacuum also is discussed briefly.

  • Received 31 May 1996

DOI:https://doi.org/10.1103/PhysRevD.54.5280

©1996 American Physical Society

Authors & Affiliations

Suzhou Huang*

  • Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

  • *Electronic address: shuang@mitlns.mit.edu

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Vol. 54, Iss. 8 — 15 October 1996

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