Abstract
Causal fields in conformal QFT 2 yield a new algebra structure: the exchange algebra in which “braid” matrices (special Yang-Baxter structures) appear. They are directly related to the possible dimensional spectra of local fields. The Virasoro structure, i.e. the central extension charge (=Casimir energy) is part of the representation theory. An extension of Unruh’s idea allows us to calculate correlation functions of arbitrary conformal QFT’s on higher genus Riemann surfaces directly in terms of the flat space correlations. As a generalization of Hawking’s temperature, the new positive definite states are characterized by 3g — 3 “temperatures”.
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References
J.E. Wess, Nuovo Cimento 18, 1086 (1960).
H.A. Kastrup, Ann. Phys. 7, 388 (1962).
L. Castell, Nucl. Phys. B4, 343 (1967).
R.F. Streater and A.S. Wightman, “PCT, Spin and Statistics, And All That”, Mathematical Physics Monograph Series, Benjamin Inc. (1964).
R. Jost, “General Theory of Quantized Fields”, Americ. Math. Soc. Publication (1963).
A.A. Migdal, Phys. Lett. 37B, 98 (1971).
A.A. Migdal, Phys. Lett. 37B, 383 (1971).
A.M. Polyakov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 12, 583 (1970).
A.M. Polyakov, Sov. Phys. JETP Lett. 12, 381 (1970).
G. Mack and K. Szymanzik, Commun. Math. Phys. 27, 247 (1972).
M. Hortacsu, R. Seiler and B. Schroer, Phys. Rev. D2, 2519 (1972).
J.A. Swieca and A.H. Volkel, Commun. Math. Phys. 29, 319 (1973).
B. Schroer and J.A. Swieca, Phys. Rev. D10, 480 (1974).
B. Schroer, J.A. Swieca and A.H. Volkel, Phys. Rev. Dll, 1509 (1975).
M. Lüscher and G. Mack, Commun. Math. Phys. 41, 203 (1975).
M. Lüscher, Commun. Math. Phys. 50, 23 (1976).
G. Mack, Commun. Math. Phys. 53, 155 (1977).
J. Kupsch, W. Rühl and B.C. Yunn, Ann. Phys. (N.Y.). 89, 115 (1975).
A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Nucl. Phys. B241, 333 (1984).
D. Friedan, Z. Qiu and S. Shenker, Phys. Rev. Lett. 52, 1575 (1984).
P. Goddard, A. Kent and P. Olive, Commun. Math. Phys. 103, 105 (1986).
V.J.S. Dotsenko and V.A. Fateev, Nucl. Phys. B240, 312 (1984).
V.G. Kac, Lecture Notes in Physics. 94, 441 (1979).
B.L. Feigin and D.B. Fuchs, Funct. Anal. Appl. 16, 144 (1982).
B.L. Feigin and D.B. Fuchs, Funct. Anal. Appl. 17, 241 (1983).
K.H. Rehren and B. Schroer, “Quasiprimary Fields: An Approach to Positivity of 2D Conformal Quantum Field Theory”, FU Berlin preprint (July 1987).
K.H. Rehren and B. Schroer, “Exchange Algebra on the Light-Cone and Order/Disorder 2n-Point Function in the Ising Field Theory”, FU Berlin preprint (June 1987), to be published in Phys. Lett. B.
B. Schroer “Operator Approach to Conformal Invariant Quantum Field Theories and Related Problems”, CERN-TH 4566/87, (1987) Nucl. Phys. B295 [FS21],4 (1988).
J. Cardy, Nucl. Phys. B270 (FS16), 186 (1986).
B. Klaiber, Lecture Notes in Theoretical Physics, Boulder Lectures (1967), Gordon and Breach N.Y.
S. Mandelstam, Phys. Rev. Dll, 3026 (1975).
S. Coleman, Phys. Rev. Dll, 2088 (1975).
J.B. Frenkel and V. G. Kac, Invent. Math. 62, 23 (1980).
V.G. Kac and D.H. Peterson, Adv. in Mathematics, 53, 125 (1984)
A. Rocha-Caridi, in: “Vertex Operators in Mathematics and Physics”, eds. J. Lepowski, S. Mandelstam and I. Singer, M.S.R.I. 3, 451, Springer, Berlin-New-York (1984).
E. Witten, Comm. Math. Phys. 92 (1984) 455.
D. Gepner and E. Witten, Nucl. Phys. B278, 493 (1986).
V.G. Kinshnik and A.B. Zamolodchikov, Nucl. Phys. B247, 83 (1984).
K.H. Rehren, “Locality of Conformal Fields In Two Dimensions: Exchange Algebra On The Light Cone”, FUB preprint (Sept. 87).
R. Longo, “Algebraic and modular structure of von Neumann algebras of physics”, in: Proceedings of Symposia in Pure Mathematics 38, 2, Providence; Am. Math. Society (1982).
A. Connes, “Classification des factures”, in: Proceedings of Symposia in Pure Mathematics 38, 2, Providence; Am. Math. Society (1982).
A.M. Polyakov, Phys. Letters. 103B, 207 (1981).
B. Schroer, R. Seiler and J.A. Swieca, Phys. Rev. D2, 12 (1970) 2927.
L. Alvarez-Gaumé, Lectures given at this school.
W.G. Unruh, Phys. Rev. D14, 870 (1976).
S.W. Hawking, Phys. Rev. 43, 199 (1975).
E. Verlinde and H. Verlinde, “Chiral Bosonization, Determinants and the String Partition Function”, University of Utrecht preprint (1986).
M. Martinelli and N. Sanchez, Phys. Lett. B192, 361 (1987).
M.A. Neimark, Normierte Algebra, Berlin V.E.B. Deutscher Verlag der Wissenschaften 1959.
R. Haag, N.M. Hugenholts and M. Winnink, Commun. Math. Phys. 5, 214 (1979). 47 L. Bers, “Riemann Surfaces”, Lecture Notes, New York University, Inst, of Math. Sciences, Lecture Notes 1957.
A. Capelli, C. Itzykson and H.B. Zuber, Nucl. Phys. B, to appear.
E. Witten, in: “Geometry, Anomalies, Topology”, W.A. Bardeen and A.R. White (eds.), World Scientific (1985).
A.M. Polyakov, Phys. Lett. 103B, 211 (1981).
B. Schroer, “on Non-Commutative Geometry And Its Possible Role In Physics”, PUC Rio de Janeiro preprint, March 88.
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© 1988 Plenum Press, New York
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FU Berlin. (1988). New Methods and Results in Conformal QFT2 and the “String Idea”. In: ’t Hooft, G., Jaffe, A., Mack, G., Mitter, P.K., Stora, R. (eds) Nonperturbative Quantum Field Theory. Nato Science Series B:, vol 185. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0729-7_24
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DOI: https://doi.org/10.1007/978-1-4613-0729-7_24
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