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Block averaging renormalization group for lattice and continuum euclidean fermions: Expected and unexpected results

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Abstract

Block averaging renormalization group transformations (RGT) for lattice and continuum Euclidean fermions in d-dimensions, are presented using fermionic integralswith exponential and ‘δ-function’ weight functions. For the free field, the sequence of actions D k generated by the RGT from D, the Dirac operator, are shown to have the expected exponential decay; uniform in k after rescaling to the unit lattice. Contrary to the RG intuition, we find that the sequence of rescaled actions corresponding to the ‘δ-function’ RGT do not have uniform exponential decay. Also, we find that the two-point function D -1 admits a simple telescopic sum decomposition into fluctuation two-point functions which for the exponential weight RGT have exponential decay.

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Balaban, T., O'Carroll, M. & Schor, R. Block averaging renormalization group for lattice and continuum euclidean fermions: Expected and unexpected results. Lett Math Phys 17, 209–214 (1989). https://doi.org/10.1007/BF00401587

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AMS subject classifications (1980)

  • 81E15
  • 82A68