By Alexey A Petrov and Andrew E Blechman
World Scientific
The importance of effective field theory (EFT) techniques cannot be over-emphasised. In fact, all theories are, in some sense, effective. A book that discusses these techniques, groups different cases in which EFTs are necessary, and provides numerous examples, is therefore necessary.
After illustrating the ubiquitousness of EFTs with a discussion of Newtonian gravity, superconductivity, and the Euler–Heisemberg theory of photon–photon scattering below the electron mass, the book splits into different directions to examine qualitatively diverse situations where EFTs are used. Fermi theory, chiral perturbation theory, heavy-quark effective theory, non-relativistic quantum electrodynamics (chromodynamics), and even the EFT for physics beyond the Standard Model, are all discussed with a common language that allows the reader to find analogies and appreciate the different physics of these fundamentally different systems.
Soft collinear effective theory (SCET) and non-relativistic general relativity provide a different context in which EFTs are useful as a computational tool. The text exploits the intuition developed in the previous examples to identify the relevant expansion parameters and to organise hierarchically the different contributions to the scattering amplitudes.
Admittedly, the book focuses on high-energy physics topics, neglecting many applications in soft and condensed matter.
The volume is very well written, it is continuous, and includes a rich introduction on the main topics necessary to understand and use EFTs, such as symmetries, renormalization-group methods and anomalies. As an advanced quantum field theory (QFT) book, it exploits the possibility of relying on the previous knowledge of the reader and concentrates on the relevant issues; the introduction is written in a practical way, providing EFT jargon and highlighting the differences between renormalisable and non-renormalisable theories.
The tone of the book makes it suitable not only for practitioners in the field, but also for students looking for a broad perspective on different QFT topics – the common EFT language providing the thread – and for teachers searching for analogies and similarities between advanced and classical topics.
