منابع مشابه
Divergent Perturbation Series
Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov’s method, according to which they are determined by instanton configurations of appropriate functional integrals. When the Lipatov asymptotics is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight int...
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We study eigenvalue problems for operators H0 + tiP', where the per turbat ion series is finite order by order bu t divergent for any ft. We prove that, under suitable conditions, the series nevertheless determines the level uniquely [and is not merely asymptotic] because some control of the remainder term, RN, uni form in N is present; in fact, for fi real, positive, and small, the perturbat i...
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We discuss certain special cases of algebraic approximants that are given as zeroes of so-called effective characteristic polynomials and their generalization to a multiseries setting. These approximants are useful for the convergence acceleration or summation of quantum mechanical perturbation series. Examples will be given and some properties will be discussed.
متن کاملOn Absolutely Divergent Series
We show that in the א2-stage countable support iteration of Mathias forcing over a model of CH the complete Boolean algebra generated by absolutely divergent series under eventual dominance is not isomorphic to the completion of P (ω)/fin. This complements Vojtáš’ result, that under cf(c) = p the two algebras are isomorphic [15].
متن کاملOperators and Divergent Series
We give a natural extension of the classical definition of Césaro convergence of a divergent sequence/function. This involves understanding the spectrum of eigenvalues and eigenvectors of a certain Césaro operator on a suitable space of functions or sequences. The essential idea is applicable in identical fashion to other summation methods such as Borel’s. As an example we show how to obtain th...
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ژورنال
عنوان ژورنال: Journal of Experimental and Theoretical Physics
سال: 2005
ISSN: 1063-7761,1090-6509
DOI: 10.1134/1.1995802