Renormalization, isogenies and rational symmetries of differential equations

We give an example of infinite order rational transformation that leaves a linear differential equation covariant. This example can be seen as a non-trivial but still simple illustration of an exact representation of the renormalization group.

💡 Research Summary

The paper presents a concrete and mathematically rigorous illustration of an exact renormalization‑group (RG) transformation that is of infinite order and rational. The authors start by recalling the usual role of the RG in statistical mechanics and quantum field theory: a set of scale transformations that map a physical system onto an effective description at a different length scale. In most applications the RG flow is either continuous (described by differential beta‑functions) or consists of a finite set of discrete mappings. By contrast, the transformation studied here is a single rational map of the independent variable, \