Renormalization Methods: A Guide For Beginners

by William David McComb

This book is unique in occupying a gap between standard undergraduate texts and more advanced texts on quantum field theory. It covers a range of renormalization methods with a clear physical interpretations (and motivation), including mean fields theories and high-temperature and low-density expansions. It then process by each steps to the famous epsilon expansion, ending up with the first-order corrections to critical exponents beyond mean-field theory. Nowadays there is widespread interest in applications of renormalization methods to various topics ranging over soft condensed matter,engineering dynamics, traffic queuing and fluctuations in the stock market. Hence macroscopic systems are also included with particular emphasis on the archetypal problem of fluid turbulence. The book is also unique in making this material accessible to readers other than theoretical physics, as it requires only the basic physics and mathematics which should be known to most scientists, engineers
and mathematicians.

Genres: Physics

352 pages, Paperback

First published January 21, 2004

Reviews

[Erickson · Rating 5 out of 5]

Finished Chapter 1-3, 7-10. I must say that this book is a lot better than I expected.

I am just a little disappointed at the way Chapter 10 (field-theoretic RG) was done, it felt a lot more rushed and it's hard to follow unless you are a field theorist and are willing to do brute-force computations instead of getting the conceptual ideas. I think the author is trying to follow literally the strategy in the previous chapters --- stripping difficult concept to its bare minimum --- but this time, it was a bit overkill. Maybe it's understandable since this is not a QFT book. One example is that his "random" definition of vertex function was sudden. That said, I think the author did a decent job highlighting what is renormalization and what is regularization - they always happen together and it's not always clear what is which, and when which happens.

Apart from Chapter 10, the rest are beautifully written. I was trying to re-learn what RG means, why it is important, why it is not "silver bullets" for every problem, and what it gives us (and what it does not give us). It also explains clearly what is "by choice" (coarse-graining procedure), what is robust, what is approximate, and what is exact. This book is for the most part clean - even for non-rigorous things, the book strives to spell out what the terms exactly means.

I have to say that I like one quirk of the book (which somehow didn't happen in Chapter 10): the author spells out exactly the "theoretical objectives" of each task whenever the author is trying to do something. For this topic on renormalization group, the value cannot be overstated because it is easy to get lost (for people like me) why one went all the length to do (oftentimes painful) computations to reach a particular endpoint.