Systematic generalization of the Migdal transformation

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Abstract
It is shown that the Migdal transformations should not be considered to be true lattice transformations since the same recursion relation may be derived for any lattice. A profitable point of view is to consider the various recursion transformations as approximate integrals of their common differential limit. It is then possible to construct extensions of the Migdal transformations by examining the renormalization group property and partition function invariance of a potential‐moving scheme order by order in (b‐1) where b is the length rescaling factor. Explicit conditions are given in a quasi‐continuum approximation to 0((b−1)2).