Renormalization and the Effective Field Theory Programme

Abstract

Quantum field theory (QFT) poses the following well-known problem. Calculations of values for certain quantities begin with a first-order approximation to which are added higher order corrections. In many cases, the calculation of even the very first higher order correction term yields infinite values. These infinite values are due to divergences in the theory. These divergences can be traced to their source in the standard fundamental assumptions defining QFT. No matter which version of the formalism we adopt, we are trying to incorporate into the mathematics certain fundamental physical constraints on the nature of the vacuum state, on the states that can be occupied by systems, on the comeasurability of observables, and so on. The resulting formalism contains divergences.