Effective field theories in the large-[Formula presented] limit

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 56, Issue 4, 1997, Pages 2303-2316

  Weinberg, Steven ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

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EID: 0000476106     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.56.2303     Document Type: Article

References (29)

1. For a review of the large-(Formula presented) limit in various contexts, see S. Coleman, in Aspects of Symmetry (Cambridge University Press, Cambridge, England, 1985), Chap. 8.
2. The earliest reference known to me for the O(Formula presented) linear and nonlinear (Formula presented) models is M. Gell-Mann and M. Lévy, Nuovo Cimento 16, 705 (1960).
3. The O(Formula presented) linear (Formula presented) model was studied in the large-(Formula presented) limit in statistical mechanics by H. E. Stanley, Phys. Rev. 176, 718 (1968);
4. K. Wilson, Phys. Rev. D 7, 2911 (1973);
5. and in four-dimensional relativistic quantum field theories by L. Dolan and R. Jackiw, 9, 3320 (1974);
6. H. J. Schnitzer, 10, 1800 (1974);
7. 10, 2042 (1974);
8. S. Coleman, R. Jackiw, and H. D. Politzer, 10, 2491 (1974);
9. and many later authors. The nonlinear σ model was studied in the large-(Formula presented) limit in 2+ε dimensions by W. A. Bardeen, B. W. Lee, and R. E. Shrock, Phys. Rev. D 14, 985 (1976);
10. E. Brézin and J. Zinn-Justin, Phys. Rev. B 14, 3110 (1976).
11. D. Gross and A. Neveu, Phys. Rev. D 10, 3235 (1974).
12. H. Eichenherr, Nucl. Phys. B146, 215 (1978);
13. V. Golo and A. Perelomov, Phys. Lett. 79B, 112 (1978);
14. A. D’Adda, M. Lüscher, and P. Di Vecchia, Nucl. Phys. B146, 63 (1978);
15. B152, 125 (1979);
16. E. Witten, B149, 285 (1979);
17. H. Haber, I. Hinchcliffe, and E. Rabinovici, B172, 458 (1980);
18. M. Bando, T. Kugo, and K. Yamawaki, Phys. Rep. 164, 217 (1988).
19. S. Weinberg, Physica A 96, 327 (1979).
20. See, e.g., R. de M. Koch and J. P. Rodrigues, Phys. Rev. D 54, 7794 (1996).
21. The renormalization of the 1/(Formula presented) expansion of the (Formula presented) model was shown for two and three spacetime dimensions by I. Ya Aref’eva and S. I. Azakov, Nucl. Phys. B162, 298 (1980);
22. I. Ya Aref’eva, E. R. Nissimov, and S. J. Pacheva, Commun. Math. Phys. 71, 213 (1980).
23. This is analogous to the (Formula presented) dependence that was assumed by H. J. Schnitzer, Nucl. Phys. B109, 297 (1976), in his treatment of the linear σ model in the large-(Formula presented) limit including terms in the Lagrangian of arbitrary order in the squared field.
24. S. Coleman and E. Weinberg, Phys. Rev. D 7, 1888 (1973).
25. S. Weinberg, Phys. Rev. Lett. 17, 616 (1966).
26. V. Kaplunovsky (private communication).
27. For discussions along similar lines and references to earlier works on this subject, see D. Foerster, H. B. Nielsen, and M. Ninomiya, Phys. Lett. 94B, 135 (1980);
28. T. Banks and A. Zaks, Nucl. Phys. B184, 303 (1981).
29. See, e.g., S. Weinberg, The Quantum Theory of Fields II: Modern Applications (Cambridge University Press, Cambridge, England, 1996), p. 318.