Scaling Limit and Renormalisation Group in the Critical Point Analysis of General (Quantum) Many Body Systems

We employ the machinery of smooth scaling and coarse-graining of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) to make a rigorous renormalisation group analysis of the critical regime. The approach appears to be quite general, encompassing classical, quantum, discrete and continuous systems. One of our central topics is the analysis of the famous ‘scaling hypothesis’, that is, we make a general investigation under what conditions on the l-point correlation functions a scale invariant (nontrivial) limit theory can be actually attained. Furthermore, we study in a rigorous manner questions like the quantum character of the system in the scaling limit, the phenomenon of critical slowing down etc.