Strong coupling asymptotics of the β-function in φ4 theory and QED

Applied Numerical Mathematics

Volumn 60, Issue 12, 2010, Pages 1418-1428

  Suslov, I M ^a  

^a KAPITZA INSTITUTE FOR PHYSICAL PROBLEMS   (Russian Federation)

Author keywords

Divergent series; Gell Mann Low function; Renormalization group

Indexed keywords

ARBITRARY SPACES; ASYMPTOTIC BEHAVIORS; ASYMPTOTICS; BOREL TRANSFORMATION; DIVERGENT SERIES; EXPANSION COEFFICIENTS; FINE STRUCTURE CONSTANTS; FUNCTIONAL INTEGRALS; GELL-MANN-LOW FUNCTION; RENORMALIZATION GROUP; SPACE DIMENSIONS; STRONG COUPLING; ZERO CHARGE; ZERO-DIMENSIONAL MODELS;

ALGORITHMS; CONFORMAL MAPPING; STATISTICAL MECHANICS;

ASYMPTOTIC ANALYSIS;

EID: 77958013388     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2010.05.006     Document Type: Conference Paper

References (30)

1. C.M. Bender, S.F. Brandt, J.-H. Chen, and Q. Wang Ghost busting: PT-symmetric interpretation of the Lee model Phys. Rev. D 71 2005 025014 025023
2. M. Beneke Renormalons Phys. Rept. 317 1999 1 142 Section 2.4
3. N.N. Bogolyubov, and D.V. Shirkov Introduction to the Theory of Quantized Fields 3rd ed. 1976 Nauka Moscow 1980 Wiley New York
4. E. Brezin, J.C. Le Guillou, and J. Zinn-Justin Field theoretical approach to critical phenomena C. Domb, M.S. Green, Phase Transitions and Critical Phenomena vol. VI 1976 Academic New York
5. S. Ciulli, and J. Fischer A converging set of integral equations for singlet proton-proton scattering Nucl. Phys. 24 1961 465 473 Appendix 1
6. J.P. Eckmann, and H. Epstein Borel summability of the mass and the S-matrix in φ 4 models Commun. Math. Phys. 68 1979 245 258
7. J.C. Le Guillou, and J. Zinn-Justin Critical exponents for n-vector model in three dimensions from field theory Phys. Rev. Lett. 35 1977 55 58
8. G. 't Hooft Can we make sense of quantum chromodynamics? A. Zichichi, The Whys of Subnuclear Physics Erice, 1977 1979 Plenum Press New York
9. G. Jug, and B.N. Shalaev Duality symmetry, strong coupling expansion and universal critical amplitudes in two-dimensional φ 4 field models J. Phys. A 32 1999 7249 7261
10. G. Källen, and W. Pauli On the mathematical structure of T.D. Lee's model of a renormalizable field theory Mat.-Fyz. Medd. 30 7 1955
11. D.I. Kazakov, O.V. Tarasov, and D.V. Shirkov Analytic continuation of the results of perturbation theory for the model g φ 4 to the region g ≥ 1 Teor. Mat. Fiz. 38 1979 15 25
12. N.V. Krasnikov Analyticity and renormalization group Nucl. Phys. B 192 1981 497 508
13. Yu.A. Kubyshin Sommerfeld-Watson summation of perturbation series Teor. Mat. Fiz. 58 1984 137 145
14. T.D. Lee Some special results in renormalizable field theory Phys. Rev. 95 1954 1329 1335
15. L.N. Lipatov Divergence of perturbation series and the quasiclassical theory Zh. Eksp. Teor. Fiz. 72 1977 411 427 Sov. Phys. JETP 45 1977 216 227
16. J. Magnen, and R. Seneor Phase space cell expansion and Borel summability for the Euclidean φ 3 4 theory Commun. Math. Phys. 56 1977 237 276
17. A. Pelissetto, and E. Vicari Four-point renormalized coupling constant and Callan-Symanzik β-function in O (N ) models Nucl. Phys. B 519 1998 626 660
18. A.A. Pogorelov, and I.M. Suslov Renormalization group functions for 2D phase transitions: to the problem of singular contributions Zh. Eksp. Teor. Fiz. 132 2007 406 416 JETP 105 2007 360 370
19. A.A. Pogorelov, and I.M. Suslov Critical exponents for the λ-transition in liquid helium Pis'ma Zh. Eksp. Teor. Fiz. 86 2007 41 47 JETP Lett. 86 2007 39 45
20. A.N. Sissakian, I.L. Solovtsov, and O.P. Solovtsova β-function for the φ 4 model in variational perturbation theory Phys. Lett. B 321 1994 381 384
21. I.M. Suslov High orders of perturbation theory: are renormalons significant? Zh. Eksp. Teor. Fiz. 116 1999 369 389 JETP 89 1999 197 207
22. I.M. Suslov Summing divergent perturbative series in the strong coupling limit. Gell-Mann-Low function of the φ 4 theory Zh. Eksp. Teor. Fiz. 120 2001 5 30 JETP 93 2001 1 23
23. I.M. Suslov Gell-Mann-Low function in QED. Pis'ma Zh. Eksp. Teor. Fiz. 74 2001 211 215 JETP Lett. 74 2001 191 195
24. I.M. Suslov Renormalons and analytic properties of the β-function Zh. Eksp. Teor. Fiz. 126 2004 542 548 JETP 99 2004 474 479
25. I.M. Suslov Divergent perturbation series (review) Zh. Eksp. Teor. Fiz. 127 2005 1350 1402 JETP 100 2005 1188 1233
26. I.M. Suslov Analytical asymptotics of β-function in φ 4 theory (end of the "zero charge" story) arXiv:0804.0368
27. I.M. Suslov Quantum electrodynamics at extremely small distances arXiv:0804.2650
28. I.M. Suslov Is φ 4 theory trivial? arXiv:0806.0789
29. A.A. Vladimirov, and D.V. Shirkov Renormalization group and ultraviolet asymptotics Usp. Fiz. Nauk 129 1979 407 441 Sov. Phys. Usp. 22 1979 860 884
30. H. Yamagishi Renormalization group functions and spectral functions Phys. Rev. D 25 1982 464 473