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The CPT-theorem in two-dimensional theories of local observables

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Abstract

Let ℳ be a von Neumann algebra with cyclic and separating vector Ω, and letU(a) be a continuous unitary representation ofR with positive generator and Ω as fixed point. If these unitaries induce for positive arguments endomorphisms of ℳ then the modular group act as dilatations on the group of unitaries. Using this it will be shown that every theory of local observables in two dimensions, which is covariant under translation only, can be imbedded into a theory of local observables covariant under the whole Poincaré group. This theory is also covariant under the CPT-transformation.

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  1. Institut für Theoretische Physik, Universität Göttingen, Bunsenstrasse 9, W-3400, Göttingen, Federal Republic of Germany

    H. J. Borchers

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  1. H. J. Borchers
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Communicated by H. Araki

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Borchers, H.J. The CPT-theorem in two-dimensional theories of local observables. Commun.Math. Phys. 143, 315–332 (1992). https://doi.org/10.1007/BF02099011

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  • DOI: https://doi.org/10.1007/BF02099011

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