Block renormalization group for Euclidean fermions

Block renormalization group transformations (RGT) for lattice and continuum Euclidean fermions in d dimensions are developed using fermionic integrals with exponential and 'δ-function' weight functions. For the free field the sequence of actions Dk generated by the RGT from D, the Dirac operator, are shown to have exponential decay; uniform in k, after rescaling to the unit lattice. It is shown 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. Contrary to RG intuition the sequence of rescaled actions corresponding to the 'δ-function' RGT do not have uniform exponential decay and we give examples of initial actions in one dimension where this phenomena occurs for the exponential weight RGT also. (orig.)