Abstract
We continue our program to establish the Higgs mechanism and mass gap for the abelian Higgs model in two and three dimensions. We develop a multiscale cluster expansion for the high frequency modes of the theory, within a framework of iterated renormalization group transformations. The expansions yield decoupling properties needed for a proof of exponential decay of correlations. The result of this analysis is a gauge invariant unit lattice theory with a deep Higgs potential of the shape required to exhibit the Higgs mechanism.
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Communicated by A. Jaffe
Research partially supported by the National Science Foundation under Grant DMS-8602207 and by the Air Force Office of Scientific Research under Grant AFOSR-86-0229
Alfred P. Sloan Research Fellow. Research partially supported by the National Science Foundation under Grants PHY-84-13285 and PHY-85-13554
Research partially supported by the National Science Foundation under Grant PHY-85-13554
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Bałaban, T., Imbrie, J.Z. & Jaffe, A. Effective action and cluster properties of the abelian Higgs model. Commun.Math. Phys. 114, 257–315 (1988). https://doi.org/10.1007/BF01225038
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DOI: https://doi.org/10.1007/BF01225038