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In these notes we give an overview of different topics in resurgence theory from a physics point of view, but with particular mathematical flavour.
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1952
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C. A. Hurst, The Enumeration of Graphs in the Feynman-Dyson Technique
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C. M. Bender and T. T. Wu, Anharmonic Oscillator
1969
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C. M. Bender and T. Wu, Anharmonic Oscillator 2: A Study of Perturbation Theory in Large Order
1973
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Academic Press, 1973
R. B. Dingle, Asymptotic Expansions: Their Derivation and Interpretation · 1973
Earlier work this paper cites.
C. M. Bender and T. T. Wu, Statistical Analysis of Feynman Diagrams
1976
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L. Lipatov, Divergence of the Perturbation Theory Series and the Quasiclassical Theory
1977
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G. ’t Hooft, Can We Make Sense Out of Quantum Chromodynamics?
1979
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E. Bogomolny, Calculation of Instanton—Anti–Instanton Contributions in Quantum Mechanics
1980
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J. Zinn-Justin, Perturbation Series at Large Orders in Quantum Mechanics and Field Theories: Application to the Problem of Resummation
1981
Earlier work this paper cites.
Publ. Math. Orsay, 1981
J. Ecalle, Les Fonctions Resurgentes · 1981
Earlier work this paper cites.
J. Zinn-Justin, Multi–Instanton Contributions in Quantum Mechanics
1981
Earlier work this paper cites.
A. Voros, The Return of the Quartic Oscillator: The Complex WKB Method
1983
Earlier work this paper cites.
J. Zinn-Justin, Multi–Instanton Contributions in Quantum Mechanics 2
1983
Earlier work this paper cites.
F. Pham, Vanishing homologies and the n variable saddlepoint method
1983
Earlier work this paper cites.
M. V. Berry and C. J. Howls, Hyperasymptotics
1990
Cited alongside, same era.
M. V. Berry and C. J. Howls, Hyperasymptotics for integrals with saddles
1991
Cited alongside, same era.
A. Voros, Résurgence Quantique
1993
Cited alongside, same era.
M. V. Berry and C. J. Howls, Unfolding the high orders of asymptotic expansions with coalescing saddles: singularity theory, crossover and duality
1993
Cited alongside, same era.
E. Delabaere and F. Pham, Resurgent Methods in Semi–Classical Asymptotics
1999
Cited alongside, same era.
M. Beneke, Renormalons
1999
Cited alongside, same era.
G. V. Dunne and M. Ünsal, Resurgence and Trans–Series in Quantum Field Theory: The ℂ ℙ N − 1 {\mathbb{CP}}^{N-1} Model
2012
Later among the works it cites.
P. Argyres and M. Ünsal, A Semiclassical Realization of Infrared Renormalons
2012
Later among the works it cites.
P. C. Argyres and M. Ünsal, The Semi–Classical Expansion and Resurgence in Gauge Theories: New Perturbative, Instanton, Bion, and Renormalon Effects
2012
Later among the works it cites.
J. Gair, N. Yunes and C. M. Bender, Resonances in Extreme Mass-Ratio Inspirals: Asymptotic and Hyperasymptotic Analysis,
2012
Later among the works it cites.
S. Garoufalidis, A. Its, A. Kapaev and M. Mariño, Asymptotics of the Instantons of Painlevé I
2012
Later among the works it cites.
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2004
Cited alongside, same era.
M. Mariño, R. Schiappa and M. Weiss, Nonperturbative Effects and the Large–Order Behavior of Matrix Models and Topological Strings
2008
Cited alongside, same era.
M. Mariño, Open String Amplitudes and Large–Order Behavior in Topological String Theory
2008
Cited alongside, same era.
CRC Press, 2008
O. Costin, Asymptotics and Borel summability · 2008
Cited alongside, same era.
G. A. Edgar, Transseries for Beginners
2009
Cited alongside, same era.
S. Pasquetti and R. Schiappa, Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c = 1 c=1 Matrix Models
2010
Cited alongside, same era.
M. Cristoforetti, F. Di Renzo and L. Scorzato, New approach to the sign problem in quantum field theories: High density QCD on a Lefschetz thimble
2012
Later among the works it cites.
M. P. Heller, R. A. Janik and P. Witaszczyk, Hydrodynamic Gradient Expansion in Gauge Theory Plasmas
2013
Later among the works it cites.
G. V. Dunne and M. Ünsal, Continuity and Resurgence: Towards a Continuum Definition of the ℂ ℙ N − 1 {\mathbb{CP}}^{N-1} Model
2013
Later among the works it cites.
G. Basar, G. V. Dunne and M. Unsal, Resurgence theory, ghost-instantons, and analytic continuation of path integrals,
2013
Later among the works it cites.
M. Mariño, Lectures on Non–Perturbative Effects in Large N N Gauge Theories, Matrix Models and Strings
2014
Closest in time.
A. Cherman, D. Dorigoni, G. V. Dunne and M. Ünsal, Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
2014
Closest in time.
G. V. Dunne and M. Ünsal, Generating Energy Eigenvalue Trans–Series from Perturbation Theory
2014
Closest in time.
R. Schiappa and R. Vaz, The Resurgence of Instantons: Multi–Cut Stokes Phases and the Painlevé II Equation
2014
Closest in time.
Y. Tanizaki and T. Koike, Real-time Feynman path integral with Picard–Lefschetz theory and its applications to quantum tunneling
2014
Closest in time.