Dimensional Regularization and Non-Renormalizable Quantum Field Theories

Abstract

One major problem of contemporary physics is posed by the incompatibility of the two greatest theories of the 20th century: quantum mechanics (QM) and general relativity (GR). Joining them gives rise to a perturbatively non-renormalizable quantum gravity theory. The two theories, on their own, have been amazingly successful, and quantum mechanics, in particular, gave rise to many of the recent technical advances that have revolutionized our lives. Today, however, there is a lack of an over-arching theoretical framework within which both QM and GR successes could be accommodated. This book provides an accessible guideline to a possible over-arching framework, based on well-known mathematical structures.