Classification of subsystems for local nets with trivial superselection structure

Communications in Mathematical Physics

Volumn 217, Issue 1, 2001, Pages 89-106

  Carpi, Sebastiano ^a   Conti, Roberto ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035529346     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00005550     Document Type: Article

References (47)

1. 1. Araki, H.: Symmetries in the theory of local observables and the choice of the net of local algebras. Rev. Math. Phys. Special Issue, 1-14 (1992)
2. 2. Bargmann, V.: On unitary ray representations of continuous groups. Ann. Math. 59, 1-46 (1954)
3. 3. Baumgärtel, H., Wollenberg, M.: Causal Nets of Operator Algebras. Mathematical Aspects of Algebraic Quantum Field Theory. Berlin: Akademie Verlag, 1992
4. 4. Bertozzini, P., Conti, R., Longo, R.: Covariant sectors with infinite dimension and positivity of the energy. Commun. Math. Phys. 193, 471-492 (1998)
5. 5. Borchers, H.J.: On revolutionizing quantum field theory with Tomita's modular theory. J. Math. Phys. 41, 3604-3673 (2000)
6. 6. Buchholz, D., D'Antoni, C.: Phase space properties of charged fields in theories of local observables. Rev. Math. Phys. 7, 527-557 (1995)
7. 7. Buchholz, D., Doplicher, S., Longo, R., Roberts, J.E.: A new look at Goldstone theorem. Rev. Math. Phys. Special Issue, 47-82 (1992)
8. 8. Buchholz, D., Doplicher, S., Longo, R., Roberts, J.E.: Extension of automorphisms and gauge symmetries. Commun. Math. Phys. 155, 123-134 (1993)
9. 9. Carpi, S.: Absence of subsystems for the Haag-Kastler net generated by the energy-momentum in two dimensional conformal field theory. Lett. Math. Phys. 45. 259-267 (1998)
10. 10. Carpi, S.: Quantum Noether's theorem and conformal field theory: A study of some models. Rev. Math. Phys. 11, 519-532 (1999)
11. 11. Carpi, S.: Classification of subsystems for the Haag-Kastler nets generated by c = 1 chiral current algebras. Lett. Math. Phys. 47, 353-364 (1999)
12. 12. Conti, R.: On the intrinsic definition of local observables. Lett. Math. Phys. 35, 237-250 (1995)
13. 13. Conti, R.: Teoria algebrica dei campi e inclusioni di algebre di von Neumann. Tesi di Dottorato, University of Rome "Tor Vergata" (1996)
14. 14. Conti, R., D'Antoni, C.: Extension of anti-automorphisms and PCT-symmetry. Rev. Math. Phys. 12, 725-738 (2000)
15. 15. Conti, R., Doplicher, S., Roberts, J.E.: Superselection theory for subsystems. Preprint, University of Rome "La Sapienza" (1999); Commun. Math. Phys., to appear
16. 16. D'Antoni, C.: Technical properties of the quasi-local algebra. In: [33]
17. 17. Davidson, D.R.: Classification of subsystems of local algebras. Ph.D. Thesis, University of California at Berkeley (1993)
18. 18. Dixmier, J.: Les C*-algèbres et leurs représentations. Paris: Gauthier Villars, 1964
19. 19. Dixmier, J.: Les algèbres d'opérateurs dans l'espace hilbertien. Paris: Gauthier Villars, 1969
20. 20. Doplicher, S.: Local aspects of superselection rules. Commun. Math. Phys. 85, 73-85 (1982)
21. 21. Doplicher, S.: Progress and problems in algebraic quantum field theory. In: S. Albeverio et al. (eds.), Ideas and Methods in Quantum and Statistical Physics Vol. 2. Cambridge: Cambridge University Press, 1992, pp. 390-404
22. 22. Doplicher, S., Haag, R., Roberts, J.E.: Local observable and particle statistics II. Commun. Math. Phys. 35, 49-85 (1974)
23. 23. Doplicher, S., Longo, R.: Standard and split inclusions of von Neumann algebras. Invent. Math. 75, 493-536 (1984)
24. 24. Doplicher, S., Piacitelli, G.: In preparation
25. 25. Doplicher, S., Roberts, J.E.: Why there is a field algebra with a compact gauge group describing the superselection structure structure in particle physics. Commun. Math. Phys. 131, 51-107 (1990)
26. 26. Driessler, W.: Duality and absence of locally generated sectors for CCR-type algebras. Commun. Math. Phys. 70, 213-220 (1979)
27. 27. Ge, L., Kadison, R. V.: On tensor products of von Neumann algebras. Invent. Math. 123, 453-466 (1996)
28. 28. Guido, D., Longo, R.: Relativistic invariance and charge conjugation in quantum field theory. Commun. Math. Phys. 148, 521-551 (1992)
29. 29. Guido, D., Longo, R.: An algebraic spin and statistics theorem. Commun. Math. Phys. 172, 517-533 (1995)
30. 30. Guido, D., Longo, R., Roberts, J.E., Verch, R.: Charged sectors, spin and statistics in quantum field theory on curved spacetime. Preprint, University of Rome "Tor Vergata" (1999)
31. 31. Haag, R.: Local Quantum Physics. 2nd ed. Berlin-Heidelberg-New York: Springer-Verlag, 1996
32. 32. Kadison, R.V., Ringrose, J.R.: Fundamentals of the theory of operator algebras. Volume II. New York: Academic Press, 1986
33. 33. Kastler, D. ed.: The algebraic theory of superselection sectors. Singapore: World Scientific, 1990
34. 34. Kawahigashi, Y., Longo, R., Müger, M.: Multi-interval subfactor and modularity of representations in conformal field theory. Preprint, University of Rome "Tor Vergata" (1999)
35. 35. Kuckert, B.: A new approach to Spin and Statistics. Lett. Math. Phys. 35, 319-331 (1995)
36. 36. Kuckert, B.: Spin & Statistics, localization regions, and modular symmetries in quantum field theory. Ph.D. Thesis, Universität Hamburg (1998)
37. 37. Langerholc, J., Schroer, B.: On the structure of the von Neumann algebras generated by local functions of the free Bose field. Commun. Math. Phys. 1, 215-239 (1965)
38. 38. Langerholc, J., Schroer, B.: Can current operators determine a complete theory?, Commun. Math. Phys. 4, 123-136 (1967)
39. 39. Longo, R.: Private communication
40. 40. Longo, R., Rehren, K.-H.: Nets of subfactors. Rev. Math. Phys. 7, 567-597 (1995)
41. 41. Müger, M.: Quantum double actions on operator algebras and orbifold quantum field theories. Commun. Math. Phys. 191, 137-181 (1998)
42. 42. Müger, M.: On charged fields with group symmetry and degeneracies of Verlinde's matrix S. Ann. Inst. H. Poincaré 71, 359-394 (1999)
43. 43. Reed, M., Simon, B.: Methods of modern mathematical physics Vol. II, New York: Academic Press, 1975
44. 44. Strǎtilǎ, S., Zsido, L.: The commutation theorem for tensor products over von Neumann subalgebras. J. Funct. Anal. 165, 293-346 (1999)
45. 45. Thomas, L.J. III, Wichmann, E. H.: Standard forms of local nets in quantum field theory. J. Math. Phys. 39, 2643-2681 (1998)
46. 46. Wichmann, E. H.: On systems of local operators and the duality condition. J. Math. Phys. 24. 1633-1644 (1983)
47. 47. Wigner, E.: On unitary representations of the inhomogeneous Lorentz group. Ann. Math. 40, 149-204 (1939)