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A block spin construction of ondelettes Part II: The QFT connection

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Abstract

We apply the Lemarié basis of ondelettes to the Battle-Federbush cluster expansion for the φ 43 quantum field theory. Since there is no infrared problem for this model, we also show how the large-scale ondelettes can be thrown away and replaced by unit-scale functions. Finally, we apply the block spin machine of Part I to the construction of exponentially localized ondelettes orthogonal with respect to the free, massless action of the scalar field.

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Authors and Affiliations

  1. Mathematics Department, Cornell University, 14853, Ithaca, NY, USA

    Guy Battle

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  1. Guy Battle
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Additional information

Communicated by A. Jaffe

Supported in part by the National Science Foundation under Grant No. DMS 8603795 and by the Mathematical Sciences Institute

On leave from the Mathematics Department, Texas A&M University, College Station, Texas 77843, USA

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Battle, G. A block spin construction of ondelettes Part II: The QFT connection. Commun.Math. Phys. 114, 93–102 (1988). https://doi.org/10.1007/BF01218290

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  • DOI: https://doi.org/10.1007/BF01218290

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