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On the construction of quantized gauge fields

III. The two-dimensional abelian higgs model without cutoffs

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Abstract

In this paper the construction of the two-dimensional abelian Higgs model begun in two earlier articles is completed. First we show how to remove the remaining ultraviolet cutoff on the gauge field, then we construct the infinite volume limit and verify the axioms of Osterwalder and Schrader for the expectation values of gauge invariant local fields. Finally it is shown that an auxiliary gauge field mass that was introduced to avoid infrared problems can be safely removed.

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Authors and Affiliations

  1. Department of Mathematics, University of Virginia, 22903, Charlottesville, Virginia, USA

    David C. Brydges

  2. Institut des Hautes, Etudes Scientifiques, 35 route de Chartres, F-91440, Bures-sur-Yvette, France

    Jürg Fröhlich

  3. Max-Planck-Institut für Physik und Astrophysik, Föhringer Ring 6, Postfach 401212, D-8000, München 40, Federal Republic of Germany

    Erhard Seiler

Authors
  1. David C. Brydges
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  2. Jürg Fröhlich
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  3. Erhard Seiler
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Additional information

Communicated by K. Osterwalder

Research supported in part N.S.F. Grant MCS 79-02490

Research partly supported by Centre National de la Recherche Scientifique

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Brydges, D.C., Fröhlich, J. & Seiler, E. On the construction of quantized gauge fields. Commun.Math. Phys. 79, 353–399 (1981). https://doi.org/10.1007/BF01208500

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  • DOI: https://doi.org/10.1007/BF01208500

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