further set of parameters ${\bf{K}}=(K_1,K_2,\dots)$ $$\label{transf1}
  R:\; \left(\{{\sigma}_l\}, {\bf K}\right)\longrightarrow
     \left(\{{\mu}_m\}, {\bf K}'\right)\;,$$ where $\{l\}$ and $\{m\}$ are not necessarily equal indexing sets and $\{{\mu}_m\}$ denotes the new set of blocked variables belonging to the larger scale. The quantitative prescription for the map (\[transf1\]) is then given in physical terms by including physical constraints as for example the conservation of symmetries, the maintenance of the structure of the Lagrangian or the Hamiltonian, or the preservation of physical quantities, like for example the free energy of the system. Since in most cases it is a difficult task to define a transformation which combines all needed constraints this has led to an enormous variety of approximate RG transformations developed in the last decades [@bl82].\
The most common realization of the quantitative prescription is to apply the RG transformation $R$ to the Lagrangian or the Hamiltonian as a functional which then acts on the variables and parameters given in (\[transf1\]). In the special example of a one dimensional quantum spin chain the new variables are the block spins and the new coupling constant belongs to the [*renormalized*]{} set of parameters ${\bf K}'$. For our case we generalize this RGT to an arbitrary suitable 