The Power of Perturbation Theory

F. J. Dyson, “Divergence of perturbation theory in quantum electrodynamics,” Phys. Rev. 85

1952

Earlier work this paper cites.

J. Milnor, “Morse Theory” (1963), Princeton University Press - ISBN 0-691-08008-9

1963

Earlier work this paper cites.

J. J. Loeffel, A. Martin, B. Simon and A. S. Wightman, “Pade approximants and the anharmonic oscillator,” Phys. Lett. B 30

1969

Earlier work this paper cites.

B. Simon and A. Dicke, “Coupling constant analyticity for the anharmonic oscillator,” Annals Phys. 58

1970

Earlier work this paper cites.

S. Graffi, V. Grecchi and B. Simon, “Borel summability: Application to the anharmonic oscillator,” Phys. Lett. B 32

1970

Earlier work this paper cites.

C. M. Bender and T. T. Wu, “Large order behavior of Perturbation theory,” Phys. Rev. Lett. 27

1971

Earlier work this paper cites.

G.H. Hardy, “Divergent Series ”, Oxford University Press, 1973

1973

Earlier work this paper cites.

C. M. Bender and T. T. Wu, “Anharmonic oscillator. 2: A Study of perturbation theory in large order,” Phys. Rev. D 7

1973

Earlier work this paper cites.

J.P. Eckmann, J. Magnen and R. Sénéor, “Decay properties and borel summability for the Schwinger functions in P ​ ( Φ ) 2 P(\Phi)_{2} theories”, Commun.Math. Phys. 39, 251 (1975). doi:10.1007/BF01705374

1975

Earlier work this paper cites.

J. Magnen and R. Sénéor, “Phase Space Cell Expansion and Borel Summability for the Euclidean ϕ 4 \phi^{4} in Three-Dimensions Theory,” Commun. Math. Phys. 56

1977

Earlier work this paper cites.

L. N. Lipatov, “Divergence of the Perturbation Theory Series and the Quasiclassical Theory,” Sov. Phys. JETP 45

1977

Earlier work this paper cites.

E. Brezin, J. C. Le Guillou and J. Zinn-Justin, “Perturbation Theory at Large Order. 1. The phi**2N Interaction,” Phys. Rev. D 15

1977

Earlier work this paper cites.

E. Brezin, J.-C. Le Guillou and J. Zinn-Justin, “Perturbation Theory at Large Order. 2. Role of the Vacuum Instability,” Phys. Rev. D 15

1977

Earlier work this paper cites.

E. Brezin, G. Parisi and J. Zinn-Justin, “Perturbation Theory at Large Orders for Potential with Degenerate Minima,” Phys. Rev. D 16

1977

Earlier work this paper cites.

Interestingly enough, a precursor of eq.( 3.3

1977

Cited alongside, same era.

W. E. Caswell, “Accurate Energy Levels for the Anharmonic Oscillator and a Summable Series for the Double Well Potential in Perturbation Theory,” Annals Phys. 123

1979

Cited alongside, same era.

S. J. Chang, “The Existence of a Second Order Phase Transition in the Two-Dimensional phi**4 Field Theory,” Phys. Rev. D 13

1979

Cited alongside, same era.

A. D. Sokal, “An Improvement Of Watson’s Theorem On Borel Summability,” J. Math. Phys. 21

1980

Cited alongside, same era.

J. C. Le Guillou and J. Zinn-Justin, “Critical Exponents from Field Theory,” Phys. Rev. B 21

1980

Cited alongside, same era.

J. Ecalle. 1981,“Les Fonctions Resurgentes”, vol. I - III Publ. Math. Orsay

A. Vainshtein, “Decaying Systems and Divergence of the Series of Perturbation Theory”, Novosibirsk Institute of Nuclear Physics Report, December 1964, published in “Continuous advances in QCD. Proceedings, Conference, Minneapolis, USA, May 17-23, 2002,” K.A. Olive, M.A. Shifman and M.B. Voloshin, editors

2002

Later among the works it cites.

J. Zinn-Justin, “Instantons in Quantum Mechanics: Numerical Evidence for a Conjecture,” J. Math. Phys. 25

2002

Later among the works it cites.

For a review see e.g. A. Pelissetto and E. Vicari, “Critical phenomena and renormalization group theory,” Phys. Rept. 368

2002

Later among the works it cites.

U. D. Jentschura and J. Zinn-Justin, “Instantons in quantum mechanics and resurgent expansions,” Phys. Lett. B 596

2004

Later among the works it cites.

E. Witten, “Analytic Continuation Of Chern-Simons Theory,” AMS/IP Stud. Adv. Math. 50