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Local fields with the wrong connection between spin and statistics

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Abstract

It is proved that there exist free field operators which satisfy local commutativity and which transform according to certain unitary representations of the homogeneous Lorentz group. The fields satisfy axioms similar to the Wightman axioms, and give rise to local algebras of observables obeying postulates similar to those suggested byHaag. They describe a tower of particles with spins 1/2, 1 1/2, 2 1/2, ..., but commute at space-like separation, giving rise to Bose statistics for the particles. This shows that the well-known theorem on spin and statistics cannot be extended to general theories of local observables; it also shows that the assumptions made in “S-matrix theory” do not hold for theS-matrix of a theory of interacting infinite fields.

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Authors and Affiliations

  1. Department of Physics, Imperial College, S.W. 7, London

    R. F. Streater

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  1. R. F. Streater
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The research reported in this document has been sponsored in part by the Air Force Office ofScientific Research OAR through the European Office Aerospace Research U.S. Air Force.

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Streater, R.F. Local fields with the wrong connection between spin and statistics. Commun.Math. Phys. 5, 88–96 (1967). https://doi.org/10.1007/BF01646839

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  • DOI: https://doi.org/10.1007/BF01646839

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