Abstract
Starting from a chiral conformal Haag-Kastler net on two-dimensional Minkowski space we construct associated charged pointlike localized fields which intertwine between arbitrary superselection sectors with finite statistics of the theory. This amounts to a proof of the Spin-Statistics theorem, the PCT theorem and the existence of operator product expansions.
This Letter generalizes similar results of a recently published paper by Fredenhagen and the author from the neutral vacuum sector to the the full theory with arbitrary charge and finite statistics.
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References
Araki, H.: Positive cones for von Neumann algebras, Report in the Proceedings of the Kingston Conference, 1980.
BrunettiR., GuidoD. and LongoR.: Comm. Math. Phys. 156 (1993) 201.
BisognanoJ. J. and WichmannE. H.: On the duality condition for a hermitian scalar field; On the duality condition for a quantum field, J. Math. Phys. 16 (1975), 985–1007.
BorchersH. J.: The CPT-theorem in two-dimensional theories of local observables, Comm. Math. Phys. 134 (1992) 315.
BratelliO. and RobinsonD. W.: Operator Algebras and Quantum Statistical Mechanics I, Springer-Verlag, New York, 1979.
Buchholz, D.: On the manifestation of particles, DESY-Preprint 93-155 and report in the proceedings of the Beer Sheva Conference, 1993.
BuchholzD. and FredenhagenK.: Dilations and interactions, J. Math. Phys. 18 (1977), 1107–1111.
ForsterO.: Riemannsche Flächen, Springer-Verlag, Berlin, 1977.
FredenhagenK.: A remark on the Cluster Theorem, Comm. Math. Phys. 97 (1985), 461.
FredenhagenK. and JörßM.: Conformal Haag-Kastler nets, pointlike localized fields and the existence of operator product expansions, Comm. Math. Phys. 176 (1996), 541–554.
FredenhagenK., RehrenK.-H. and SchroerB.: Superselection sectors with braid group statistics and exchange algebra I, Comm. Math. Phys. 125 (1989), 201.
Fredenhagen, K., Rehren, K.-H. and Schroer, B.: Superselection sectors with braid group statistics and exchange algebra II, Rev. Math. Phys., special issue (1992), 113.
FröhlichJ. and GabbianiF.: Operator algebras and conformal field theory, Comm. Math. Phys. 155 (1993) 569.
Guido, D. and Longo, R.: The conformal spin and statistics theorem, hep-th/9505059.
HaagR., Local Quantum Physics, Springer-Verlag, Berlin, 1992.
Isola, T.: Modular structure for the crossed product by a compact group dual, to appear in J. Operator Theory.
Jörß, M.: Lokale Netze auf dem eindimensionalen Lichtkegel, Diploma thesis, FU Berlin, 1991.
Jörß, M.: On the existence of pointlike localized fields in conformally invariant quantum physics, DESY-preprint 92-156 and report in the Proceedings of the Cambridge Conference, 1992.
LangS.: SL2(®), Springer-Verlag, Berlin, 1975.
LüscherM.: Operator product expansions on the vacuum in conformal quantum field theory in two space-time dimensions, Comm. Math. Phys. 50 (1976) 23–52.
MackG.: Convergence of operator product expansions on the vacuum in conformally invariant quantum field theory, Comm. Math. Phys. 53, (1976), 155.
SchroerB., SwiecaJ. A. and VölkelA. H.: Global operator expansions in conformally invariant relativistic quantum field theory, Phys. Rev. D 11(6) (1974), 1509.
Strebel, K.: Vorlesungen über Riemannsche Flächen, Vandenhoeck und Ruprecht; 1980.
StreaterR. and WightmanA.S.: PCT, Spin & Statistics, and All That, Benjamin, New York, 1964.
TakesakiM.: Tomita's Theory of Modular Hilbert Algebras and its Applications, Springer-Verlag, Berlin, 1970.
TrevesF.: Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, 1967.
WilsonR.: Non-Lagrangian models of current algebras, Phys. Rev. 179(5) (1969), 1499.
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Jòrß, M. The construction of pointlike localized charged fields from conformal Haag—Kastler nets. Lett Math Phys 38, 257–274 (1996). https://doi.org/10.1007/BF00398350
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DOI: https://doi.org/10.1007/BF00398350