Multi-instantons and exact results I: Conjectures, WKB expansions, and instanton interactions

Annals of Physics

Volumn 313, Issue 1, 2004, Pages 197-267

  Zinn Justin, Jean ^a,b   Jentschura, Ulrich D ^c,d  

^a CEA SACLAY   (France)

^b INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

^c UNIVERSITY OF FREIBURG   (Germany)

^d NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

Asymptotic problems and properties; General properties of perturbation theory

Indexed keywords

EID: 3843143197     PISSN: 00034916     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aop.2004.04.004     Document Type: Article

References (36)

1. Relevant reprinted articles and references can be found in the reprint volume, J.C. Le Guillou, J. Zinn-Justin (eds.), Large Order Behaviour of Perturbation Theory, Current Physics, vol. 7, North-Holland, Amsterdam, 1990. Many articles cited here are reprinted in this reference
2. Several results have also been reported in J. Zinn-Justin, contribution to the Proceedings of the Franco-Japanese Colloquium Analyse algébrique des perturbations singulières, Marseille-Luminy, October 1991, L. Boutet de Monvel ed., Collection Travaux en cours, 47, Hermann, Paris, 1994
3. Zinn-Justin J. J. Math. Phys. 22 1981 511
4. Zinn-Justin J. Nucl. Phys. B 192 1981 125
5. Zinn-Justin J. Nucl. Phys. B 218 1983 333
6. Zinn-Justin J. J. Math. Phys. 25 1984 549
7. Zinn-Justin J. Quantum Field Theory and Critical Phenomena fourth ed. 2002 Clarendon Press Oxford
8. J. Écalle, Les Fonctions Réesurgentes, Tomes I-III, Publications Mathématiques d'Orsay, France, 1981-1985
9. F. Pham, Resurgence, Quantized Canonical Transformation and Multi-Instanton, Algebraic Analysis, vol. II, 1988
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11. Delabaere E. Dillinger H. Pham F. C. R. Acad. Sci. Paris 310 1990 141
12. E. Delabaere and H. Dillinger, Ph.D. thesis, University of Nice, Nice, 1991 (unpublished)
13. Delabaere E. C. R. Acad. Sci. Paris 314 1992 807
14. See the URL http://tqd1.physik.uni-freiburg.de/~ulj
15. For a recent numerical investigation see Jentschura U.D. Zinn-Justin J. J. Phys. A 34 2001 L253
16. L.D. Landau, E.M. Lifshitz, Quantum Mechanics (Volume 3 of the Course of Theoretical Physics), Pergamon Press, London, 1958
17. This conjecture has also been partially inspired by the semi-classical calculation of order g reported in C. Bender, T.T. Wu, Phys. Rev. D 7 (1973) 1620
18. This conjecture has also been partially inspired by the semi-classical calculation of order g reported in , See also R. Damburg, R. Propin, J. Chem. Phys. 55 (1971) 612
19. Jentschura U.D. Phys. Rev. D 62 2000 076001
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26. R. Rosenfelder, private communication, 2004
27. For the WKB method, as discussed here, see also Voros A. Ann. IHP A 39 1983 211
28. Itzykson C. Zuber J.B. Quantum Field Theory 1980 McGraw-Hill New York, NY
29. This method is equivalent to the method based on eigenfunctions explained in subsection III B of reference [3]
30. H. Forkel, A Primer on Instantons, Available from hep-ph/0009136
31. Brézin E. Parisi G. Zinn-Justin J. Phys. Rev. D 16 1977 408
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33. Zinn-Justin J. Nucl. Phys. B 192 1981 125
34. Zinn-Justin J. Nucl. Phys. B 218 1983 333
35. Shifman M. Instantons in Gauge Theories 1994 World Scientific Singapore
36. J. Zinn-Justin and U. D. Jentschura, Multi-instantons and exact results II: Specific cases, higher-order effects, and numerical calculations, Ann. Phys. (NY), to appear in the next issue (2004)