Uniform WKB, multi-instantons, and resurgent trans-series
نویسندگان
چکیده
منابع مشابه
Uniform WKB, Multi-instantons, and Resurgent Trans-Series
We illustrate the physical significance and mathematical origin of resurgent trans-series expansions for energy eigenvalues in quantum mechanical problems with degenerate harmonic minima, by using the uniform WKB approach. We provide evidence that the perturbative expansion, combined with a global eigenvalue condition, contains all information needed to generate all orders of the non-perturbati...
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This is an introductory level review of recent applications of resurgent trans-series and PicardLefschetz theory to quantum mechanics and quantum field theory. Resurgence connects local perturbative data with global topological structure. In quantum mechanical systems, this program provides a constructive relation between different saddles. For example, in certain cases it has been shown that a...
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In this paper, based on lectures by the authors at the May 2015 workshop Resurgence, Physics and Numbers, at the Centro di Ricerca Matematica Ennio De Giorgio of the Scuola Normale Superiore in Pisa, we explain the origin of resurgent trans-series in the Mathieu equation spectral problem, using uniform WKB and all-orders (exact) WKB. Exact quantization conditions naturally arise, and their expa...
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We investigate some properties of the WKB series for arbitrary analytic potentials and then specifically for potentials x (N even), where more explicit formulae for the WKB terms are derived. Our main new results are: (i) We find the explicit functional form for the general WKB terms σ k, where one has only to solve a general recursion relation for the rational coefficients. (ii) We give a syst...
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We discuss various aspects of multi–instanton configurations in generic multi–cut matrix models. Explicit formulae are presented in the two–cut case and, in particular, we obtain general formulae for multi–instanton amplitudes in the one–cut matrix model case as a degeneration of the two–cut case. These formulae show that the instanton gas is ultra–dilute, due to the repulsion among the matrix ...
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ژورنال
عنوان ژورنال: Physical Review D
سال: 2014
ISSN: 1550-7998,1550-2368
DOI: 10.1103/physrevd.89.105009