Thermal States in Conformal QFT. I

Communications in Mathematical Physics

Volumn 309, Issue 3, 2012, Pages 703-735

  Camassa, Paolo ^a   Longo, Roberto ^a   Tanimoto, Yoh ^a   Weiner, Mihály ^a,b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84856107023     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-011-1337-3     Document Type: Article

References (31)

1. Araki H., Haag R., Kastler D., Takesaki M.: Extension of KMS states and chemical potential. Commun. Math. Phys. 53, 97-134 (1977).
2. Araki H., Zsido L.: Extension of the structure theorem of Borchers and its application to half-sided modular inclusions. Rev. Math. Phys. 17, 491-543 (2005).
3. Brunetti R., Guido D., Longo R.: Modular structure and duality in conformal Quantum Field Theory. Commun. Math. Phys. 156, 201-219 (1993).
4. Buchholz D., Junglas P.: On the existence of equilibrium states in Local Quantum Field Theory. Commun. Math. Phys. 121, 255-270 (1989).
5. Bratteli O., Robinson D.: Operator Algebras and quantum statistical mechanics. Vol. 2, Springer Verlag, Berlin- Heidelberg-New York (1997).
6. Camassa, P., Longo, R., Tanimoto, Y., Weiner, M.: Thermal states in conformal QFT II. arXiv: 1109. 2064.
7. Carpi S.: On the representation theory of Virasoro nets. Commun. Math. Phys. 244, 261-284 (2005).
8. Carpi S., Weiner M.: On the uniqueness of diffeomorphism symmetry in conformal field theory. Commun. Math. Phys. 258, 203-221 (2005).
9. Fröhlich J., Gabbiani F.: Operator algebras and conformal field theory. Commun. Math. Phys. 155(3), 569-640 (1993).
10. Guido D., Longo R., Roberts J. E., Verch R.: Charged sectors, spin and statistics in quantum field theory on curved spacetimes. Rev. Math. Phys. 13, 125-198 (2001).
11. Haag R.: Local Quantum Physics. Springer-Verlag, Berlin-Heidelberg-New York (1996).
12. Izumi M.: Subalgebras of infinite C*-algebras with finite Watatani indices. I. Cuntz algebras. Commun. Math. Phys. 155, 157-182 (1993).
13. Kawahigashi Y., Longo R., Müger M.: Multi-interval subfactors and modularity of representations in conformal field theory. Commun. Math. Phys. 219, 631-669 (2001).
14. Kawahigashi Y., Longo R.: Classification of local conformal nets. Case c < 1. Ann. of Math. 160, 493-522 (2004).
15. Kawahigashi Y., Longo R.: Classification of Two-Dimensional Local Conformal nets with c < 1 and 2-cohomology vanishing for tensor categories. Commun. Math. Phys. 244, 63-97 (2004).
16. Kosaki H.: Extension of Jones' theory on index to arbitrary factors. J. Funct. Anal. 66(1), 123-140 (1986).
17. Longo R.: Notes for a Quantum Index Theorem. Commun. Math. Phys. 222, 45-96 (2001).
18. Longo R.: Conformal subnets and intermediate subfactors. Commun. Math. Phys. 237(1-2), 7-30 (2003).
19. Longo, R.: Real Hilbert subspaces, modular theory, Real Hilbert subspaces, modular theory, SL(2; ℝ) and CFT and CFT. In: Von Neumann algebas in Sibiu, Theta Series in Advanced Mathematics. Bucharest: Theta, 2008, pp. 33-91.
20. Longo R., Rehren K.-H.: Nets of subfactors. Rev. Math. Phys. 7(4), 567-597 (1995).
21. Longo R., Xu F.: Topological sectors and a dichotomy in conformal field theory. Commun. Math. Phys. 251(2), 321-364 (2004).
22. Pimsner M., Popa S.: Entropy and index for subfactors. Ann. Sci. Ec. Norm. Sup. 19, 57-106 (1986).
23. Popa, S.: Classification of subfactors and their endomorphisms. CBMS Regional Conference Series in Mathematics86, Providence, RI: Amer. Math. Soc, 1995.
24. Schroer B., Wiesbrock H.-W.: Looking beyond the thermal horizon: hidden symmetries in chiral models. Rev. Math. Phys. 12(3), 461-473 (2000).
25. Takesaki M.: Theory of operator algebras II. Encyclopaedia of Mathematical Sciences, 125. Springer-Verlag, Berlin (2003).
26. Takesaki M., Winnink M.: Local normality in quantum statistical mechanics. Commun. Math. Phys. 30, 129-152 (1973).
27. Tanimoto Y.: Ground state representations of loop algebras. Ann. Henri Poincaré 12(4), 805-827 (2011).
28. Weiner M.: Conformal covariance and positivity of energy in charged sectors. Commun. Math. Phys. 265, 493-506 (2006).
29. Weiner, M.: An algebraic Haag's theorem. Commun. Math. Phys. (to appear), available at http://arxiv.org/abs/1006.4726v1 [math-ph], 2010.
30. Wiesbrock H.-W.: Half-sided modular inclusions of von-Neumann-algebras. Commun. Math. Phys. 157, 83-92 (1993).
31. Xu F.: Jones-Wassermann subfactors for disconnected intervals. Commun. Contemp. Math. 2, 307-347 (2000).