Perturbative renormalization by flow equations

Reviews in Mathematical Physics

Volumn 15, Issue 5, 2003, Pages 491-558

  Müller, Volkhard F ^a  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

Renormalization group

Indexed keywords

EID: 0041829273     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X03001692     Document Type: Article

References (85)

1. F. J. Dyson, The Radiation theories of Tomonaga, Schwinger, and Feynman, Phys. Rev. 75 (1949), 486-502.
2. F. J. Dyson, The S matrix in quantum electrodynamics, Phys. Rev. 75 (1949), 1736-1755.
3. N. N. Bogoliubov and O. S. Parasiuk, Über die Multiplikation der Kausalfunktionen in der Quantentheorie der Felder, Acta Math. 97 (1957), 227-266.
4. K. Hepp, Théorie de la Renormalisation, Lecture Notes in Physics, Springer, Berlin, 1969.
5. W. Zimmermann, Local Operator Products and Renormalization in Quantum Field Theory, in Lectures on Elementary Particles and Quantum Field Theory, 1970 Brandeis University Summer Institute in Theoretical Physics, Vol. 1, M.I.T. Press, Cambridge, 1970.
6. W. Pauli and F. Villars, On invariant regularization in relativitic quantum theory, Rev. Mod. Phys. 21 (1949), 434-444.
7. E. Speer, Generalized Feynman Amplitudes, Princeton University, Princeton, 1969.
8. G. 't Hooft and M. Veltman, Regularization and renormalization of Gauge fields, Nucl. Phys. B44 (1972), 189-213.
9. C. G. Bollini and J. J. Giambiagi, Lowest order "divergent" Graphs in ν-dimensional space, Phys. Lett. 40B (1972), 566-568.
10. P. Breitenlohner and D. Maison, Dimensional Renormalization and the Action Principle, Comm. Math. Phys. 52 (1977), 11-38.
11. P. Breitenlohner and D. Maison, Dimensionally renormalized Green's functions for theories with massless particles. I, II, Comm. Math. Phys. 52 (1977), 39-54, 55-75.
12. A. S. Wightman and G. Velo (eds.), Renormalization Theory, Erice 1975, Reidel, 1976.
13. W. Zimmermann, Convergence of Bogoliubov's method of renormalization in momentum space, Comm. Math. Phys. 15 (1969), 208-234.
14. J. H. Lowenstein, Convergence theorems for renormalized Feynman integrals with zero-mass propagators, Comm. Math. Phys. 47 (1976), 53-68.
15. G. 't Hooft, Renormalization of massless Yang-Mills fields, Nucl. Phys. B33 (1971), 173-199.
16. G. 't Hooft, Renormalizable Lagrangians for massive Yang-Mills fields, Nucl. Phys. B35 (1971), 167-188.
17. G. 't Hooft and M. Veltman, Combinatorics of Gauge fields, Nucl. Phys. B50 (1972), 318-353.
18. K. G. Wilson, Renormalization group and critical phenomena. I. renormalization group and the Kadanoff scaling picture, Phys. Rev. B4 (1971), 3174-3183.
19. K. G. Wilson, Renormalization group and critical phenomena. II. phase-space-cell analysis of critical behaviour, Phys. Rev. B4 (1971), 3184-3205.
20. K. G. Wilson and J. Kogut, The Renormalization Group and the ε Expansion, Phys. Rep. 12C (1974), 75-199.
21. K. Gawedzki and A. Kupiainen, Gross-Neveu model through convergent perturbation expansions, Comm. Math. Phys. 102 (1985), 1-30.
22. J. Feldman, J. Magnen, V. Rivasseau and R. Sénéor, A renormalizable field theory: the massive Gross-Neveu model in two dimensions, Comm. Math. Phys. 103 (1986), 67-103.
23. D. C. Brydges, Functional Integrals and their Applications, Lausanne lectures 1992, mp-arc 93-24.
24. V. Rivasseau, Constructive Renormalization Theory, arXiv: math-ph/9902023.
25. V. Rivasseau, Prom Perturbative to Constructive Renormalization, Princeton University Press, 1991.
26. G. Gallavotti and F. Nicolo, Renormalization theory in four-dimensional scalar fields I, II, Comm. Math. Phys. 100 (1985), 545-590; 101 (1986), 247-282.
27. G. Gallavotti and F. Nicolo, Renormalization theory in four-dimensional scalar fields I, II, Comm. Math. Phys. 100 (1985), 545-590; 101 (1986), 247-282.
28. G. Gallavotti, Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods, Rev. Mod. Phys. 57 (1985), 471-562.
29. J. S. Feldman, T. R. Hurd, L. Rosen and J. D. Wright, QED: A proof of renormalizability, Springer, Lecture Notes in Physics 312, 1988.
30. J. Polchinski, Renormalization And Effective Lagrangians, Nucl. Phys. B231 (1984), 269-295.
31. P. K. Mitter and T. R. Ramadas, "The two-dimensional O(N) nonlinear σ-model: renormalisation and effective actions, Comm. Math. Phys. 122 (1989), 575-596.
32. 4, Helv. Phys. Acta 65 (1992), 32-52.
33. G. Keller and Ch. Kopper, Perturbative renormalization of composite operators via flow equations I, Comm. Math. Phys. 148 (1992), 445-467.
34. G. Keller and Ch. Kopper, Perturbative renormalization of composite operators via flow equations II: Short distance expansion, Comm. Math. Phys. 153 (1993), 245-276.
35. Ch. Wieczerkowski, Symanzik's improved actions from the viewpoint of the renormalization group, Comm. Math. Phys. 120 (1988), 148-176.
36. 4, Helv. Phys. Acta 66 (1993), 453-470.
37. 4: A simple proof via differential flow equations, Comm. Math. Phys. 161 (1994), 311-323.
38. 4 with flow equations, Comm. Math. Phys. 161 (1994), 515-532.
39. G. Keller and Ch. Kopper, Perturbative renormalization of QED via flow equations, Phys. Lett. B273 (1991), 323-332.
40. G. Keller and Ch. Kopper, Renormalizability proof for QED based on flow equations, Comm. Math. Phys. 176 (1996), 193-226.
41. C. Kim, A renormalization group flow approach to decoupling and irrelevant operators, Ann. Phys. (N.Y.) 243 (1995), 117-143.
42. G. Keller, Ch. Kopper and C. Schophaus, Perturbative renormalization with flow equations in Minkowski space, Helv. Phys. Acta 70 (1997), 247-274.
43. Ch. Kopper and V. P. Müller, Renormalization proof for spontaneously broken Yang-Mills theory with flow equations, Comm. Math. Phys. 209 (2000), 477-516.
44. Ch. Kopper, V. F. Müller and Th. Reisz, Temperature independent renormalization of finite temperature field theory, Ann. Henri Poincaré 2 (2001), 387-402.
45. M. Salmhofer, Renormalization, An Introduction, Springer, 1999.
46. M. Bonini, M. D' Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B409 (1993), 441-464.
47. Ch. Wetterich, Exact evolution equation for the effective potential, Phys. Lett. B301 (1993), 90-94.
48. M. Bonini, M. D'Attanasio and G. Marchesini, Ward identities and Wilson renormalization group in QED, Nucl. Phys. B418 (1994), 81-112.
49. M. Bonini, M. D'Attanasio and G. Marchesini, Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B421 (1994), 429-455.
50. M. Bonini, M. D'Attanasio and G. Marchesini, BRS - symmetry for Yang-Mills theory and exact renormalization group, Nucl. Phys. B437 (1994), 163-186.
51. L. Girardello and A. Zaffaroni, Exact renormalization group equation and decoupling in quantum field theory, Nucl. Phys. B424 (1994), 219-238.
52. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, arXiv: hep-th/ 9607188.
53. M. Bonini and F. Vian, Chiral gauge theories and anomalies in the Wilson renormalization group approach, Nucl. Phys. B511 (1998), 479-494.
54. M. Bonini and F. Vian, Wilson renormalization group for supersymmetric gauge theories and gauge anomalies, Nucl. Phys. B532 (1998), 473-497.
55. M. D' Attanasio and T. R. Morris, Gauge invariance, the quantum action principle, and the renormalization group, Phys. Lett. B378 (1996), 213-221.
56. S. Arnone, Y. A. Kubyshin, T. R. Morris and J. F. Tighe, A gauge invariant regulator for the ERG, Int. J. Mod. Phys. A16 (2001), 1989.
57. U. Ellwanger, Flow equations and BRS invariance for Yang-Mills theories, Phys. Lett. B335 (1994), 364-370.
58. U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Phys. C69 (1996), 687-697.
59. U. Ellwanger, Confinement, monopoles and Wilsonian effective action, Nucl. Phys. B531 (1998), 593-612.
60. M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B417 (1994), 181-214.
61. M. Reuter and C. Wetterich, Exact evolution equation for scalar electrodynamics, Nucl. Phys. B427 (1994), 291-324.
62. M. Reuter and C. Wetterich, Gluon condensation in nonperturbative flow equations, Phys. Rev. D56 (1997), 7893-7916.
63. H. Gies, Running coupling in Yang-Mills theory - a flow equation study, Phys. Rev. D66 (2002), 025006.
64. O. Lauscher and M. Reuter, Towards nonperturbative renormalizability of quantum Einstein gravity, Int. J. Mod. Phys. A17 (2002), 993-1002.
65. O. Lauscher and M. Reuter, Is quantum Einstein gravity nonperturbatively renormalizable? Class. Quant. Grav. 19 (2002), 483-492.
66. C. Bagnuls and C. Bervillier, Exact renormalizsation group equations. An introductory review, Phys. Rep. 348 (2001), 91-157.
67. Ch. Kopper, Renormierungstheorie mit Flussgleichungen, Shaker Verlag, Aachen, 1998.
68. J. Glimm and A. Jaffe, Quantum Physics, Sec. ed., Springer, New York, 1987, Chap. 9.1.
69. T. Hida, Stationary Stochastic Processes, Princeton, 1970, Theo. 4.2.
70. Y. Yamasaki, Measures on Infinite Dimensional Spaces, World Scientific, Singapore, 1985, Part A, Theo. 17.1.
71. Ch. Kopper and F. Meunier, Large momentum bounds from flow equations, Ann. Henri Poincaré 3 (2002), 435-449.
72. S. Weinberg, High energy behaviour in quantum field theory, Phys. Rev. 118 (1960), 838-849.
73. N. P. Landsman and C. van Weert, Real- and imaginary-time field theory at finite temperature and density, Phys. Rep. 145 (1987), 141-249.
74. N. Bourbaki, Fonctions d'une variable réelle, Editions Hermann, Paris, 1976, Chap. 6.
75. Y. M. P. Lam, Perturbation Lagrangian theory for scalar fields - Ward-Takahashi identity and current algebra, Phys. Rev. D6 (1972), 2145-2161.
76. Y. M. P. Lam, Equivalence theorem on Bogoliubov-Parasiuk-Hepp-Zimmermann-renormalized Lagrangian field theories, Phys. Rev. D7 (1973), 2943-2949.
77. J. H. Lowenstein, Differential vertex operations in Lagrangian field theory, Comm. Math. Phys. 24 (1971), 1-21.
78. O. Piguet and S. P. Sorella, Algebraic Renormalization, Springer, Berlin, 1995.
79. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, Sec. ed., Clarendon Press, Oxford, 1993.
80. A. A. Slavnov, Math. Theor. Phys. 10 (1972), 99.
81. J. C. Taylor, Ward identities and charge renormalization of the Yang-Mills field, Nucl. Phys. B33 (1971), 436-444.
82. C. Becchi, A. Rouet and R. Stora, Renormalization of the Abelian Higgs-Kibble Model, Comm. Math. Phys. 42 (1975), 127-162.
83. C. Becchi, A. Rouet and R. Stora, Renormalization of gauge theories, Ann. Phys. (N.Y.) 98 (1976), 287-321.
84. L. D. Faddeev and A. A. Slavnov, Gauge Fields: Introduction to Quantum Theory, Benjamin, Reading MA, 1980.
85. V. F. Müller, Perturbative renormalization by flow equations, arXiv hep-th/0208211, Proposition 4.4.