Abstract
Starting from the principles of local relativistic Quantum Theory without long range forces, we study the structure of the set of superselection sectors (charge quantum numbers) and its implications for the particle aspects of the theory. Without assuming the commutation properties (or even the existence) of unobservable fields connecting different sectors (charge-carrying fields), one has a particle-antiparticle symmetry, an intrinsic notion of statistics for identical particles, and a spin-statistics theorem. Particles in “pseudoreal sectors” cannot be their own antiparticles (a variant of Carruthers' theorem). We also show how scattering states and transition probabilities are obtained in this frame.
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References
Doplicher, S., Haag, R., Roberts, J. E.: Commun. math. Phys.23, 199–230 (1971)
Epstein, H.: J. Math. Phys.8, 750–767 (1967)
Carruthers, P.: J. Math. Phys.9, 928–945 (1968)
Doplicher, S., Roberts, J. E.: Commun. math. Phys.28, 331–348 (1972)
Doplicher, S., Haag, R., Roberts, J. E.: Commun. math. Phys.15, 173–200 (1969)
Eilenberg, S., Kelly, G. M.: Closed categories. In: Proceedings of the Conference on Categorical Algebra, La Jolla 1965. Berlin-Heidelberg-New York: Springer 1966
Borchers, H. J.: Commun. math. Phys.1, 281–307 (1965)
Wightman, A.S.: Analytic functions of several complex variables. Lectures at Les Houches Summer School 1960. Paris: Hermann 1960
Feldman, G., Matthews, P. T.: Phys. Rev.151, 1176–1180 (1966)
Streater, R. F.: Local fields with the wrong connection between spin and statistics. Commun. math. Phys.5, 88–96 (1967)
Doplicher, S., Haag, R., Roberts, J. E.: Commun. math. Phys.13, 1–23 (1969)
Wigner, E. P.: Group theory. New York: Academic Press 1959
Jost, R.: The general theory of quantized fields. Providence, Rhode Island: Am. Math. Soc. 1965
Hepp, K.: Commun. math. Phys.1, 95–111 (1965)
Ruelle, D.: Helv. Phys. Acta35, 147 (1962)
Araki, H., Haag, R.: Commun. math. Phys.4, 77–91 (1967)
Araki, H.: Lecture notes, ETH, Zürich (1961/62)
Haag, R., Swieca, J. A.: Commun. math. Phys.1, 308–320 (1965)
Dixmier, J.: Les algèbres d'opérateurs dans l'espace Hilbertien. Paris: Gauthier-Villars 1969
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Doplicher, S., Haag, R. & Roberts, J.E. Local observables and particle statistics II. Commun.Math. Phys. 35, 49–85 (1974). https://doi.org/10.1007/BF01646454
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DOI: https://doi.org/10.1007/BF01646454