From infinities in quantum electrodynamics to the general renormalization group

Chapter 4 describes a few important steps which have led from the discovery of infinities in quantum electrodynamics in the calculation of Feynman diagrams (ultraviolet divergences (UV divergences)) to the concept of renormalization and renormalization groups (RG). The constructions of quantum (or statistical) field theories (QFTs) and the deeply related RG have been some of the major theoretical achievements in physics of the last century. RG today plays an essential role in the understanding of the properties of QFT and of continuous macroscopic phase transitions. The existence of RG fixed points makes it possible to understand universality when there is no scale decoupling. In particle physics, it leads to the notion of effective field theory and the fine tuning problem in the Higgs particle sector.

Exact Renormalization Groups As a Form of Entropic Dynamics

The Renormalization Group (RG) is a set of methods that have been instrumental in tackling problems involving an infinite number of degrees of freedom, such as, for example, in quantum field theory and critical phenomena. What all these methods have in common—which is what explains their success—is that they allow a systematic search for those degrees of freedom that happen to be relevant to the phenomena in question. In the standard approaches the RG transformations are implemented by either coarse graining or through a change of variables. When these transformations are infinitesimal, the formalism can be described as a continuous dynamical flow in a fictitious time parameter. It is generally the case that these exact RG equations are functional diffusion equations. In this paper we show that the exact RG equations can be derived using entropic methods. The RG flow is then described as a form of entropic dynamics of field configurations. Although equivalent to other versions of the RG, in this approach the RG transformations receive a purely inferential interpretation that establishes a clear link to information theory.