When Is A Semiclassical Approximation Self-consistent?

Details When Is A Semiclassical Approximation Self-consistent? When Is A Semiclassical Approximation Self-consistent?

1996-05-31

arxiv.org/abs/hep-ph/9605461v1

Phys.Rev. D54 (1996) 5280-5289

Physics

High Energy Physics

High Energy Physics - Phenomenology

15 pages in ReVTeX, 7 postscript figures

Scientific paper

10.1103/PhysRevD.54.5280

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 is also briefly discussed.

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