The University of Southampton
University of Southampton Institutional Repository

Nonperturbative ambiguities and the reality of resurgent transseries

Nonperturbative ambiguities and the reality of resurgent transseries
Nonperturbative ambiguities and the reality of resurgent transseries
In a wide range of quantum theoretical settings -- from quantum mechanics to quantum field theory, from gauge theory to string theory -- singularities in the complex Borel plane, usually associated to instantons or renormalons, render perturbation theory ill-defined as they give rise to nonperturbative ambiguities. These ambiguities are associated to choices of an integration contour in the resummation of perturbation theory, along (singular) Stokes directions in the complex Borel plane (rendering perturbative expansions non-Borel summable along any Stokes line). More recently, it has been shown that the proper framework to address these issues is that of resurgent analysis and transseries. In this context, the cancelation of all nonperturbative ambiguities is shown to be a consequence of choosing the transseries median resummation as the appropriate family of unambiguous real solutions along the coupling-constant real axis. While the median resummation is easily implemented for one-parameter transseries, once one considers more general multi-parameter transseries the procedure becomes highly dependent upon properly understanding Stokes transitions in the complex Borel plane. In particular, all Stokes coefficients must now be known in order to explicitly implement multi-parameter median resummations. In the cases where quantum-theoretical physical observables are described by resurgent functions and transseries, the methods described herein show how one may cancel nonperturbative ambiguities, and define these observables nonperturbatively starting out from perturbation theory. Along the way, structural results concerning resurgent transseries are also obtained.
hep-th, math-ph, math.CA, math.MP, quant-ph
0010-3616
183-245
Aniceto, Inês
0061ca0c-1ad8-4510-9b12-008e5c27a7ea
Schiappa, Ricardo
7b7a5b7d-7ecc-454e-ba14-51c2adc24c5f
Aniceto, Inês
0061ca0c-1ad8-4510-9b12-008e5c27a7ea
Schiappa, Ricardo
7b7a5b7d-7ecc-454e-ba14-51c2adc24c5f

Aniceto, Inês and Schiappa, Ricardo (2015) Nonperturbative ambiguities and the reality of resurgent transseries. Communications in Mathematical Physics, 335 (1), 183-245. (doi:10.1007/s00220-014-2165-z).

Record type: Article

Abstract

In a wide range of quantum theoretical settings -- from quantum mechanics to quantum field theory, from gauge theory to string theory -- singularities in the complex Borel plane, usually associated to instantons or renormalons, render perturbation theory ill-defined as they give rise to nonperturbative ambiguities. These ambiguities are associated to choices of an integration contour in the resummation of perturbation theory, along (singular) Stokes directions in the complex Borel plane (rendering perturbative expansions non-Borel summable along any Stokes line). More recently, it has been shown that the proper framework to address these issues is that of resurgent analysis and transseries. In this context, the cancelation of all nonperturbative ambiguities is shown to be a consequence of choosing the transseries median resummation as the appropriate family of unambiguous real solutions along the coupling-constant real axis. While the median resummation is easily implemented for one-parameter transseries, once one considers more general multi-parameter transseries the procedure becomes highly dependent upon properly understanding Stokes transitions in the complex Borel plane. In particular, all Stokes coefficients must now be known in order to explicitly implement multi-parameter median resummations. In the cases where quantum-theoretical physical observables are described by resurgent functions and transseries, the methods described herein show how one may cancel nonperturbative ambiguities, and define these observables nonperturbatively starting out from perturbation theory. Along the way, structural results concerning resurgent transseries are also obtained.

Full text not available from this repository.

More information

e-pub ahead of print date: 5 October 2014
Published date: April 2015
Keywords: hep-th, math-ph, math.CA, math.MP, quant-ph

Identifiers

Local EPrints ID: 424136
URI: https://eprints.soton.ac.uk/id/eprint/424136
ISSN: 0010-3616
PURE UUID: 07d2cb3a-a614-410e-9e43-f4ebce8753f5

Catalogue record

Date deposited: 05 Oct 2018 11:30
Last modified: 01 Nov 2018 17:30

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×