Quantization of Gauge Systems by Marc Henneaux (PDF)

Description

This book is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac’s analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and gauge invariance is carefully explained. The authors then proceed to the canonical quantization of gauge systems, first without ghosts (reduced phase space quantization, Dirac method) and second in the BRST context (quantum BRST cohomology). The path integral is discussed next. The analysis covers indefinite metric systems, operator insertions, and Ward identities. The antifield formalism is also studied and its equivalence with canonical methods is derived. The examples of electromagnetism and abelian 2-form gauge fields are treated in detail. The book gives a general and unified treatment of the subject in a self-contained manner. Exercises are provided at the end of each chapter, and pedagogical examples are covered in the text.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I bought this book more than a year ago, and it took me a long time to make progress in my spare time. Let me summarize it up front: it is a true gem, and it is a great reference book. However, it will never make it as a textbook for a second (advanced) Graduate course on Quantum Field Theory (QFT), or even for an advanced graduate seminar class. Its approach and its contents are too formal (in the mathematical sense) even for most theoretical physicists. If you don’t already know a great deal about the general topics covered in this book before you read it, you probably will not learn them by reading this book. Specifically, you should be very familiar with the Dirac-Hamiltonian constraint formalism, Gauge Invariance, Path Integral Field Quantization a la Faddeev and Popov, BRST symmetry etc. You will learn the rigorous foundations of all of these explained in glorious (and sometimes hard to follow) mathematical details.The book starts with a formal review of Dirac’s treatment of the constrained Hamiltonian systems, followed by the second chapter on the Geometry of constraint surfaces. Frankly the second chapter adds little value to the later discussion. Feel free to skip it for the first read. Chapter 3 is very important: Gauge Invariance and its relationship to the constrained Dirac-Hamiltonian formalism. Once again I would recommend skipping chapters 4 and 5 on the first read, if you are anxious to reach the real core stuff as quickly as possible. “Generally Covariant Systems” is a cute little chapter but it can wait for a later reading. Chapters 6 and 7 cover Fermionic degrees of freedom with anti-commuting (Grassmann) variables. These two are simple and straightforward chapters for anybody who has completed a one year graduate course on QFT.The real meat of the book starts in Chapter 8. In fact Chapters 8 through 14 are all on the BRST symmetry of the gauge fixed Lagrangians. This is why I read this book in the first place. I was familiar with the BRST symmetry to the extent that most physicists are, i.e. in its use in proving the renormalizability of gauge theories. After reading these seven chapters I learned a lot more about the beautiful mathematical foundations behind this symmetry, and its implications for the field theories. Even so, I think I only got a glimpse of what’s there. I definitely need a second (and maybe a third) read to clarify what I still do not understand. In fact, making progress was rather difficult for me starting with Chapter 9 and onwards. The authors are very strongly mathematically inclined and often make statements which must be obvious to them, but were not to me. Just as an example take the mini section 9.4.3, which is only three short paragraphs long. However, the statements made there are either trivial or very profound, I cannot fathom which.I effectively stopped reading the book after Chapter 16, and I never read Chapters 17 and 18 which are about the anti-field methods (which I was not interested in.) Ironically, the last two chapters (18 and 19) are the simplest material in this book and should be familiar to any student who completed a standard graduate level QFT class before.I very highly recommend this as a reference book which should be in the library of every theoretical physicist.

⭐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.

⭐

⭐

Keywords

Free Download Quantization of Gauge Systems in PDF format
Quantization of Gauge Systems PDF Free Download
Download Quantization of Gauge Systems 2020 PDF Free
Quantization of Gauge Systems 2020 PDF Free Download
Download Quantization of Gauge Systems PDF
Free Download Ebook Quantization of Gauge Systems