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This is an introductory level review of recent applications of resurgent trans-series and Picard-Lefschetz theory to quantum mechanics and quantum field theory.
1954
Earlier work this paper cites.
C. M. Bender and T. T. Wu, Anharmonic oscillator
1973
Earlier work this paper cites.
S. R. Coleman, The Uses of Instantons
1979
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E. Bogomolny, Calculation of instanton-anti-instanton contributions in quantum mechanics
1981
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E. Witten, Constraints on Supersymmetry Breaking
1982
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M. V. Fedoryuk, The saddle-point method
1983
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I. Balitsky and A. Yung, Instanton Molecular Vacuum in N = 1 N=1 Supersymmetric Quantum Mechanics
1988
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E. Delabaere, H. Dillinger and F. Pham, “Exact semiclassical expansions for one-dimensional quantum oscillators”, J. Math. Phys. 38
1997
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T. Schäfer and E. V. Shuryak, Instantons in QCD
1998
Earlier work this paper cites.
M. V. Berry and C. J. Howls, Hyperasymptotics for integrals with saddles
2002
Earlier work this paper cites.
J. Zinn-Justin and U. D. Jentschura, “Multi-instantons and exact results I: Conjectures, WKB expansions, and instanton interactions,” Annals Phys. 313
2004
Earlier work this paper cites.
Publ. Math. Orsay, 1981; O. Costin, Asymptotics and Borel Summability
J. Ecalle, Les Fonctions Resurgentes, Vol. I-III · 2007
Earlier work this paper cites.
2008
Earlier work this paper cites.
G. Guralnik and Z. Guralnik, Complexified path integrals and the phases of quantum field theory
2010
Cited alongside, same era.
M. Ünsal, Magnetic bion condensation: A New mechanism of confinement and mass gap in four dimensions
2011
Cited alongside, same era.
E. Witten, A New Look At The Path Integral Of Quantum Mechanics
2011
Cited alongside, same era.
D. Harlow, J. Maltz, and E. Witten, Analytic Continuation of Liouville Theory
2011
Cited alongside, same era.
2014
Later among the works it cites.
2014
Later among the works it cites.
M. Kontsevich, Resurgence from the path integral perspective
2015
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2015
Closest in time.
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2012
Cited alongside, same era.
2012
Cited alongside, same era.
I. Aniceto and R. Schiappa, Nonperturbative Ambiguities and the Reality of Resurgent Transseries
2012
Cited alongside, same era.
2012
Cited alongside, same era.
2013
Cited alongside, same era.
2013
Cited alongside, same era.
2013
Cited alongside, same era.
G. V. Dunne and M. Ünsal, Generating Non-perturbative Physics from Perturbation Theory
2014
Cited alongside, same era.
2015
Closest in time.
2015
Closest in time.
2015
Closest in time.
2015
Closest in time.
H. , M. C. Ogilvie, and K. Pangeni, Complex saddle points in QCD at finite temperature and density
2015
Closest in time.
T. Kanazawa and Y. Tanizaki, Structure of Lefschetz thimbles in simple fermionic systems
2015
Closest in time.
T. Misumi, M. Nitta, and N. Sakai, Neutral bions in the ℂ P N − 1 {\mathbb{C}}P^{N-1} model
2015
Closest in time.
2015
Closest in time.