Friday, January 08, 2010

New book on the lattice

There was a time when the only textbooks on lattice QCD were Montvay&Münster and Creutz. Not so any more. Now the new textbook "Quantum Chromodynamicson the Lattice: An Introductory Presentation" by Christof Gattringer and Christian Lang (Lecture Notes in Physics 788, Springer) offers a thorough and accessible introduction for beginners.

Gattringer and Lang start from a derivation of the path integral in the context of Quantum Mechanics, and after deriving the naive discretisation of lattice fermions and the Wilson gauge action present first the lattice formulation of pure gauge theory, including the Haar measure and gauge fixing, with Wilson and Polyakov loops and the static quark potential as the observables of interest. Numerical simulation techniques for pure gauge theory are discussed along with the most important data analysis methods. Then fermions are introduced properly, starting from the properties of Grassmann variables and a discussion of the doubling problem and the Wilson fermion action, followed by chapters on hadron spectroscopy (including some discussion of methods for extracting excited states), chiral symmetry on the lattice (leading through the Nielsen-Ninomiya theorem and the Ginsparg-Wilson relation to the overlap operator) and methods for dynamical fermions. Chapters on Symanzik improvement and the renormalisation group, on lattice fermion formulations other than Wilson and overlap, on matrix elements and renormalisation, and on finite temperature and density round off the volume.

The book is intended as an introduction, and as such it is expected that more advanced topics are treated briefly or only hinted at. Whether the total omission of lattice perturbation theory (apart from a reference to the review by Capitani) is justified probably depends on your personal point of view -- the book clearly intends to treat lattice QCD as a fully non-perturbative theory in all respects. There are some other choices leading to the omission or near-omission of various topics of interest: The Wilson action is used both for gluons and quarks, although staggered, domain wall and twisted mass fermions, as well as NRQCD/HQET, are discussed in a separate chapter. The calculation of the spectrum takes the front seat, whereas the extraction of Standard Model parameters and other issues related to renormalisation are relegated to a more marginal position.

All of these choices are, however, very suitable for a book aimed at beginning lattice theorists who will benefit from the very detailed derivations of many important relations that are given with many intermediate steps shown explicitly. Very little prior knowledge of field theory is assumed, although some knowledge of continuum QFT is very helpful, and a good understanding of general particle physics is essential. The bibliographies at the end of each chapter are up to date on recent developments and should give readers an easy way into more advanced topics and into the research literature.

In short, this book is a gentle, but thorough introduction to the field for beginners which may also serve as a useful reference for more advanced students. It definitely represents a nice addition to your QCD bookshelf.