What Is the Mean of Quantum Fluctuations in TGD Framework?

Abstract

What does one mean with quantum fluctuation? Often Uncertainty Principle is assigned with quantum fluctuations. Eigenstate of, say, momentum is necessary delocalized maximally, and one could say that there are quantum fluctuations in position. Same applies to eigenstates of energy. Path integral formalism provides a nice definition of quantum fluctuation. In path integral formalism one interprets transition amplitude as a sum over all paths - not only classical one - leading from given initial to given final state. In stationary phase approximation making possible perturbative approach one performs path integral around the classical path. The paths which differ from the classical path correspond naturally to quantum fluctuations. For interacting quantum field theories (QFT) the expansion in powers of coupling constant - say α = e2/4πħ would give radiative corrections identifiable as being due quantum fluctuations. The problem of path integral formalism is that path integral does not exist in a strict mathematical sense. Since TGD is quantum critical one can ask whether a stronger notion for which quantum fluctuation would be analogous to thermodynamical fluctuation at criticality could exists. In this article I proposed this kind of notion relying on Zero Energy Ontology, hierarchy of Planck constants, and other basic elements of TGD. This view also nice description of quantum phase transitions.