A non-Abelian square root of Abelian vertex operators

Journal of Mathematical Physics

Volumn 39, Issue 6, 1998, Pages 3073-3090

  Frieler, K ^a   Rehren, K H ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032363395     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532240     Document Type: Article

References (26)

1. A. S. Wightman, "Introduction to some aspects of the relativistic dynamics of quantized fields," in Cargèse Lectures in Theoretical Physics, edited by M. Levy (Gordon and Breach, New York, 1967), pp. 171-291.
2. E. H. Lieb, T. D. Schultz, and C. D. Mattis, "Two soluble models of an antiferromagnetic chain," Ann. Phys. (N.Y.) 16, 407-466 (1961); B. M. McCoy, "Spin correlation functions of the X-Y model," Phys. Rev. 173, 531-541 (1968).
3. E. H. Lieb, T. D. Schultz, and C. D. Mattis, "Two soluble models of an antiferromagnetic chain," Ann. Phys. (N.Y.) 16, 407-466 (1961); B. M. McCoy, "Spin correlation functions of the X-Y model," Phys. Rev. 173, 531-541 (1968).
4. B. Schroer and T. T. Truong, "The order/disorder quantum field operators associated with the two-dimensional Ising model in the continuum limit," Nucl. Phys. B 144, 80-122 (1978).
5. L. P. Kadanoff, "Correlations along a line in the two-dimensional Ising model," Phys. Rev. 188, 859-863 (1969); H. Ceva and L. P. Kadanoff, "Determination of an operator algebra for the two-dimensional Ising model," Phys. Rev. B 3, 3918-3939 (1971).
6. L. P. Kadanoff, "Correlations along a line in the two-dimensional Ising model," Phys. Rev. 188, 859-863 (1969); H. Ceva and L. P. Kadanoff, "Determination of an operator algebra for the two-dimensional Ising model," Phys. Rev. B 3, 3918-3939 (1971).
7. ∞ functions in spacelike directions," Nuovo Cimento 33, 1600-1613 (1964).
8. K.-H. Rehren and B. Schroer, "Exchange algebra on the light-cone and order/disorder 2n-point functions in the Ising field theory," Phys. Lett. B 198, 84-88 (1987).
9. A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, "Infinite dimensional symmetries in two-dimensional quantum field theory," Nucl. Phys. B 241, 333-380 (1984).
10. P. Goddard, A. Kent, and D. Olive, "Unitary representations of the Virasoro and super-Virasoro algebras," Commun. Math. Phys. 103, 105-119 (1986).
11. L. V. Belvedere, K. D. Rothe, B. Schroer, and J. A. Swieca, "Generalized two-dimensional abelian gauge theories and confinement," Nucl. Phys. B 153, 112-140 (1979).
12. V. G. Knizhnik and A. B. Zamolodchikov, "Current algebra and Wess-Zumino model in two dimensions," Nucl. Phys. B 247, 83-103 (1984).
13. E. Witten, "Non-abelian bosonization in two dimensions," Commun. Math. Phys. 92, 455-472 (1984).
14. K. Frieler, "Nicht-abelsche Faktorisierungen abelscher Vertex-Operatoren," Diploma thesis, Hamburg University, 1997 (in German).
15. H. Lehmann and J. Stehr, "The Bose field structure associated with a free massive Dirac field in one space dimension," DESY preprint 76-29, 1976.
16. B. Schroer and J. A. Swieca, "Conformal transformations for quantized fields," Phys. Rev. D 10, 480-485 (1974).
17. A. L. Carey, S. N. M. Ruijsenaars, and J. D. Wright, "The massless Thirring model: positivity of Klaiber's n-point functions," Commun. Math. Phys. 99, 347-364 (1985).
18. S. Mandelstam, "Soliton operators for the quantized sine-Gordon equation," Phys. Rev. D 11, 3026-3030 (1975).
19. K.-H. Rehren, "Bounded Bose fields," Lett. Math. Phys. 40, 299-306 (1997).
20. B. Schroer, J. A. Swieca, and A. H. Völkel, "Global operator expansions in conformally invariant relativistic quantum field theory," Phys. Rev. D 11, 1509-1520 (1975).
21. K. Fredenhagen, K.-H. Rehren, and B. Schroer, "Superselection sectors with braid group statistics and exchange algebras, II," Rev. Math. Phys. (Special Issue), 113-157 (1992).
22. M. Jörß, "The construction of pointlike localized charged fields from conformal Haag-Kastler nets," Lett. Math. Phys. 38, 257-274 (1996).
23. I. B. Frenkel, J. Lepowsky, and A. Meurman, "Vertex operator algebras and the monster," Pure and Applied Mathematics (Boston, Academic, New York, 1988); Vol. 8. especially Chap. 8.
24. I. B. Frenkel and V. G. Kac, "Basic representations of affine Lie algebras and dual resonance models," Invent. Math. 62, 23-66 (1980).
25. K.-H. Rehren, "Space-time fields and exchange fields," Commun. Math. Phys. 132, 461-483 (1990).
26. G. C. Hegerfeldt, "Prime field decomposition and infinitely divisible states on Borchers' tensor algebra," Commun. Math. Phys. 45, 137-151 (1975).