No comments about The Language of Physics: The Calculus and the Development of Theoretical Physics in Europe, 1750 - 1870.

No comments about Leonard of Pisa and the New Mathematics of the Middle Ages.

1 comments about Diffraction Effects in Semiclassical Scattering (Montroll Memorial Lecture Series in Mathematical Physics).

1. I have studied Physics with the Nussenzveig's collection "Física Básica" (just avaiable in Brazil) and I can say he is a very good Physics Teacher, and better, a hardline Physics Teacher! His book on diffaction would not be different, and I think who wants to know what matters about diffraction should read this book!

No comments about Conférence Moshé Flato 1999: Quantization, Deformations, and Symmetries Volume I (Mathematical Physics Studies).

No comments about Computational Complexity and Statistical Physics (Santa Fe Institute Studies in the Sciences of Complexity Proceedings).

3 comments about Quantum Field Theory for Mathematicians (Encyclopedia of Mathematics and its Applications).

1. This book is far from perfect, but I think it begins to fill an important niche in the world of QFT books: it presents most aspects of the theory, from basic principles to Feynman rules, gauge fields and renormalization, in a form that is unusually accessible to mathematicians. I'm coming at this from the perspective of a mathematician who has tried and failed to learn QFT from a variety of other books, and I wish I had discovered this one before even opening Weinberg or Peskin & Schroeder. Ticciati doesn't completely avoid the kind logical sleight of hand that is commonplace among physicists, but when doing manipulations whose mathematical basis is questionable, he's usually at least honest enough to point this out to the reader. I especially enjoyed the chapter on Lie algebra representation theory, which is closer to a mathematician's presentation of this subject than a physicist's, yet not without plenty of physical motivation. I'd criticize this book only for two things: (1) it's riddled with misprints (some obvious, some not) and (2) some topics are explained rather more concisely than they deserve, and not always in the most logical order; Ticciati has a tendency to use certain subtle concepts implicitly a few sections before he defines them precisely. One may hope that such errors will be corrected in a future edition.



2. Yes this book isn't perfect, but what book on physics is? That aside, there is no question this is an excellent field theory book with a rigorous approach. Physicists could learn from this style to produce better textbooks rather than following their usual mysterious approach to writing. This book is clearly laid out not only in mathematical style but also with clear and concise explanations of many physical concepts. It is in my opinion far better than Weinberg's book, written in a more readable style. It is also better than books like Peskin and Schroeder and Kaku which seem sloppily put together. Put the book together with Ryder and you will have the tools needed to get a good understanding of field theory. The title might be unfortunate, because it might keep physics professors from considering using it in their classes instead of the usual lousy standby's, which is too bad for the students.



3. I preface my comments by stating that this book is not intended as an introduction to QFT.
   
   The student should have a solid understanding of SR, QM, tensor analysis, group theory including Lie Groups, and Hilbert spaces.
   
   I will not regurgitate what the book covers, one need only use the "search inside" tab to look at the contents.
   
   Having said this, this book is an excellent and indispensible to tool to BROADEN and DEEPEN your understanding of QFT. If all you want to do is calculate scattering amplitudes and decay rates I would not recommend this book, there are plenty of better applied QFT books available for this.
   
   This books fills in the gaps other books fail to close. There is no "hand waving" of results which was refreshing. As a consequence you begin to understanding the subtle points of QFT and why the theory is the way it is.
   
   As mentioned in the title of the review there are plenty of "pearls". For example, there is an entire chapter on internal and external symmetries and their representations by groups of matrices ( lie groups ). There is a complete description of the importance of Lie alegbras and how the generators of the Lie Algebra create conserved currents and quantities ( operators ) which help one study the evolution of states since these quantities are conserved. By studying the structure of the lie algebra one gains importance insights into the commutative properties of the corresponding conserved current and quantity operators. There is a great section on the derivation of the S matrix and the relations between the "Schrodinger " " Heisenberg " and "Interaction" pictures of QM. We see that the evolution of the interacting state can be entirely derived from the free field hamiltonians with certain restrictions. One thing I really liked about this section is that it explains the limitations of the S matrix approach ( has to do with the assumptions of turning "on and off" interactions )which I have not come across in other standard QFT texts. This motivates the need for functional integral quantization.
   
   Another point of contention I have had with standard presentations of QFT is that they just assume that Noether's theorem from classical field theory can be applied after the quantization process. This book explains mathematically why it can be.
   
   Succinctly, the defects in QFT presentation in other texts is explained, which makes understanding the material more difficult. However, the payoff is that one understands the motivation behind the IDEAS of QFT.
   
   The book is also filled with little "homework" assignments to solidfy knowledge.
   
   The logical and organized presentation of the material made it very difficult for me to put this book down for any length of time until it was finished.

2 comments about Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics (Cambridge Mathematical Library).

1. Thermodynamic formalism is an area of mathematics developed to describe physical systems with a large number of components. A combination of advanced physics and mathematics, it is used to describe dynamic systems moving towards equilibrium and quantum mechanics applied to systems. The level of this book is advanced, generally the material would only be suitable for students at the graduate level. Exercises are given at the end of each chapter, although solutions are not provided. Additional background material on the necessary physics is included in a series of appendices.
   The treatment of thermodynamic formalism is brief, detailed and complete. I strongly recommend the book as a textbook or study aid in that area.



2. Rating a book like this is very difficult, because it's not like anything else. Thermodynamic Formalism is a book on the mathematical analysis of statistical thermodynamics, and its very dense. By "mathematical analysis" I mean the logical derivation of relationships of symbols from abstract definitions. Therefore, if you can show any subject matches the definitions, all the remaining results hold, whether the system is a gas, an economy, or a painting. Ruelle mentions early that this has been done in constructive quantum field theory and differential dynamical systems. There is no physics in the work, except to try to explain the symbols. It reads rather annoyingly like a poorly written homework set by an extremely clever graduate student.
   
   That said, when you've figured out what's going on it's an rewarding book. This completely formal approach does give a complimentary perspective on the topics covered. In the end, though, this is a book on Gibbs ensembles and classical thermodynamics, not on Fermi or Bose quantum systems. I do not know what would be required to incorporate those, and how many results will still hold when the probability measures are changed.
   
   Appendix B, Open Problems, presents topics that were unsolved at the time of publication of the first edition (of 1976) at least one for every chapter after the first, and Appendix D is an update for the second edition. This is a very nice touch. There are also simple problems at the end of every chapter so you can figure out how little you understand before you move on to the next chapter.
   
   I work in (experimental) solid state physics and have some (not much) scholastic background in applied analysis at the graduate level, and still I had to spend an afternoon trying to figure out what the symbols meant (that is, how x|L should be read, not what it corresponded to in real life; that was step two of three). The book didn't get any easier. As interesting as the book is, I have to warn anyone without a very strong mathematical background away from this book, at least until he's worked through an analysis text of some kind.

4 comments about Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics.

1. The theory of angular momentum is important in many fields of chemistry and physics.This book is a magnificently sadistic way to waste time and go crazy. I recommended to every introspective scientist that has no personal life and enjoys wasting time with the arcane.



2. This is a well-written and very interesting book with (perhaps) an unfortunate title. My first reaction was "A book devoted to angular momentum? Who would read such a thing?"

   Ignore the title and look at the sub-title: "Understanding Spatial Aspects in Chemistry and Physics." This book covers everything from polarized fluorescence spectroscopy to molecular beam scattering to molecular reorientation in liquids. All of these topics have one thing in common -- they are spatially anisotropic, and Zare leads the reader through a tutorial on their analysis.

   There are other books on this topic. (The monographs by Rose and by Brink and Satchler come to mind.) To my taste, they are dry and boring.

   Zare's book is different. Although he presents the material with the same rigor, he also includes 16 "applications" (i.e. problem sets) that showcase some of the most elegant physical chemistry/chemical physics problems of the century. For example, their are applications dealing with scattering, polarized fluorescence, Zeeman quantum beats, correlation functions in spectroscopy, and the spectroscopy of diatomic molecules. These applications usually cover real molecular problems -- not watered down analogues. Zare's discussion of spherical tensor operators deserves special note for its clarity.

   This book should be approachable to anyone with at least one semester of graduate quantum chemistry or physics under their belt.




3. There are, of course, several other books that derive and explain the details and myriad equations involved in our understanding of angular momentum (e.g. Edmonds, Judd). However, none of them explain the mathematics and physical results in "simple English" as well as Zare's. The problem sets and applications are particularly helpful and relevant to a wide variety of common experimental techniques and data analyses. I also strongly recommend purchasing the companion solutions manual. The only derogatory comment that I can make is that there are much better programs available for calculating the 3, 6, and 9J symbols than those found in the appendix. I doubt this comes as a surprise to anyone.



4. I have read this book with a great joy. The author of this book is a leading authority in the field of reaction dynamics, and has played a key role in applyingp the vector correlation in physical chemistry problems. The best part of this book probably is the example/problem set part where the reader is asked to use the knowledge obtained from the chapter to solve the "real" problem (mostly on spectroscopy and the gas phase reaction dynamics). I highly recommend this book.

No comments about Collisions, Rings, and Other Newtonian N-Body Problems (Cbms Regional Conference Series in Mathematics).

No comments about Diffusion-Wave Fields: Mathematical Methods and Green Functions.