Scaling Limit and Renormalisation Group in General (Quantum) Many Body Theory

Using the machinery of smooth scaling and coarse-graining of observables, developed recently in the context of so-called fluctuation operators (originally developed by Verbeure et al), we extend this approach to a rigorous renormalisation group analysis of the critical regime. The approach is completely general, encompassing classical, quantum, discrete and continuous systems. Our central theme is the analysis of the famous `scaling hypothesis', that is, we make a general investigation under what cluster conditions of the l-point correlation functions a scale invariant (non-trivial) limit theory can be actually attained.