On the Renormalisation group, protein folding, and naturalness

TL;DR

This paper extends the renormalisation group concept into a category-theoretic framework, offering new insights into naturalness and protein folding by exploring morphisms and regularisation functions.

Contribution

It introduces a renormalisation category with a group structure on morphisms, broadening the mathematical tools for understanding complex systems like naturalness and protein folding.

Findings

New mathematical structure called renormalisation category.

Existence of a group structure at the level of morphisms.

Implications for understanding naturalness and protein folding.

Abstract

I am showing how the ideas behind the renormalisation group can be generalised in order to produce the desired reduction in the degrees of freedom other that the ones considered up to now. Instead of looking only at the renormalisation group flow, inspiration from optimisation tools for regulators of truncated theories is used to show that there exists another mathematical structure in the morphisms between various renormalisation groups, characterised by their operations, encoded by means of various regularisation functions. This expands the idea of renormalisation group to a renormalisation category. A group structure exists at the level of those morphisms, leading to new information emerging in the flowing process. Impact on problems like the naturalness and protein folding is being presented briefly.