Non-perturbative renormalization

Non-Perturbative Renormalization

Volumn , Issue , 2008, Pages 1-290

  Mastropietro, Vieri ^a  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84967351039     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/6748     Document Type: Book

References (76)

1. Itzykson C. and Zuber J. The quantum theory of fields, McGraw-Hill, New York, 1985.
2. Weinberg, S., The Quantum Theory of Fields, Cambridge University Press, 1995.
3. Glimm J. and Jaffe A.Quantum Physics: a Functional Integralpoint of wiew, Springer, 1987.
4. Streater R.F., Wightman A.S.PCT, spin and statistics and all that.Benjiamin Publishing, 1964.
5. Osterwalder K., Schrader R.: Axioms for Euclidean Green’s Functions. Comm. Math. Phys.31,83-112, 1973
6. Osterwalder K., Schrader R.: Comm. Math. Phys.42,281-305, 1975.
7. Wilson K.G. The Renormalization Group and critical phenomena Rev. Mod.Phys.55, 583, 1983.
8. Polchinski, J.Nucl. Phys. B231, 269, 1984.
9. Gallavotti G.: Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods. Rev.Mod.Phys.57,471-562, 1985.
10. Rivasseau V.: From perturbative to constructive renormalization, Princeton University Press, Princeton, 1994.
11. Benfatto G., Gallavotti G., Renormalization group.Physics Notes, 1. Prince ton Paperbacks. Princeton University Press, 1995.
12. Salmhofer M. Renormalization. An introduction.Texts and Monographs in Physics. Springer-Verlag, Berlin, 1999.
13. Itzykson C., Drouffe, J. Statistical field theory, Cambridge monographs in Mathematical Notes, Cambr. Univ. Press, 1989.
14. Gallavotti G.:Statistical Mechanics. Springer, 1999.
15. Baxter R.J. Exactly solved models in statistical mechanics. Academic Press, 1982.
16. Abrikosov A.A., Gorkov L.P., Dzyaloshinski I.Y.: Methods of Quantum Field Theory in Statistical Physics, Dover Publications, New York, 1965.
17. Negele J.W., Orland H.Quantum many particle systems Addison-Wesley, 1987.
18. c cuprates, Prince ton Press, Princeton, 1997.
19. Mattis D. C., Lieb E. H.: Exact Solution of a Many-Fermion System and its Associated Boson Field. J. Math. Phys.6,304-312, 1965.
20. Feldman, J, Knoerrer H. and Trubowitz E.Fermion functional integral and the Renormalization GroupAmerican Math. Soc. (2000).
21. Gallavotti G., Nicolo F.: Renormalization theory for four dimensional scaler fields, I, Comm. Math. Phys100(1985), 545-590
22. Gallavotti G., Nicolo F.: Renormalization theory for four dimensional scaler fields, II, Comm. Math. Phys. 101(1985), 471-562.
23. Caianiello E.R.: Number of Feynman graphs and convergence, Nuovo Ci mento 3(1956), No. 1, 223-225.
24. Battle G., Federbush P. A phase cell cluster expansion for Euclidean field theories. Ann.Phys. 142,95, 1982.
25. Brydges D.: A short course on Cluster Expansions, Les Houches 1984, K. Osterwalder, R. Stora eds., North Holland Press, (1986).
26. Gawedzki K., Kupiainen A.: Gross-Neveu model through convergent pertur bation expansions. Comm.Math.Phys.102,1-30, 1985.
27. 2 quantum field theory. Comm. Math. Phys.108,437-467, 1987.
28. Feldman J., Magnen J., Rivasseau V, Seneor R.: Massive Gross-Neveu Model: A renormalizable field theory in two dimensions. Comm. Math. Phys.103, 67-103, 1986.
29. Mastropietro V.: Non-perturbative Adler-Bardeen Theorem. J. Math. Phys. (2007).
30. Benfatto G., Mastropietro V.: Renormalization group, hidden symmetries and approximate Ward identities in the XYZ model. Rev. Math. Phys.13, 1323-1435, 2001.
31. Benfatto G., Mastropietro V.: On the density-density critical indices in interacting Fermi systems. Comm. Math. Phys.231,97-134, 2002.
32. Benfatto G., Mastropietro V.: Ward identities and vanishing of the Beta function for d =1 interacting Fermi systems. J. Stat. Phys.115,143-184, 2004.
33. Benfatto G., Mastropietro V.: Ward identities and chiral anomaly in the Luttinger liquid. Comm. Math. Phys.258,609-655, 2005.
34. Adler S. L., Bardeen W.A.: Absence of higher order corrections in the anoma lous axial vector divergence equation. Phys. Rev.182, 1517-1536, 1969.
35. Georgi H., Rawls J.M.: Anomalies of the Axial-Vector Current in Two di mensions. Phys. Rev.D3,874-879, 1971.
36. Gomes M., Lowenstein J.H.: Asymptotic scale invariance in a massive Thirring model. Nucl. Phys. B45,252-266, 1972.
37. Metzner W., Di Castro C.:Conservation laws and correlation functions in the Luttinger liquid. Phys. Rev. B47, 16107 (1993).
38. Benfatto G., Gallavotti G.: Perturbation theory of the Fermi surface in a quantum liquid. A general quasiparticle formalism and one dimensional systems, J. Statist. Phys. 59(1990), No. 3-4, 541-664.
39. Benfatto G., Gallavotti G., Procacci A., Scoppola B.: Beta functions andSchwinger functions for a many fermions system in one dimension, Comm. Math. Phys. 160(1994), 93-171.
40. Mastropietro V.: Non-perturbative aspects of chiral anomalies. J. Phys. A40, 33, 10349-10365 (2007).
41. Benfatto G., Falco P., Mastropietro V.: Functional Integral Construction of the Massive Thirring model: Verification of Axioms and Massless Limit, Comm. Math. Phys.273, 67-118, (2007).
42. Osterwalder K., Seiler E.: Gauge Field Theories on a Lattice. Ann.Phys.110, 440-471, 1978.
43. Mastropietro V. Renormalization Group and Ward Identities for Infrared QED4. J. Math. Phys.48, 102-303 (2007).
44. Kasteleyn P.W.: Dimer Statistics and phase transitions, J. Math.Phys.4,287 (1963).
45. Hurst C.: New approach to the Ising problem, J.Math. Phys.7,2, 305-310 (1966).
46. Samuel S., The use of anticommuting variable integrals in statistical mechan ics, J. Math. Phys.21 (1980) 2006.
47. Spencer T.: A mathematical approach to universality in two dimensions. Physica A279, 250-259 (2000).
48. Pinson P., Spencer T.: Universality in 2D critical Ising model. To appear in Comm. Math. Phys.
49. Mastropietro V.: Non Universality in Ising models with four spin interaction. Journ. Stat. Phys.,111, 201-259 (2003).
50. Mastropietro V.: Ising models with four spin interaction at criticality. Comm. Math. Phys.244, 3 (2004), 595-642.
51. Giuliani A., Mastropietro V.: Anomalous Universality in the Ashkin-Teller model. Comm. Math. Phys.2003.
52. Giuliani A., Mastropietro V.: Anomalous critical exponents in the anisotropic Ashkin-Teller model 93 (2005) Phys. Rev. Lett. 190603-190607.
53. Tomonaga S.I.: Progress of Theoretical Physics.5, 544 (1950).
54. Bonetto F., Mastropietro, V.: Beta Function and anomaly of the Fermi surface for a d=1 system of interacting fermions in a periodic potential F. Bonetto, V.Mastropietro. Comm. Math. Phys.172, 1, 57-93 (1992).
55. Bonetto F., Mastropietro V.: Critical indeces in a d =1 filled band Fermi systems, Phys. Rev. B56,3,1296-1308 (1997).
56. Bonetto F., Mastropietro V.: Critical Indices for the Yukawa2 model, Nucl.Phys.B497, 541-554 (1997).
57. Mastropietro V.:Small denominators and anomalous behaviour in the incom mensurate Holstein-Hubbard model, Commun. Math. Phys., 201, 81-115 (1999).
58. Mastropietro V.: Incommensurate Charge Density Waves in the adiabatic Hubbard-Holstein model, Phys. Rev.B65,75113, (2002).
59. Gentile G., Mastropietro V.: Renormalization group for fermions: a review on mathematical results, Physics Reports352 (2001), no. 4-6, 273-437.
60. Mastropietro V.: Rigorous proof of Luttinger liquid behavior in the 1d Hub bard model, J. Stat. Phys.121 (2005), no. 3-4, 373-432
61. Mastropietro V.: The absence of Logarithmic corrections in the 1d Hubbard model. J. Phys. A40, 13, 3347 (2007).
62. Lieb E.H., Wu F.Y.: Phys. Rev. Lett.20,1445-1449 (1968).
63. Feldman J., Magnen J., Rivasseau V., Trubowitz E.: An infinite volume expansion for many fermions Green functions, Helv. Phys. Acta 65(1992), 679-721.
64. Disertori M., Rivasseau, V.: Interacting Fermi Liquid in Two Dimensions at Finite Temperature. Comm. Math. Phys. 215,251-290, 2000
65. Disertori M., Rivasseau, V.: Interacting Fermi Liquid in Two Dimensions at Finite Temperature. Comm. Math. Phys. 215, 251-290, 2000.
66. Benfatto G., Giuliani A., Mastropietro V.: Low temperature analysis of two dimensional Fermi systems with symmetric Fermi surface, Annales Henry Poincare’ n.4 (2003) 137-193.
67. Benfatto G., Giuliani A., Mastropietro V.: Proof of Fermi liquid behavior in the 2D Hubbard model. Annales Henry Poincare’7 (2006), no. 5, 809-898.
68. Pedra S., Salmhofer M.: Proceeding of ICMP 2003.
69. Rivasseau V.: J. Stat. Phys.106,693-722 (2002).
70. Afchain S., Magnen J., Rivasseau V.: Ann. Henri Poincare’6,399-448
71. Afchain S., Magnen J., Rivasseau V.: Ann. Henri Poincare’449-483 (2005).
72. Feldman J., Knoerrer H., Trubowitz E.: Comm. Math. Phys.247,1-320 (2004).
73. Shankar, R. Renormalization Grouyp approach to interacting fermions. Rev.Math. Phys.66,129 (1994).
74. Bardeen J, Cooper L N, Schrieffer J R. Phys. Rev.108,1175 (1957).
75. Mastropietro V.: Mass generation in a fermionic model. Comm. Math. Phys.269 (2007), no. 2, 401-424
76. Giuliani A. PHD thesis, Rome University (2005).