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From the Euclidean group to the Poincaré group via Osterwalder-Schrader positivity

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Abstract

Given a continuous representation of the Euclidean group inn+1 dimensions, together with a covariant system of subspaces, which satisfies Osterwalder-Schrader positivity, we construct a continuous unitary representation of the orthochronous Poincaré group inn+1 dimensions satisfying the spectral condition. A similar result holds for the covering groups of the Euclidean and Poincaré group.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 92717, Irvine, CA, USA

    Abel Klein

  2. Mathematics Department, Bedford College, University of London, Regent's Park, NW14NS, London, England

    Lawrence J. Landau

Authors
  1. Abel Klein
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  2. Lawrence J. Landau
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Communicated by A. Jaffe

Partially supported by the N.S.F. under grant MCS 8202045

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Klein, A., Landau, L.J. From the Euclidean group to the Poincaré group via Osterwalder-Schrader positivity. Commun.Math. Phys. 87, 469–484 (1983). https://doi.org/10.1007/BF01208260

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  • DOI: https://doi.org/10.1007/BF01208260

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