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Bounds on the coupling constant in two dimensional boson models

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Abstract

We consider two dimensional boson field theories with an interaction potentialV (φ). We show how to define a cut-off, renormalised Hamiltonian for a certain class of non-polynomialV (φ), which are defined via an integral transform. We formulate precisely a variational argument devised by Coleman, obtaining a constraint on the coupling constant of the theory with generalV (φ), and illustrate the argument with several examples.

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Adelaide, 5000, Adelaide, South Australia

    A. L. Carey

  2. Department of Mathematical Physics, University of Adelaide, 5000, Adelaide, South Australia

    M. A. Lohe & D. M. O'Brien

Authors
  1. A. L. Carey
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  2. M. A. Lohe
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  3. D. M. O'Brien
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Communicated by K. Osterwalder

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Carey, A.L., Lohe, M.A. & O'Brien, D.M. Bounds on the coupling constant in two dimensional boson models. Commun.Math. Phys. 82, 191–210 (1981). https://doi.org/10.1007/BF02099916

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  • DOI: https://doi.org/10.1007/BF02099916

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