Two-dimensional models as testing ground for principles and concepts of local quantum physics

Annals of Physics

Volumn 321, Issue 2, 2006, Pages 435-479

  Schroer, Bert ^a,b  

^a CENTRO BRASILEIRO DE PESQUISAS FÍSICAS   (Brazil)

^b FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 30944432999     PISSN: 00034916     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aop.2005.08.002     Document Type: Article

References (115)

1. W. Lenz Physikalische Zeitschrift 21 1920 613
2. E. Ising Z. f. Physik 31 1925 253
3. K. Reich, contribution (1999) about the history of physics at the University of Hamburg in the Festschrift "80 Jahre Universitaet Hamburg".
4. W. Heisenberg Z. Phys. 49 1928 619
5. R. Peierls Proc. Cambridge Phil. Soc. 32 1936 477
6. H.A. Kramers G.H. Wannier Phys Rev. 60 1941 252 263
7. A.A. Belavin A.M. Polyakov A.B. Zamolodchikov Nucl. Phys. B 241 1984 333
8. J. Mund Lett. Math. Phys. 43 1998 319
9. J. Mund J. Math. Phys. 44 2003 2037
10. P. Jordan Beiträge zur Neutrinotheorie des Lichts, Zeitschr. für Physik 114 1937 229 and earlier papers quoted therein
11. B. Klaiber A.O. Barut W.E. Brittin Lectures in Theoretical Physics vol. 10A 1968 Gordon and Breach New York 141-176
12. W. Thirring Ann. Phys. 3 1958 91
13. J.M. Luttinger J. Math. Phys. 4 1963 1154
14. A. Pais Inward Bound 1986 Clarendon Press Oxford University Press
15. S. Coleman Phys. Rev. D 11 1975 2088
16. J. Schwinger Phys. Rev. 128 1962 2425 and Gauge Theory of Vector Particles, in: Theoretical Physics Trieste lectures 1962 Wien IAEA 1963
17. J.H. Lowenstein J.A. Swieca Ann. Phys. 68 1971 172
18. E. Abdalla M.C.B. Abdalla K. Rothe Non-perturbative Methods in Two-dimensional Quantum Field Theory 1991 World Scientific Singapore
19. N. Nielsen B. Schroer Nucl. Phys. B 127 1977 493
20. O.A. Castro Alvaredo, Bootstrap Methods in 1+1-Dimensional Quantum Field Theories: The Homogenous Sine-Gordon Models, FU-Thesis. Available from: < hep-th/0109212>.
21. J. Glimm A. Jaffe Quantum Physics. A Functional Integral Point of View 1987 Springer Berlin
22. R. Jackiw, Topological aspects of gauge theories. Available from: < hep-th/0501178>.
23. J. Swieca Phys. Rev. D 13 1976 312
24. R.F. Streater A.S. Wightman PCT, Spin and Statistics and All That 1964 Benjamin New York
25. P. Furlan G. Sotkov I. Todorov Riv. Nuovo Cim. 12 1989 1-203
26. P. Ginsparg, Applied conformal field theory, in fields, strings and critical phenomena, in: E. Brezin, J. Zinn-Justin, Les Houches 1988, North Holland, Amsterdam, 1990.
27. P. Di Francesco P. Mathieu D. Sénéchal Conformal Field Theory 1996 Springer Berlin, Heidelberg, New York
28. R. Haag Local Quantum Physics 1992 Springer Berlin-Heidelberg
29. S. Carpi R. Conti Commun. Math. Phys. 253 2005 423
30. S. Coleman J. Mandula Phys. Rev. 159 1967 1251
31. R. Brunetti K. Fredenhagen R. Verch Commun. Math. Phys. 237 2003 31
32. R. Brunetti and K. Fredenhagen, Algebraic Approach to Quantum Field Theory. Available from: .
33. R. Brunetti D. Guido R. Longo Commun. Math. Phys. 156 1993 201
34. Y. Kawahigashi R. Longo M. Mueger Commun. Math. Phys. 219 2001 631
35. S. Doplicher R. Longo Inv. Math. 75 1984 493
36. S. Doplicher R. Haag J.E. Roberts Commun. Math. Phys. 23 1971 199
37. S. Doplicher R. Haag J.E. Roberts Commun. Math. Phys. 35 1974 49
38. S. Doplicher J.E. Roberts Commun. Math. Phys. 131 1990 51
39. J.J. Bisognano E.H. Wichmann J. Math. Phys. 16 1975 985
40. S. Summers, Tomita-Takesaki modular theory, in: Encyclopedia of Mathematical Physics (to appear).
41. J. Mund Ann. H. Poinc. 2 2001 907
42. B. Schroer Ann. Phys. 319 2005 48
43. R. Brunetti D. Guido R. Longo Rev. Math. Phys. 14 2002 759
44. L. Fassarella B. Schroer J. Phys. A 35 2002 9123
45. J. Mund, String-localized quantum fields. Available from: .
46. J. Mund B. Schroer J. Yngvason Phys. Lett. B 596 2004 156
47. B. Schroer Int. J. Mod. Phys. B 6 1992 2041
48. D. Buchholz G. Mack I. Todorov Nucl. Phys. B, Proc. Suppl. B 5 1988 20
49. C.P. Staszkiewicz, Die lokale Struktur abelscher Stromalgebren auf dem Kreis, PhD thesis, Fu-Berlin 1995.
50. S.R. Coleman Commun. Math. Phys. 31 1973 259
51. I. Frenkel J. Lepowski A. Meurman Vertex Operators and the Monster 1988 Academic Press New York
52. D. Buchholz Nucl. Phys. B 496 1996 333
53. R. Dashen, Y. Frishman, Thirring model with U(n) symmetry, Institute for Advanced Study Princeton report 1973 (unpublished).
54. P.K. Mitter P.H. Weisz Phys. Rev. D 8 1973 4410
55. B. Schroer, A trip to Scalingland, Brazilian Symposium on Theoretical physics, Rio de Janeiro, January 1974, vol. I, ed. Erasmo Ferreira, Livros Técnicos e Cientificos, Editora S.A.
56. H. Babujian M. Karowski Int. J. Mod. Phys. A 19 2004 34
57. B. Mc Coy C.A. Tracy T.T. Wu Phys. Rev. Lett. 38 1977 793
58. B. Schroer T.T. Truong Phys. Lett. B 72 1978 149
59. K.-H. Rehren B. Schroer Phys. Lett. B 198 1987 84
60. K. Frieler K.-H. Rehren J. Math. Phys. 39 1998 3073-3090
61. R. Koeberle E.C. Marino Phys. Lett. B 126 1983 475
62. M. Lüscher G. Mack Commun. Math. Phys. 41 1975 203
63. I.E. Segal, Causality and Symmetry in Cosmology and the Conformal Group, Montreal 1976, in: Proceedings, Group Theoretical Methods in Physics, New York 1977, 433 and references therein to earlier work of the same author.
64. B. Schroer J.A. Swieca Phys. Rev. D 10 1974 480
65. B. Schroer J.A. Swieca A.H. Voelkel Phys. Rev. D 11 1975 11
66. N.M. Nicolov I.T. Todorov Int. J. Mod. Phys. A 19 2004 3605
67. N.M. Nicolov, I.T. Todorov, K.-H. Rehren, Partial wave expansion and Wightman positivity in conformal field theory. Available from: < hep-th/0504146>.
68. D. Friedan Z. Qiu S. Shenker Phys. Rev. Lett. 52 1984 1575
69. K.H. Rehren B. Schroer Nucl. Phys. B 229 1988 229
70. G. Moore N. Seiberg Commun. Math. Phys. 123 1989 177
71. F. Gabbiani J. Froehlich Commun. Math. Phys. 155 1993 569
72. O.W. Greenberg Ann. Phys. 16 1961 158
73. J. Lowenstein Commun. Math. Phys. 6 1967 49
74. K. Baumann Commun. Math. Phys. 47 1976 67
75. E. Witten Comm. Math. Phys. 92 1984 455
76. B. Schroer Phys. Lett. B 506 2001 337
77. R. Longo K.-H. Rehren Rev. Math. Phys. 7 1995 567
78. Y. Kawahigashi and R. Longo, Classification of local conformal nets, case c < 1. Available from: < math-ph/0201015>.
79. Y. Kawahigashi R. Longo Commun. Math. Phys. 244 2004 63
80. Y. Kawahigashi, R. Longo, K.-H. Rehren, The classification of non-local CFT with c < 1. Available from: < math-OA/0505130>
81. H.-J. Borchers J. Math. Phys. 41 2000 3604
82. J. Yngvason, The role of type III factors in quantum field theory. Available from: .
83. B. Schroer, New constructions in local quantum physics. Available from: .
84. R. Kaehler H.-W. Wiesbrock J. Math. Phys. 42 2000 74
85. B. Schroer H.-W. Wiesbrock Rev. Math. Phys. 12 2000 139
86. L. Fassarella B. Schroer Phys. Lett. B 538 2002 415
87. R. Longo F. Xu Topological Sectors and a Dichotomy in Conformal Field Theory Commun. Math. Phys. 251 2004 321
88. 1) covariance (in preparation).
89. S. Carpi, M. Weiner, On the Uniqueness of Diffeomorphism Symmetry in Conformal Quantum Field Theory. Available from: .
90. O. Lehto K.I. Virtanen Quasiconformal Maps in the Plane 1973 Springer New York
91. K.-H. Rehren, QFT Lectures on AdS-CFT. Available from: .
92. K.H. Rehren B. Schroer Nucl. Phys. B 312 1989 715
93. K. Fredenhagen, K.-H. Rehren, B. Schroer, Rev. Math. Phys. SI1 (special issue) (1992) 113.
94. G. Mack V. Schomerus Nucl. Phys. B 370 1992 185
95. J. Cardy, Boundary Conformal Field Theory. Available from: , contribution to this encyclopedia.
96. Yi-Zhi Huang, Vertex operator algebras, the Verlinde conjecture and modular tensor categories. Available from: < math-QA/0412261>.
97. A. Klein L. Landau J. Funct. Anal. 42 1981 368
98. K.-H. Rehren Commun. Math. Phys. 208 2000 689
99. J. Bros D. Buchholz Nucl. Phys. B 429 1994 291
100. E. Verlinde Nucl. Phys. 300 1988 360
101. R. Longo K.-H. Rehren Rev. Math. Phys. 16 2004 909
102. H.J. Borchers, D. Buchholz, B. Schroer, Commun. Math. Phys. 219 (2001) 125. Available from: .
103. G. Lechner, Towards the construction of quantum field theories from a factorizing S-matrix. Available from: and references therein.
104. M. Karowski P. Weisz Nucl. Phys. B 139 1978 445
105. B. Schroer J.A. Swieca Nucl. Phys. B 121 1977 505-513
106. K. Fredenhagen, in: D. Kaster (Ed.), Algebraic Theory of Superselection Sectors, Introduction and Recent Results, World Scientific, Singapore, 1990, Proceedings of the 1989 Palermo Conference.
107. M. Mueger Rev. Math. Phys. 10 1998 1147
108. F. Dashen B. Hasslacher A. Neveu Phys. Rev. D 11 1975 3424
109. B. Schroer T.T. Truong P. Weisz Ann. Phys. (N.Y.) 102 1976 156
110. M. Karowski H.-J. Thun T.T. Truoung P. Weisz Phys. Lett. B 67 1977 321
111. M. Karowski P. Weisz Phys. Rev. B 139 1978 445
112. A.B. Zamolodchikov Al.B. Zamolodchikov Ann. Phys. (N.Y.) 120 1979 253
113. F.A. Smirnov, Advance Series in Mathematical Physics, vol. 14, World Scientific, Singapore, 1992.
114. S.S. Schweber QED and the Men Who Made it; Dyson, Feynman, Schwinger and Tomonaga 1994 Princeton University Press Princeton
115. J. Mund, B. Schroer, J. Yngvason, String-localized quantum fields and modular localization (in preparation).