An explicit large versus small field multiscale cluster expansion

Reviews in Mathematical Physics

Volumn 9, Issue 2, 1997, Pages 123-199

  Abdesselam, A ^a   Rivasseau, V ^a  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040007941     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X97000063     Document Type: Article

References (46)

1. A. Abdesselam, Ph.D. Thesis, Ecole Polytechnique, in preparation.
2. A. Abdesselam and V. Rivasseau, "Trees, forests and jungles: a botanical garden for cluster expansions, in Constructive physics", Proceedings, Palaiseau, France 1994, Lecture Notes in Phys. 446, Springer, 1995.
3. 4 model", in preparation.
4. T. Balaban, Commun. Math. Phys. 85 (1982) 603; 86 (1982) 555; 89 (1983) 571; 109 (1987) 249; 116 (1988) 1.
5. T. Balaban, Commun. Math. Phys. 85 (1982) 603; 86 (1982) 555; 89 (1983) 571; 109 (1987) 249; 116 (1988) 1.
6. T. Balaban, Commun. Math. Phys. 85 (1982) 603; 86 (1982) 555; 89 (1983) 571; 109 (1987) 249; 116 (1988) 1.
7. T. Balaban, Commun. Math. Phys. 85 (1982) 603; 86 (1982) 555; 89 (1983) 571; 109 (1987) 249; 116 (1988) 1.
8. T. Balaban, Commun. Math. Phys. 85 (1982) 603; 86 (1982) 555; 89 (1983) 571; 109 (1987) 249; 116 (1988) 1.
9. G. A. Battle, "A new combinatoric estimate for cluster expansions", Commun. Math. Phys. 94 (1984) 133.
10. G. A. Battle and P. Federbush, "A phase cell cluster expansion for Euclidean field theories", Ann. Phys. 142 (1982) 95; "A note on cluster expansions, tree graph identities, extra 1/N! factors!!!", Lett. Math. Phys. 8 (1984) 55.
11. G. A. Battle and P. Federbush, "A phase cell cluster expansion for Euclidean field theories", Ann. Phys. 142 (1982) 95; "A note on cluster expansions, tree graph identities, extra 1/N! factors!!!", Lett. Math. Phys. 8 (1984) 55.
12. D. Brydges, "A short course on cluster expansions, in Critical phenomena, random systems, gauge theories", Les Houches session XLIII, 1984, Elsevier Science Publishers, 1986.
13. D. Brydges, "Functional integrals and their applications", Cours de Troisième Cycle de la Physique en Suisse Romande, taken by R. Fernandez, Université de Lausanne or Univ. of Virginia, preprint, (1992).
14. D. Brydges, "Weak perturbations of massless Gaussian measures", Mathematical Quantum Theory I: Field Theory and Many Body Theory, ed. J. Feldman, R. Froese, and L. Rosen, CRM Proceedings Lecture Notes.
15. D. Brydges and P. Federbush, "A new form of the Mayer expansion in classical statistical mechanics", Math. Phys. 19 (1978) 2064.
16. D. Brydges and T. Kennedy, "Mayer expansions and the Hamilton-Jacobi equation", J. Stat. Phys. 48 (1987) 19.
17. D. Brydges and H. T. Yau, "Grad Φ perturbations of massless Gaussian fields", Commun. Math. Phys. 129 (1990) 351.
18. 4 in 4-ε dimensions-I", preprint.
19. 4 in 4-ε dimensions-I", preprint.
20. "Constructive Quantum field theory", Proc. 1973 Erice Summer School, ed. G. Velo and A. Wightman, Lecture Notes in Phys. 25, Springer, 1973.
21. 4 by a phase space expansion", Commun. Math. Phys. 109, (1987) 473.
22. 4 by a phase space expansion", Commun. Math. Phys. 109, (1987) 473.
23. J. Feldman, J. Magnen, V. Rivasseau and E. Trubowitz, "An infinite volume expansion for many Fermion Green's functions", Helvetica Physica Acta, 65 (1992) 679; "Fermionic many-body models", Mathematical Quantum Theory I: Field Theory and Many Body Theory, ed. J. Feldman, R. Froese and L. Rosen, CRM Proceedings Lecture Notes.
24. J. Feldman, J. Magnen, V. Rivasseau and E. Trubowitz, "An infinite volume expansion for many Fermion Green's functions", Helvetica Physica Acta, 65 (1992) 679; "Fermionic many-body models", Mathematical Quantum Theory I: Field Theory and Many Body Theory, ed. J. Feldman, R. Froese and L. Rosen, CRM Proceedings Lecture Notes.
25. 3 quantum field theories", Ann. Phys. 97 (1976) 80.
26. J. Feldman and E. Trubowitz, "Perturbation theory for many Fermion systems", Helv. Phys. Acta 63 (1990) 156; "The flow of an electron-phonon system to the superconducting state", Helvetica Physica Acta 64 (1991) 214.
27. J. Feldman and E. Trubowitz, "Perturbation theory for many Fermion systems", Helv. Phys. Acta 63 (1990) 156; "The flow of an electron-phonon system to the superconducting state", Helvetica Physica Acta 64 (1991) 214.
28. 3 hamiltonian", Fortschr. Phys. 21 (1973) 327.
29. J. Glimm and A. Jaffe, Quantum Physics, A Functional Integral Point of View. Springer, 1987.
30. 2 model and other applications of high temperature expansions, Part II: The cluster expansionφ, in [14] above.
31. 4 theory: Rigorous control of a renormalizable asymptotically free model", Commun. Math. Phys. 99, (1985) 197: "Gross-Neveu model through convergent perturbation expansions", Commun. Math. Phys. 102 (1985) 1.
32. 4 theory: Rigorous control of a renormalizable asymptotically free model", Commun. Math. Phys. 99, (1985) 197: "Gross-Neveu model through convergent perturbation expansions", Commun. Math. Phys. 102 (1985) 1.
33. D. Iagolnitzer and J. Magnen, Commun. Math. Phys. 110 (1987) 511; 111 (1987) 81: 119 (1988) 567; 119 (1988) 609.
34. D. Iagolnitzer and J. Magnen, Commun. Math. Phys. 110 (1987) 511; 111 (1987) 81: 119 (1988) 567; 119 (1988) 609.
35. D. Iagolnitzer and J. Magnen, Commun. Math. Phys. 110 (1987) 511; 111 (1987) 81: 119 (1988) 567; 119 (1988) 609.
36. D. Iagolnitzer and J. Magnen, Commun. Math. Phys. 110 (1987) 511; 111 (1987) 81: 119 (1988) 567; 119 (1988) 609.
37. C. Kopper, J. Magnen, and V. Rivasseau, "Mass generation in the large N Gross Neveu model", Commun. Math. Phys. 169 (1995) 121.
38. P. Lemberger, "Large-field versus small-field expansions and Sobolev inequalities. J. Stat. Phys. 79 (1995) 525.
39. G. Mack and A. Pordt, "Convergent perturbation expansions for Euclidean quantum field theory", Commun. Math. Phys. 97 (1985) 267.
40. 3-theory", Commun. Math. Phys. 56 (1977) 237.
41. 4 with an infrared cutoff", Commun. Math. Phys. 155 (1993) 325.
42. G. Poirot, "A single slice 2d Anderson model at weak disorder", Ecole Polytechnique preprint.
43. A. Pordt, "Renormalization theory for hierarchical models", Helv. Phys. Acta, 66 (1993) 105; "On renormalization group flows and polymer algebras", Constructive Physics, Proceedings, Palaiseau, France 1994, Lecture Notes in Phys. 446, Springer, 1995.
44. A. Pordt, "Renormalization theory for hierarchical models", Helv. Phys. Acta, 66 (1993) 105; "On renormalization group flows and polymer algebras", Constructive Physics, Proceedings, Palaiseau, France 1994, Lecture Notes in Phys. 446, Springer, 1995.
45. V. Rivasseau, From Perturbative to Constructive Renormalization, Princeton Univ. Press, 1991.
46. V. Rivasseau, "Cluster expansions with small/large field conditions", Mathematical Quantum Theory I: Field Theory and Many Body Theory, ed. J. Feldman, R. Froese, and L. Rosen, CRM Proceedings Lecture Notes.