Asymptotics and Borel Summability
By O. Costin. 2008
235 citations recorded by the source corpus.
Subfields: Applied Mathematics, Mathematical Physics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/2256762a0d26f0807daf955dea40758cdb58d457
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Mathematical Physics
In Numerical Analysis
Citations in the corpus
- An introduction to resurgence, trans-series and alien calculus (2014, background): “es a simple power series expansion is not good enough and one has to use a trans-series expansion. We will not discuss in details the hyperasymptotic expansion for ODEs, so we refer to the literature [41] for a more detailed exposition of this interesting subject. It is nonetheless instructive to an”
- Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles (2014, background): “1.1 Problems with perturbation theory and the semi-classical expansion 1 1.2 Resurgence theory 2 1.3 Beyond the topological classification of NP saddles 3 1.4 Application: Principal Chiral Model 5 1.5 Outline 6”
- Chern-Simons theory, analytic continuation and arithmetic (2007, unknown): “The transseries conclusion of the proposition below (without any claims on the mixed Gevrey type) follows from the resurgence hypothesis on G(z) alone, and are studied systematically in the upcoming book of Costin [Co2], as well as in [Co3].”
- Resurgence and trans-series in Quantum Field Theory: the $\mathbb{C}{{\mathbb{P}}^{N-1 }}$ model (2012, methodology): “The instanton-anti-instanton molecule amplitude is [II]θ=0± = Re [II] + i Im [II]θ=0± (6.9) As shown explicitly in quantum mechanics, these two classes of ambiguities, between the the re-summed perturbation theory around the perturbative vacuum and the non-perturbative amplitudes associated with neu”
- Transseries for beginners (2008, background): “Descriptions of the system of transseries are found, for example, in [1, 10, 15, 33].”
- Uniform WKB, Multi-instantons, and Resurgent Trans-Series (2014, background): “There is some body of work concerning trans-series expansions for wave-functions, special functions and solutions to Schrödinger-like equations, as well as nonlinear differential equations [16, 17, 28, 29].”
- The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects (2012, methodology): “For a quantum field theorist, perhaps the most interesting aspect of this framework is BorelÉcalle (BE) summability, which provides tools for dealing with non-Borel summable series [36].”
- A primer on resurgent transseries and their asymptotics (2018, unknown): “, [55, 56, 69–71, 50, 91, 212, 162].”