Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
نویسندگان
چکیده
منابع مشابه
Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
Resurgence theory implies that the non-perturbative (NP) and perturbative (P) data in a QFT are quantitatively related, and that detailed information about nonperturbative saddle point field configurations of path integrals can be extracted from perturbation theory. Traditionally, only stable NP saddle points are considered in QFT, and homotopy group considerations are used to classify them. Ho...
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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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Different perturbation theory treatments of the Ginzburg–Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical exponents consistent with the known exact solutions in two dimensions. The new values of critical exponents are discussed and compared to the results of numerica...
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To compute the maximum likelihood estimates the log-likelihood function L is maximized with respect to all model parameters. To check that the maximization has been achieved two things have to be satisfied: 1. The vector of first derivatives with respect to the model parameter L′ should be equal to 0. 2. The negative of the matrix of the second derivatives −L′′ should be a positive definite mat...
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We show that the semi-classical analysis of generic Euclidean path integrals necessarily requires complexification of the action and measure, and consideration of complex saddle solutions. We demonstrate that complex saddle points have a natural interpretation in terms of the Picard-Lefschetz theory. Motivated in part by the semi-classical expansion of QCD with adjoint matter on R × S, we study...
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ژورنال
عنوان ژورنال: Journal of High Energy Physics
سال: 2015
ISSN: 1029-8479
DOI: 10.1007/jhep10(2015)056