Summary
By introducing the concepts of asymptopia and bi-asymptopia, we show how braided tensor C*-categories arise in a natural way. This generalizes constructions in algebraic quantum field theory by replacing local commutativity by suitable forms of asymptotic Abelianness.
Supported in part by the MURST, CNR-GNAFA, INdAM-GNAMPA and the European Union under contract HPRN-CT2002-00280.
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References
D. Buchholz: The Physical State Space of Quantum Electrodynamics. Comm. Math. Phys. 85:49–71 (1982).
D. Buchholz and S. Doplicher: Exotic Infrared Representations of Interacting Systems. Ann. Inst. H. Poincaré 40:175–184 (1984).
D. Buchholz, S. Doplicher, G. Morchio, J.E. Roberts and F. Strocchi: A Model for Charges of Electromagnetic Type. In: Proceedings of the Conference on Operator Algebras and Quantum Field Theory, Rome 1966 (ed.: S. Doplicher et al.), International Press, 1997.
D. Buchholz, S. Doplicher, G. Morchio, J.E. Roberts and F. Strocchi: The Quantum Delocalization of the Electric Charge. Ann. of Phys. 290:53–66 (2001).
D. Buchholz and K. Fredenhagen: Locality and the Structure of Particle States. Comm. Math. Phys. 84:1–54 (1982).
S. Doplicher, R. Haag and J.E. Roberts: Local Observables and Particle Statistics I. Comm. Math. Phys. 23:199–230 (1971) and II. Comm. Math. Phys. 35:49–85 (1974).
S. Doplicher and R. Longo: Standard and Split Inclusions of von Neumann Algebras. Invent. Math. 75:493–536 (1984).
S. Doplicher and J.E. Roberts: A New Duality Theory for Compact Groups. Invent. Math. 98:157–218 (1989).
S. Doplicher and J.E. Roberts: Why There is a Field Algebra With a Compact Gauge Group Describing the Superselection Structure in Particle Physics. Comm. Math. Phys. 131:51–107 (1990).
S. Doplicher and M. Spera: Representations Obeying the Spectrum Condition. Comm. Math. Phys. 84:505–513 (1982).
J. Fröhlich: The Charged Sectors of Quantum Electrodynamics in a Framework of Local Observables. Comm. Math. Phys. 66:223–265 (1979).
J. Fröhlich, G. Morchio and F. Strocchi: Charged Sectors and Scattering States in Quantum Electrodynamics. Ann. Phys. 119:241–284 (1979).
R. Haag and D. Kastler: An Algebraic Approach to Quantum Field Theory. J. Math. Phys. 5:848–861 (1964).
R. Longo and J.E. Roberts: A Theory of Dimension. K-Theory 11:103–159 (1997).
A. Kishimoto: The Representations and Endomorphisms of a Separable Nuclear C*-algebra. Internat. J. Math. 14:313–326 (2003).
A. Kishimoto, N. Ozawa and S. Sakai: Homogeneity of the Pure State Space of a Separable C*-Algebra. Canad. Math. Bull. 4:365–372 (2003).
J.E. Roberts: Lectures on Algebraic Quantum Field Theory. In: The Algebraic Theory of Superselection Sectors. Introduction and Recent Results (ed.: D. Kastler), pp. 1–112. World Scientific, Singapore, 1990.
D. Salvitti: Generalized Particle Statistics in Two-Dimensions: Examples from the Theory of Free Massive Dirac Field. e-print: hep-th/0507107, and Doctoral Thesis, Rome, 2004.
M. Takesaki: Algebraic Equivalence of Locally Normal Representations. Pacific J. Math. 34:807–816 (1970).
J.C. Wick, A.S. Wightman and E.P. Wigner: The Intrinsic Parity of Elementary Particles. Phys. Rev. 88:101–105 (1952).
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Buchholz, D., Doplicher, S., Morchio, G., Roberts, J.E., Strocchi, F. (2007). Asymptotic Abelianness and Braided Tensor C*-Categories. In: de Monvel, A.B., Buchholz, D., Iagolnitzer, D., Moschella, U. (eds) Rigorous Quantum Field Theory. Progress in Mathematics, vol 251. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7434-1_5
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DOI: https://doi.org/10.1007/978-3-7643-7434-1_5
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