Uses of Envelopes for Global and Asymptotic Analysis; geometrical meaning of renormalization group equation

Details Uses of Envelopes for Global and Asymptotic Analysis; geometrical meaning of renormalization group equation Uses of Envelopes for Global and Asymptotic Analysis; geometrical meaning of renormalization group equation

1997-09-20

arxiv.org/abs/patt-sol/9709003v1

Physics

High Energy Physics

High Energy Physics - Theory

Talk presented at RIMS (Kyoto) Workshop on Geometrical Methods for Asymptotic Analysis 1997.5.20 -- 5.23. LaTex, 15 pages

Scientific paper

We give a comprehensive review of the renormalization group method for global and asymptotic analysis, putting an emphasis on the relevance to the classical theory of envelopes and the existence of invariant manifolds of the dynamics under consideration. We clarify that an essential point of the method is to convert the problem from solving differential equations to obtaining suitable initial (or boundary) conditions. We mention that the notion of envelopes is also useful for constructing global and asymptotic behavior of wave functions of quantum systems such as the ones with the quartic potential or double-well potential.

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