Friday, February 16, 2007

New Book on the Lattice

There is a new book about lattice QCD by Tom DeGrand and Carleton DeTar (D&D). It is still quite new, and in fact I am still waiting for my copy to be delivered, but a senior colleague here in Regina was so nice to let me borrow his copy, so you can get my review.

D&D is a comprehensive overview of the current state of the art in lattice QCD. In the space of just 327 pages (excluding front and back matter) they manage to cover pretty much everything one needs to know about in order to be able to read the current research literature. To the best of my knowledge, this is the first lattice monograph to discuss such crucial topics as data analysis for lattice simulations, improved actions and operator matching, chiral extrapolations, and finite-volume effects.

Compared to Montvay and Münster (M&M) at 442 pages, and to Rothe at 481 pages, both of whom cover much less material, D&D are necessarily rather terse. There are no detailed derivations or proofs, and no discussion of the results of lattice simulations is given anywhere. The latter omission is very rightly justified by the authors, as to include them "would be to invite obsolescence". While the terseness of the presentation probably limits the usefulness of D&D as a graduate textbook, the authors' stated aim to bridge the gap between what a conventional (non-lattice) theorist already knows and the current research literature which often presupposes an enormous amount of specialised knowledge appear to have been met admirably well.

After a brief overview of continuum QCD and a quick introduction to path integrals for bosons and fermions, and to the renormalisation group, D&D turn to introducing the lattice discretisation of pure gauge theories, including topics such as gauge fixing and strong coupling expansions. A comprehensive overview of lattice fermion actions follows, covering naive, Wilson, twisted mass, staggered and exactly chiral fermions as well as heavy-quark actions (HQET, NRQCD and Fermilab action). This is succeeded by chapters discussing simulation algorithms for both gluonic and fermionic actions, including such state-of-the-art algorithms as RHMC, BiCGStab and Lüscher's implementation of Schwartz decomposition. Data analysis methods, including correlated fitting, bootstrap methods and Bayesian (constrained) fitting, are discussed in a chapter of their own. The design of improved lattice actions (covering both Symanzik and tadpole improvement, as well as "fat link" actions) also gets a chapter of its own, as does the design of measurement operators for spectroscopic quantities. This is followed by a chapter on Lattice Perturbation Theory (which even cites this paper) and one on matching operators between the lattice and the continuum. Chiral perturbation theory, including such difficult subjects as quenched and staggered χPT, also gets a chapter, as do finite-volume effects and their applications. An overview of Standard Model observables amenable to testing via lattice simulations and a brief introduction simulations of finite-temperature QCD round off this very comprehensive book (including even such specialised topics as dimensional reduction of thermal QCD or the maximum entropy method for extracting spectral functions). The bibliography and the index, while also rather terse, appear useful.

In short, D&D have written a comprehensive introduction to state-of-the-art lattice QCD, which should serve both as a useful introduction to those who know a little, but want to know much more, and as a quick reference for active researchers (although a more extensive bibliography will be missed by the latter). This book definitely belongs on the bookshelf of every lattice theorist as an important contemporary counterpoint to M&M's classic.


Matthew said...

What to they have to say about the "root[ing] of all evil"?

Georg said...

They call the fourth root approximation "understandably controversial", and say: "So far we have neither proof that the approximation is harmless, nor any indications that it is harmful. Despite the controversy, some of the (apparently) most successful and precise results in contemporary lattice gauge theory are based on this approximation." -- which I think is a fair assessment.