From multi-instantons to exact results

Jean Zinn-Justin[1]

  • [1] CEA, Service de Physique Théorique de Saclay, CNRS URA 2306, 91191 Gif-sur-Yvette Cedex (France)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 4, page 1259-1285
  • ISSN: 0373-0956

Abstract

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In these notes, conjectures about the exact semi-classical expansion of eigenvalues of hamiltonians corresponding to potentials with degenerate minima, are recalled. They were initially motivated by semi-classical calculations of quantum partition functions using a path integral representation and have later been proven to a large extent, using the theory of resurgent functions. They take the form of generalized Bohr--Sommerfeld quantization formulae. We explain here their relation with the corresponding WKB expansion of the Schrödinger equation. We show how these conjectures naturally emerge from an evaluation of multi-instanton contributions in the path integral formulation of quantum mechanics.

How to cite

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Zinn-Justin, Jean. "From multi-instantons to exact results." Annales de l’institut Fourier 53.4 (2003): 1259-1285. <http://eudml.org/doc/116067>.

@article{Zinn2003,
abstract = {In these notes, conjectures about the exact semi-classical expansion of eigenvalues of hamiltonians corresponding to potentials with degenerate minima, are recalled. They were initially motivated by semi-classical calculations of quantum partition functions using a path integral representation and have later been proven to a large extent, using the theory of resurgent functions. They take the form of generalized Bohr--Sommerfeld quantization formulae. We explain here their relation with the corresponding WKB expansion of the Schrödinger equation. We show how these conjectures naturally emerge from an evaluation of multi-instanton contributions in the path integral formulation of quantum mechanics.},
affiliation = {CEA, Service de Physique Théorique de Saclay, CNRS URA 2306, 91191 Gif-sur-Yvette Cedex (France)},
author = {Zinn-Justin, Jean},
journal = {Annales de l’institut Fourier},
keywords = {singular perturbations; turning point theory; WKB methods; resurgence phenomena},
language = {eng},
number = {4},
pages = {1259-1285},
publisher = {Association des Annales de l'Institut Fourier},
title = {From multi-instantons to exact results},
url = {http://eudml.org/doc/116067},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Zinn-Justin, Jean
TI - From multi-instantons to exact results
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 4
SP - 1259
EP - 1285
AB - In these notes, conjectures about the exact semi-classical expansion of eigenvalues of hamiltonians corresponding to potentials with degenerate minima, are recalled. They were initially motivated by semi-classical calculations of quantum partition functions using a path integral representation and have later been proven to a large extent, using the theory of resurgent functions. They take the form of generalized Bohr--Sommerfeld quantization formulae. We explain here their relation with the corresponding WKB expansion of the Schrödinger equation. We show how these conjectures naturally emerge from an evaluation of multi-instanton contributions in the path integral formulation of quantum mechanics.
LA - eng
KW - singular perturbations; turning point theory; WKB methods; resurgence phenomena
UR - http://eudml.org/doc/116067
ER -

References

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