Ground State Representations of Loop Algebras

Annales Henri Poincare

Volumn 12, Issue 4, 2011, Pages 805-827

  Tanimoto, Yoh ^a  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79953690786     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-011-0095-2     Document Type: Article

References (22)

1. Baumgärtel H.: Operator Algebraic Methods in Quantum Field Theory. Akademie Verlag, Berlin (1995).
2. Bratteli, O., Robinson, D. W.: Operator algebras and quantum statistical mechanics. 1. C*- and W*-Algebras, Symmetry Groups, Decomposition of States. Texts and Monographs in Physics, 2nd edn. Springer, New York (1987).
3. Bratteli, O., Robinson, D. W.: Operator algebras and quantum statistical mechanics. 2. Equilibrium States. Models in Quantum Statistical Mechanics. Texts and Monographs in Physics, 2nd edn. Springer, Berlin (1997).
4. Buchholz D., Schulz-Mirbach H.: Haag duality in conformal quantum field theory. Rev. Math. Phys. 2(1), 105-125 (1990).
5. Camassa, P., Longo, R., Tanimoto, Y., Weiner, M.: [arXiv: 1101. 2865].
6. Carpi S.: On the representation theory of Virasoro nets. Commun. Math. Phys. 244(2), 261-284 (2004).
7. Di Francesco, P., Mathieu, P., Sénéchal, D.: Conformal field theory. In: Graduate Texts in Contemporary Physics. Springer, New York (1997).
8. Furlan P., Sotkov G. M., Todorov I. T.: Two-dimensional conformal quantum field theory. Riv. Nuovo Cimento (3) 12(6), 1202 (1989).
9. Gabbiani F., Fröhlich J.: Operator algebras and conformal field theory. Commun. Math. Phys. 155(3), 569-640 (1993).
10. Garland H.: The arithmetic theory of loop algebras. J. Algebra 53(2), 480-551 (1978).
11. Kawahigashi Y., Longo R.: Classification of local conformal nets. Case c & 1. Ann. Math. (2) 160(2), 493-522 (2004).
12. Kawahigashi Y., Longo R., Müger M.: Multi-interval subfactors and modularity of representations in conformal field theory. Commun. Math. Phys. 219(3), 631-669 (2001).
13. Milnor, J.: Remarks on infinite-dimensional Lie groups. In: Relativity, groups and topology, II (Les Houches, 1983), pp. 1007-1057. North-Holland, Amsterdam (1984).
14. Neeb, K.-H.: On differentiable vectors for representations of infinite dimensional lie groups. [arXiv: 1002. 1602].
15. Pressley, A., Segal, G.: Loop Groups. Oxford Mathematical Monographs. Oxford University Press, New York (1986).
16. Roberts J. E.: Some applications of dilatation invariance to structural questions in the theory of local observables. Commun. Math. Phys 37, 273-286 (1974).
17. Schottenloher, M.: A Mathematical Introduction to Conformal Field Theory. Lecture Notes in Physics, 2nd edn., vol. 759. Springer, Berlin (2008).
18. Tanimoto, Y.: Covariant representations of Diff(R) (in preparation).
19. 1). Internet J. Math. (in press).
20. Toledano Laredo V.: Positive energy representations of the loop groups of non-simply connected Lie groups. Commun. Math. Phys. 207(2), 307-339 (1999).
21. Wassermann A.: Operator algebras and conformal field theory. III. Fusion of positive energy representations of LSU(N) using bounded operators. Invent. Math. 133(3), 467-538 (1998).
22. Xu F.: Algebraic coset conformal field theories. Commun. Math. Phys. 211(1), 1-43 (2000).