Block renormalization group for Euclidean Fermions |
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Authors: | Tadeusz Balaban Michael O'Carroll Ricardo Schor |
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Institution: | (1) Mathematics Department, Boston University, Boston, MA, USA;(2) Departmento de Física do ICEx, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brasil |
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Abstract: | Block renormalization group transformations (RGT) for lattice and continuum Euclidean Fermions in d dimensions are developed using Fermionic integrals with exponential and -function weight functions. For the free field the sequence of actionsD
k
generated by the RGT from D, the Dirac operator, are shown to have exponential decay; uniform ink, after rescaling to the unit lattice. It is shown that the two-point functionD
–1 admits a simple telescopic sum decomposition into fluctuation two-point functions which for the exponential weight RGT have exponential decay. Contrary to RG intuition the sequence of rescaled actions corresponding to the -function RGT do not have uniform exponential decay and we give examples of initial actions in one dimension where this phenomena occurs for the exponenential weight RGT also. |
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