Asymptotic improvement of resummations and perturbative predictions in quantum field theory

Journal of Physics G: Nuclear and Particle Physics

Volumn 26, Issue 10, 2000, Pages 1545-1568

  Jentschura, U D ^a   Weniger, E J ^b,c   Soff, G ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

^b UNIVERSITY OF REGENSBURG   (Germany)

^c MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034392877     PISSN: 09543899     EISSN: None     Source Type: Journal    
DOI: 10.1088/0954-3899/26/10/309     Document Type: Article

References (111)

1. Le Guillou J C and Zinn-Justin J (ed) 1990 Large-Order Behaviour of Perturbation Theory (Amsterdam: North-Holland)
2. Baker G A Jr and Graves-Morris P 1996 Padé Approximants 2nd edn (Cambridge: Cambridge University Press)
3. Borel E 1899 Ann. Sci. Ecole Norm. Suppl. Paris 16 9
4. Borel E 1928 Leçons sur les Séries Divergentes 2nd edn (Paris: Gauthier-Villars) Reprinted by Éditions Jacques Gabay, Paris 1988. Translated by Critchfield C L and Vakar A Lectures on Divergent Series Los Alamos Scientific Laboratory, Translation LA-6140-TR 1975
5. Borel E 1928 Leçons sur les Séries Divergentes 2nd edn (Paris: Gauthier-Villars) Reprinted by Éditions Jacques Gabay, Paris 1988. Translated by Critchfield C L and Vakar A Lectures on Divergent Series Los Alamos Scientific Laboratory, Translation LA-6140-TR 1975
6. Weniger E J 1989 Comput. Phys. Rep. 10 189
7. Roy D, Bhattacharya R and Bhowmick S 1996 Comput. Phys. Commun. 93 159 Bhattacharya R, Roy D and Bhowmick S 1996 Comput. Phys. Commun. 101 213 Roy D, Bhattacharya R and Bhowmick S 1998 Comput. Phys. Commun. 113 131 Sarkar A, Sen D, Haldar S and Roy D 1998 Mod. Phys. Lett. B 12 639
8. Roy D, Bhattacharya R and Bhowmick S 1996 Comput. Phys. Commun. 93 159 Bhattacharya R, Roy D and Bhowmick S 1996 Comput. Phys. Commun. 101 213 Roy D, Bhattacharya R and Bhowmick S 1998 Comput. Phys. Commun. 113 131 Sarkar A, Sen D, Haldar S and Roy D 1998 Mod. Phys. Lett. B 12 639
9. Roy D, Bhattacharya R and Bhowmick S 1996 Comput. Phys. Commun. 93 159 Bhattacharya R, Roy D and Bhowmick S 1996 Comput. Phys. Commun. 101 213 Roy D, Bhattacharya R and Bhowmick S 1998 Comput. Phys. Commun. 113 131 Sarkar A, Sen D, Haldar S and Roy D 1998 Mod. Phys. Lett. B 12 639
10. Roy D, Bhattacharya R and Bhowmick S 1996 Comput. Phys. Commun. 93 159 Bhattacharya R, Roy D and Bhowmick S 1996 Comput. Phys. Commun. 101 213 Roy D, Bhattacharya R and Bhowmick S 1998 Comput. Phys. Commun. 113 131 Sarkar A, Sen D, Haldar S and Roy D 1998 Mod. Phys. Lett. B 12 639
11. Weniger E J 1996 Int. J. Quantum Chem. 57 265 Weniger E J 1996 Int. J. Quantum Chem. 58 319 Weniger E J 1996 Ann. Phys., NY 246 133
12. Weniger E J 1996 Int. J. Quantum Chem. 57 265 Weniger E J 1996 Int. J. Quantum Chem. 58 319 Weniger E J 1996 Ann. Phys., NY 246 133
13. Weniger E J 1996 Int. J. Quantum Chem. 57 265 Weniger E J 1996 Int. J. Quantum Chem. 58 319 Weniger E J 1996 Ann. Phys., NY 246 133
14. Weniger E J 1996 Phys. Rev. Lett. 77 2859
15. Weniger E J 1996 Comput. Phys. 10 496
16. Jentschura U D, Mohr P J and Soff G 1999 Phys. Rev. Lett. 82 53
17. Jentschura U D, Mohr P J, Soff G and Weniger E J 1999 Comput. Phys. Commun. 116 28
18. Weniger E J, Čížek J and Vinette F 1993 J. Math. Phys. 34 571
19. Weniger E J 1997 Phys. Rev. A 56 5165
20. Jentschura U, Becher J, Weniger E and Soff G 2000 Phys. Rev. Lett. 85 2446 (Jentschura U, Becher J, Weniger E and Soff G 1999 Los Alamos Preprint hep-ph/9911265)
21. Jentschura U, Becher J, Weniger E and Soff G 2000 Phys. Rev. Lett. 85 2446 (Jentschura U, Becher J, Weniger E and Soff G 1999 Los Alamos Preprint hep-ph/9911265)
22. Graffi S and Grecchi V 1978 J. Math. Phys. 19 1002
23. Gilewicz J 1973 Padé Approximants and Their Applications ed PR Graves-Morris p 99 (London: Academic)
24. Elias V, Steele T G, Chishtie F, Migneron R and Sprague K 1998 Phys. Rev. D 58 116007
25. Steele T G and Elias V 1998 Mod. Phys. Lett. A 13 3151
26. Chishtie F A, Elias V, Miransky V A and Steele T G 1999 Los Alamos Preprint hep-ph/9905291
27. Chishstie F, Elias V and Steele T G 1999 Phys. Lett. B 446 267
28. Chishstie F, Elias V and Steele T G 1999 Phys. Rev. D 59 105013
29. Chishstie F, Elias V and Steele T G 2000 J. Phys. G: Nucl. Part. Phys. 26 93
30. Elias V, Chishtie F A and Steele T G 2000 J. Phys. G: Nucl. Part. Phys. 26 1239 (Elias V, Chishtie F A and Steele T G 2000 Los Alamos Preprint hep-ph/0004140)
31. Elias V, Chishtie F A and Steele T G 2000 J. Phys. G: Nucl. Part. Phys. 26 1239 (Elias V, Chishtie F A and Steele T G 2000 Los Alamos Preprint hep-ph/0004140)
32. Samuel M A and Li G 1991 Phys. Rev. D 44 3935
33. Samuel M A, Li G and Steinfelds E 1993 Phys. Rev. D 48 869
34. Samuel M A 1995 Int. J. Theor. Phys. 33 1461
35. Samuel M A, Li G and Steinfelds E 1994 Phys. Lett. B 323 188
36. Samuel M A and Li G 1994 Phys. Lett. B 331 114
37. Samuel M A, Ellis J and Karliner M 1995 Phys. Rev. Lett. 74 4380
38. Samuel M A 1995 Int. J. Theor. Phys. 34 903
39. Samuel M A 1995 Int. J. Theor. Phys. 34 1113
40. Samuel M A, Li G and Steinfelds E 1995 Phys. Rev. E 51 3911 Samuel M A, Li G and Steinfelds E 1997 Phys. Rev. E 55 2072 (Erratum)
41. Samuel M A, Li G and Steinfelds E 1995 Phys. Rev. E 51 3911 Samuel M A, Li G and Steinfelds E 1997 Phys. Rev. E 55 2072 (Erratum)
42. Ellis J, Gardi E, Karliner M and Samuel M A 1996 Phys. Lett. B 366 268
43. Ellis J, Gardi E, Karliner M and Samuel M A 1996 Phys. Rev. D 54 6986
44. Gardi E 1997 Phys. Rev. D 56 68
45. Ellis J, Karliner M and Samuel M A 1997 Phys. Lett. B 400 176
46. Samuel M A, Abraha T and Yu J 1997 Phys. Lett. B 394 165
47. Jack I, Jones D R T and Samuel M A 1997 Phys. Lett. B 407 143
48. Karliner M 1998 Acta Phys. Polon. B 29 1505
49. Ellis J, Jack I, Jones D R T, Karliner M and Samuel M A 1998 Phys. Rev. D 57 2665
50. Burrows P, Abraha T, Samuel M, Steinfelds E and Masuda H 1996 Phys. Lett. B 272 223
51. Cvetič G and Kögerler R 1998 Nucl. Phys. B 522 396
52. Cvetič G 1998 Phys. Rev. D 57 R3209
53. Cvetič G 1998 Nucl. Phys. B 517 506
54. Cvetič G and Yu J Y 2000 Mod. Phys. Lett. A 15 1227 (Cvetič G and Yu J Y 2000 Los Alamos Preprint hep-ph/0003241 )
55. Cvetič G and Yu J Y 2000 Mod. Phys. Lett. A 15 1227 (Cvetič G and Yu J Y 2000 Los Alamos Preprint hep-ph/0003241 )
56. Weniger E J 2000 J Comput. Appl. Math. in press
57. (Weniger E J 2000 Los Alamos Preprint math. CA/0002111)
58. Graffi S, Grecchi V and Simon B 1970 Phys. Lett. B 32 631
59. Fischer J 1997 Acta Phys. Polon. B 27 2549
60. Fischer J 1997 Int. J. Mod. Phys. A 12 3625
61. Fischer J 1999 Rep. Math. Phys. 43 109
62. Caprini I and Fischer J 1999 Phys. Rev. D 60 054014
63. Caprini I and Fischer J 2000 Phys. Rev. D 62 054007 (Caprini I and Fischer J 2000 Los Alamos Preprint hep-ph/0002016)
64. Caprini I and Fischer J 2000 Phys. Rev. D 62 054007 (Caprini I and Fischer J 2000 Los Alamos Preprint hep-ph/0002016)
65. West G 1991 Phys. Rev. Lett. 67 1388
66. West G 1999 Found. Phys. 30 695 (West G 1999 Los Alamos Preprint hep-ph/9911416)
67. West G 1999 Found. Phys. 30 695 (West G 1999 Los Alamos Preprint hep-ph/9911416)
68. Dunne G V and Hall T M 1999 Phys. Rev. D 60 065002
69. Schwinger J 1951 Phys. Rev. 82 664
70. Jentschura U D 2000 Phys. Rev. D 076001
71. (Jentschura U D 2000 Los Alamos Preprint hep-ph/0001135)
72. Carleman T 1926 Les Fonctions Quasi-Analytiques (Paris: Gauthier-Villars)
73. Reed M and Simon B 1978 Methods of Modern Mathematical Physics IV: Analysis of Operators (New York: Academic)
74. Shawyer B and Watson B 1994 Borel's Method of Summability (Oxford: Oxford University Press)
75. Sternin B Yu and Shatalov V E 1996 Borel-Laplace Transform and Asymptotic Theory (Boca Raton, FL: Chemical Rubber Company)
76. Ra̧czka P A 1991 Phys. Rev. D 43 R9
77. Pindor M 1999 Los Alamos Preprint hep-th/9903151
78. Cuyt A and Wuytack L 1987 Nonlinear Methods in Numerical Analysis (Amsterdam: North-Holland)
79. Wynn P 1956 Math. Tables Aids Comput. 10 91
80. Baker G A Jr 1965 Adv. Theor. Phys. 1 1
81. Brezinski C 1991 History of Continued Fractions and Padé Approximants (Berlin: Springer)
82. Brezinski C and Redivo Zaglia M 1991 Extrapolation Methods (Amsterdam: North-Holland)
83. Wynn P 1966 SIAM J. Numer. Anal. 3 91
84. Levin D 1973 Int. J. Comput. Math. B 3 371
85. Smith D A and Ford W F 1982 Math. Comput. 38 481
86. Cvetic G and Yu J Y 1999 Los Alamos Preprint hep-ph/9911376
87. Itzykson C and Zuber J B 1980 Quantum Field Theory (New York: McGraw-Hill)
88. Abramowitz M and Stegun I A 1972 Handbook of Mathematical Functions 10th edn (Washington, DC: US Govt Printing Office)
89. Beneke M 1999 Phys. Rep. 317 1
90. Broadhurst D and Kreimer D 1999 Phys. Lett. B 475 63 (Broadhurst D and Kreimer D 1999 Los Alamos Preprint hep-ph/9912093)
91. Broadhurst D and Kreimer D 1999 Phys. Lett. B 475 63 (Broadhurst D and Kreimer D 1999 Los Alamos Preprint hep-ph/9912093)
92. Suslov I M 1999 Zh. Éksp. Teor. Fiz. 116 369 (Engl. transl. 1999 Sov. Phys.-JETP 89 197) Lipatov L N 1976 Zh. Éksp. Teor. Fiz. Piz. 24 179 (Engl. transl. 1976 Sov. Phys.-JETP Lett. 24 157)
93. Suslov I M 1999 Zh. Éksp. Teor. Fiz. 116 369 (Engl. transl. 1999 Sov. Phys.-JETP 89 197) Lipatov L N 1976 Zh. Éksp. Teor. Fiz. Piz. 24 179 (Engl. transl. 1976 Sov. Phys.-JETP Lett. 24 157)
94. Suslov I M 1999 Zh. Éksp. Teor. Fiz. 116 369 (Engl. transl. 1999 Sov. Phys.-JETP 89 197) Lipatov L N 1976 Zh. Éksp. Teor. Fiz. Piz. 24 179 (Engl. transl. 1976 Sov. Phys.-JETP Lett. 24 157)
95. Suslov I M 1999 Zh. Éksp. Teor. Fiz. 116 369 (Engl. transl. 1999 Sov. Phys.-JETP 89 197) Lipatov L N 1976 Zh. Éksp. Teor. Fiz. Piz. 24 179 (Engl. transl. 1976 Sov. Phys.-JETP Lett. 24 157)
96. Lipatov L N 1977 Zh. Éksp. Teor. Fiz. 72 411 (Engl. transl. 1977 Sov. Phys.-JETP 45 216)
97. Lipatov L N 1977 Zh. Éksp. Teor. Fiz. 72 411 (Engl. transl. 1977 Sov. Phys.-JETP 45 216)
98. Lautrup B 1977 Phys. Lett. B 69 109
99. Itzykson C, Parisi G and Zuber J B 1977 Phys. Rev. D 16 996
100. Balian R, Itzykson C, Zuber J B and Parisi G 1978 Phys. Rev. D 17 1041
101. Zinn-Justin J 1996 Quantum Field Theory and Critical Phenomena 3rd edn (Oxford: Clarendon)
102. Jentschura U, Becher J, Meyer-Hermann , Mohr P J, Weniger E and Soff G 2000 Resummation of the derivative expansion of the QED effective action, in preparation
103. Jentschura U D, Becher J, Soff G, Mohr P J and Weniger E J 1999 Lepton Moments '99 (Heidelberg) http://www.physi.uni-heidelberg.de/∼muon/lep/lep.html
104. Dyson F J 1952 Phys. Rev. 85 631
105. van Ritbergen T, Vermaseren J A M and Larin S A 1997 Phys. Lett. B 400 379
106. Kataev A L and Starshenko V S 1995 Phys. Rev. D 52 402
107. Karshenboim S G 1993 Yad. Fiz. 56 115 (Engl. transl. 1993 Phys. At. Nucl. 56 777)
108. Karshenboim S G 1993 Yad. Fiz. 56 115 (Engl. transl. 1993 Phys. At. Nucl. 56 777)
109. Cvetič G 2000 Phys. Lett. B 486 100 (Cvetič G 2000 Los Alamos Preprint hep-ph/0003123)
110. Cvetič G 2000 Phys. Lett. B 486 100 (Cvetič G 2000 Los Alamos Preprint hep-ph/0003123)
111. Elias V, Sprague K B and Xue Y 2000 Found. Phys. 30 439