On charged fields with group symmetry and degeneracies of Verlinde’s matrix S *
Annales de l'I.H.P. Physique théorique, Tome 71 (1999) no. 4, p. 359-394
@article{AIHPA_1999__71_4_359_0,
     author = {M\"uger, Michael},
     title = {On charged fields with group symmetry and degeneracies of Verlinde's matrix $S^\ast $},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {71},
     number = {4},
     year = {1999},
     pages = {359-394},
     zbl = {0938.81018},
     mrnumber = {1721563},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1999__71_4_359_0}
}
Müger, Michael. On charged fields with group symmetry and degeneracies of Verlinde’s matrix $S^\ast $. Annales de l'I.H.P. Physique théorique, Tome 71 (1999) no. 4, pp. 359-394. https://www.numdam.org/item/AIHPA_1999__71_4_359_0/

[1] C. D'Antoni and R. Longo, Interpolation by type I factors and the flip automorphism, J. Funct. Anal. 51 (1983) 361-371. | MR 703083 | Zbl 0535.46036

[2] C. D'Antoni, Technical properties of the quasilocal algebra, in: D. Kastler, ed., The Algebraic Theory of Superselection Sectors. Introduction and Recent Results, World Scientific, 1990.

[3] J. Böckenhauer and D.E. Evans, Modular invariants, graphs and α-induction for nets of subfactors I, Commun. Math. Phys. 197 (1998) 361-386. | MR 1652746 | Zbl 0924.46047

[4] R. Brunetti, D. Guido and R. Longo, Modular structure and duality in QFT, Commun. Math. Phys. 156 (1993) 201-219. | MR 1234110 | Zbl 0809.46086

[5] D. Buchholz, G. Mack and I. Todorov, The current algebra on the circle as a germ of local field theories, Nucl. Phys. B (Proc. Suppl.) 5B (1988) 20-56. | MR 1002955 | Zbl 0958.22500

[6] D. Buchholz, S. Doplicher and R. Longo, On Noether's theorem in quantum field theory, Ann. Phys. 170 (1986) 1-17. | MR 848392 | Zbl 0609.46037

[7] D. Buchholz, S. Doplicher, R. Longo and J. Roberts, Extensions of automorphisms and gauge symmetries, Commun. Math. Phys. 155 (1993) 123- 134. | MR 1228529 | Zbl 0792.46052

[8] R. Conti, unpublished.

[9] R. Dijkgraaf, C. Vafa, E. Verlinde and H. Verlinde, The operator algebra of orbifold models, Commun. Math. Phys. 123 (1989) 485-527. | MR 1003430 | Zbl 0674.46051

[10] S. Doplicher, R. Haag and J.E. Roberts, Fields, observables and gauge transformations I, Commun. Math. Phys. 13 (1969) 1-23. | MR 258394 | Zbl 0175.24704

[11] S. Doplicher, R. Haag and J.E. Roberts, Fields, observables and gauge transformations II, Commun. Math. Phys. 15 (1969) 173-200. | MR 260294 | Zbl 0186.58205

[12] S. Doplicher, R. Haag and J.E. Roberts, Local observables and particle statistics I, Commun. Math. Phys. 23 (1971) 199-230. | MR 297259

[13] S. Doplicher and J.E. Roberts, Fields, statistics and non-abelian gauge groups, Commun. Math. Phys. 28 (1972) 331-348. | MR 325053

[14] S. Doplicher, R. Haag and J.E. Roberts, Local observables and particle statistics II, Commun. Math. Phys. 35 (1974) 49-85. | MR 334742

[15] S. Doplicher, Local aspects of superselection rules, Commun. Math. Phys. 85 (1982) 73-86. | MR 667768 | Zbl 0515.46065

[16] S. Doplicher and R. Longo, Standard and split inclusions of von Neumann algebras, Invent. Math. 75 (1984) 493-536. | MR 735338 | Zbl 0539.46043

[17] S. Doplicher and J.E. Roberts, A remark on compact automorphism groups of C*-algebras, J. Funct. Anal. 66 (1986) 67-72. | MR 829377 | Zbl 0589.46052

[18] S. Doplicher and J.E. Roberts, Duals of compact Lie groups realized in the Cuntz algebras and their actions on C*-algebras, J. Funct. Anal. 74 (1987) 96- 120. | MR 901232 | Zbl 0619.46053

[19] S. Doplicher and J.E. Roberts, Compact group actions on C*-algebras, J. Oper. Theor. 19 (1988) 283-305. | MR 960981 | Zbl 0689.46020

[20] S. Doplicher and J.E. Roberts, Endomorphisms of C*-algebras, cross products and duality for compact groups, Ann. Math. 130 (1989) 75-119. | MR 1005608 | Zbl 0702.46044

[21] S. Doplicher and J.E. Roberts, A new duality theory for compact groups, Invent. Math. 98 (1989) 157-218. | MR 1010160 | Zbl 0691.22002

[22] 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. | MR 1062748 | Zbl 0734.46042

[23] K. Fredenhagen, K.-H. Rehren and B. Schroer, Superselection sectors with braid group statistics and exchange algebras I, General theory, Commun. Math. Phys. 125 (1989) 201-226. | MR 1016869 | Zbl 0682.46051

[24] 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. (Special Issue) (1992) 113-157. | MR 1199171 | Zbl 0774.46041

[25] J. Fuchs, A.N. Schellekens and C. Schweigert, A matrix S for all simple current extensions, Nucl. Phys. B 473 (1996) 323-366. | MR 1409292 | Zbl 0921.17014

[26] F. Gabbiani and J. Fröhlich, Operator algebras and conformal field theory, Commun. Math. Phys. 155 (1993) 569-640. | MR 1231644 | Zbl 0801.46084

[27] D. Guido and R. Longo, The conformal spin-statistics theorem, Commun. Math. Phys. 181 (1996) 11-35. | MR 1410566 | Zbl 0858.46053

[28] R. Haag, Local Quantum Physics, 2nd Ed., Springer, 1996. | MR 1405610 | Zbl 0857.46057

[29] E. Hewitt and K.A. Ross, Abstract Harmonic Analysis I, 2nd Ed., Springer, 1979. | MR 551496

[30] D. Kastler (ed.), The Algebraic Theory of Superselection Sectors. Introduction and Recent Results, World Scientific, 1990. | MR 1147460

[31] R. Longo, Simple injective subfactors, Adv. Math. 63 (1987) 152-171. | MR 872351 | Zbl 0616.46054

[32] R. Longo, Index of subfactors and statistics of quantum fields I, Commun. Math. Phys. 126 (1989) 217-247. | MR 1027496 | Zbl 0682.46045

[33] R. Longo and K.-H. Rehren, Nets of subfactors, Rev. Math. Phys. 7 (1995) 567- 597. | MR 1332979 | Zbl 0836.46055

[34] R. Longo and J.E. Roberts, A theory of dimension, K-Theory 11 (1997) 103- 159. | MR 1444286 | Zbl 0874.18005

[35] M. Lüscher and G. Mack, Global conformal invariance in QFT, Commun. Math. Phys. 41 (1975) 203-234. | MR 371282

[36] M. Müger, Quantum double actions on operator algebras and orbifold quantum field theories, Commun. Math. Phys. 191 (1998) 137-181. | MR 1603762 | Zbl 0897.46059

[37] M. Müger, Superselection structure of massive quantum field theories in 1 + 1 dimensions, Rev. Math. Phys. 10 (1998) 1147-1170. | MR 1670186 | Zbl 0918.46070

[38] M. Müger, On the algebraic structure of rational conformal theories, in preparation.

[39] K.-H. Rehren, Braid group statistics and their superselection rules, in: D. Kastler, ed., The Algebraic Theory of Superselection Sectors. Introduction and Recent Results, World Scientific, 1990. | MR 1147467

[40] K.-H. Rehren, Markov traces as characters for local algebras, Nucl. Phys. B (Proc. Suppl.) 18B (1990) 259-268. | MR 1128146 | Zbl 0957.81526

[41] J.E. Roberts, Cross products of von Neumann algebras by group duals, Sympos. Math. 20 (1976) 335-363. | MR 473859 | Zbl 0441.46053

[42] J.E. Roberts, Local cohomology and superselection structure, Commun. Math. Phys. 51 (1976) 107-119. | MR 471753 | Zbl 0334.53033

[43] J.E. Roberts, Net cohomology and its applications to field theory, in: L. Streit, ed., Quantum Fields, Particles, Processes, Springer, 1980. | MR 601815 | Zbl 0484.57024

[44] J.E. Roberts, Lectures on algebraic quantum field theory, in: D. Kastler, ed., The Algebraic Theory of Superselection Sectors. Introduction and Recent Results, World Scientific, 1990. | MR 1147460

[45] A.N. Schellekens and S. Yankielowicz, Simple currents, modular invariants, and fixed points, Int. J. Mod. Phys. A 5 (1990) 2903-2952. | MR 1067813 | Zbl 0706.17012

[46] S.J. Summers, Normal product states for Fermions and twisted duality for CCR- and CAR-type algebras with application to the Yukawa2 quantum field model, Commun. Math. Phys. 86 (1982) 111-141. | MR 678005 | Zbl 0505.46051

[47] E. Verlinde, Fusion rules and modular transformations in 2D conformal field theory, Nucl. Phys. B 300 (1988) 360-376. | MR 954762