Quantization of Gauge Systems

Rating:
Summary: Excellent overview of quantum gauge theory
Review: Anyone interested in how to quantize gauge theories and BRST cohomology will want to read this book. The authors do a fine job of motivating the problem and discussing in depth where the essential problems arise. The book starts naturally with a discussion of constrained Hamiltonian systems, and this chapter is especially well written as it sets up the geometry for later discussions on quantization. Most of the discussion in the next few chapters is on geometrical constructions in classical gauge field theory. The authors do a fine job of explaining how Grassman algebra constructions come into play in classical field theory. To a beginner in the subject the appearance of "spin" degrees of freedom in classical field theory may be strange at first, but the chapter on Fermi degrees of freedom alleviates any skepticism on why one should proceed this way. BRST constructions occupy the next few chapters, and here one sees the role of ghosts as being a sort of "Lagrange multiplier" in the quantization of constrained systems. The authors discuss path integral quantization in the last chapters of the book, and do so in a way that is mostly formal, given that path integrals are not well defined from a mathematical standpoint. By far the best part of this discussion is on the Koszul-Tate complex and how it is related to the Schwinger-Dyson equations. It would take a lot of searching in the journal literature to obtain the knowledge gained from the reading of this book. Definitely a fine addition to the literature on this very difficult topic.

Rating:
Summary: Excellent overview of quantum gauge theory
Review: Anyone interested in how to quantize gauge theories and BRST cohomology will want to read this book. The authors do a fine job of motivating the problem and discussing in depth where the essential problems arise. The book starts naturally with a discussion of constrained Hamiltonian systems, and this chapter is especially well written as it sets up the geometry for later discussions on quantization. Most of the discussion in the next few chapters is on geometrical constructions in classical gauge field theory. The authors do a fine job of explaining how Grassman algebra constructions come into play in classical field theory. To a beginner in the subject the appearance of "spin" degrees of freedom in classical field theory may be strange at first, but the chapter on Fermi degrees of freedom alleviates any skepticism on why one should proceed this way. BRST constructions occupy the next few chapters, and here one sees the role of ghosts as being a sort of "Lagrange multiplier" in the quantization of constrained systems. The authors discuss path integral quantization in the last chapters of the book, and do so in a way that is mostly formal, given that path integrals are not well defined from a mathematical standpoint. By far the best part of this discussion is on the Koszul-Tate complex and how it is related to the Schwinger-Dyson equations. It would take a lot of searching in the journal literature to obtain the knowledge gained from the reading of this book. Definitely a fine addition to the literature on this very difficult topic.