Borchers' commutation relations for sectors with braid group statistics in low dimensions

Annales Henri Poincare

Volumn 10, Issue 1, 2009, Pages 19-34

  Mund, Jens ^a  

^a FEDERAL UNIVERSITY OF JUIZ DE FORA   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 63949087354     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-009-0403-2     Document Type: Article

References (36)

1. C Adler, Braid group statistics in two-dimensional quantum field theory, Rev. Math. Phys. 7 (1996), 907-924.
2. P. Bertozzini, R. Conti, and R. Longo, Covariant sectors with infinite dimension and positivity of the energy, Commun. Math. Phys. 141 (1998), 471-492.
3. H. J. Borchers, Local rings and the connection of spin with statistics, Commun. Math. Phys. 1 (1965), 281-307.
4. H. J. Borchers, The CPT-theorem in two-dimensional theories of local observables, Commun. Math. Phys. 143 (1992), 315-332.
5. H. J. Borchers, On Poincaré transformations and the modular group of the algebra associated with a wedge, Lett. Math. Phys. 46 (1998), 295-301.
6. H. J. Borchers, On revolutionizing quantum field theory with Tomita's modular theory, J. Math. Phys. 41 (2000), 3604-3673.
7. H. J. Borchers and D. Buchholz, The energy-momentum spectrum in local field theories with broken Lorentz-symmetry, Commun. Math. Phys. 97 (1985), 169-185.
8. H. J. Borchers and J. Yngvason, On the PCT-theorem in the theory of local observables, Mathematical Physics in Mathematics and Physics (Siena) (R. Longo, ed.), Fields Institute Communications, vol. 30, 2001, pp. 39-64.
9. O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics 1, second ed., TMP, Springer, New York, 1987.
10. R. Brunetti, D. Guido, and R. Longo, Modular structure and duality in conformal field theory, Commun, Math. Phys. 156 (1993), 201-219.
11. D. Buchholz and K. Fredenhagen, Locality and the structure of particle states, Commun. Math. Phys 84 (1982), 1-54.
12. A. Connes, The Tomita-Takesaki theory and classification of type-III factors, Proc. Int. School Phys. Enrico Fermi, 1973, pp. 29-46.
13. S. Doplicher, R. Haag, and J. E. Roberts, Local observables and particle statistics I, Commun, Math. Phys. 23 (1971), 199.
14. S. Doplicher, R. Haag, and J. E. Roberts, Local observables and particle statistics II, Commun. Math. Phys. 35 (1974), 49-85.
15. S. Doplicher and J. E. Roberts, Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics, Commun. Math. Phys. 131 (1990), 51-107.
16. M. Florig, On Borchers' theorem, Lett. Math. Phys. 46 (1998), 289-293.
17. K. Fredenhagen, On the existence of antiparticles, Commun. Math. Phys 79 (1981), 141-151.
18. K. Fredenhagen, Structure of superselection sectors in low dimensional quantum field theory, Proceedings (Lake Tahoe City), L. L. Chau and W. Nahm (eds.), 1989.
19. K. Fredenhagen, Generalizations of the theory of superselection sectors, The algebraic theory of superselection sectors. Introduction and recent results, D. Kastler (ed.), World Scientific, 1990.
20. K. Fredenhagen, K.-H. Rehren, and B. Schroer, Superselection sectors with braid group statistics and exchange algebras II: Geometric aspects and conformal covariance, Rev. Math. Phys. SI1 (1992), 113-157.
21. J. Fröhlich and P. A. Marchetti, Quantum field theories of vortices and anyons, Commun. Math. Phys. 121 (1989), 177-223.
22. D. Guido and R. Longo, Relativistic invariance and charge conjugation in quantum field theory, Commun. Math. Phys. 148 (1992), 521-551.
23. D. Guido and R. Longo, The conformal spin and statistics theorem, Commun. Math. Phys. 181 (1996), 11.-35.
24. D. Guido and R. Longo, Natural energy bounds in quantum thermodynamics, Commun. Math. Phys. 218 (2001), 513-536.
25. R. Haag, Local quantum physics, second ed., Texts and Monographs in Physics, Springer, Berlin, Heidelberg, 1996.
26. B. Kuckert, Two uniqueness results on the Unruh effect and on PCT-symmetry, Commun. Math. Phys. 221 (2001), 77-100.
27. R. Longo, An analogue of the Kac-Wakimoto formula and black hole conditional entropy, Commun. Math. Phys. 186 (1997), 451-479.
28. R. Longo, On the spin-statistics relation for topological charges, Operator Algebras and Quantum Field Theory, S. Doplicher, R. Longo, J. Roberts, and L. Zsido (eds.), Int. Press, Cambridge, MA, 1997, pp. 661-669.
29. M. Müger, Superselection structure of massive quantum field theories in 1 + 1 dimensions, Rev. Math. Phys. 10 (1998), 1147-1170.
30. J. Mund, The CPT and Bisognano-Wichmann theorems for Anyons and Plektons in d = 2 + 1, in preparation.
31. J. Mund, The Bisognano-Wichmann theorem, for massive theories, Ann. H. Poinc. 2 (2001), 907-926.
32. K.-H. Rehren, Spin statistics and CPT for solitons, Lett. Math. Phys. 95 (1998), 110.
33. J. E. Roberts, Local cohomology and superselection structure, Commun. Math. Phys. 51 (1976), 107-119.
34. B. Schroer and H.-W. Wiesbrock, Modular theory and geometry, Rev. Math. Phys. 12 (2000), 139-158.
35. S. Strǎtilǎ, Modular theory in operator algebras, Abacus Press, Tunbridge Wells, England, 1981.
36. H.-W. Wiesbrock, Superselection structure and localized Connes' cocycles, Rev. Math. Phys. 7 (1995), 133-160.