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We report in a series of papers two types of generalized Migdal-Kadanoffbond-moving renormalization group transformation recursion procedures. In thisfirst part the symmetrical operation of half length bonds on translationalinvariant lattices are considered. As an illustration of their predominance inapplication, the procedures are used to study the critical behavior of thespin-continuous Gaussian model constructed on the triangular lattices. Resultssuch as the correlation length critical exponents obtained by this means arefound to be in good conformity with the classical results from other studies.

Generalized Migdal-Kadanoff Bond-moving Renormalization Recursion  Procedure I: Symmetrical Half-length Bond Operation on Translational  Invariant Lattices