From: George Jones Subject: Re: Self-learning quantum mechanics Date: Thu, 28 Dec 2000 10:18:37 -0400 Newsgroups: sci.physics.research Summary: [missing] In article <91vrbs$al7$1@nnrp1.deja.com>, stanley.shapiro@wcom.com wrote: > I want to learn quantum mechanics on my own and would like advice on > suitable textbooks. > My Ph.D is in optimal control engineering, so I have a solid applied > math background - differential equations, linear algebra. My suggestion is "Quantum Mechanics and the Particles of Nature: An Outline for Mathematicians" by Sudbery. This book is one of my favourites, although I don't like the title. To me, the title makes it sound like the book is applied functional analysis for professional mathematicians, which is certainly not the case. This book will not turn you into a licensed quantum mechanic, but will provide a good quantitative grounding in the foundations of quantum theory. It starts from scratch, introduces quantum theory, covers quantum metaphysics, and ends with chapters that are quantitative introductions to elementary particles and quantum field theory, including quantum flavourdynamics. This is all done in 350 pages, which may mean that the is book is a little too terse for self-study, but this could also be taken as one of the book's strengths. There are also about 150 problems in the book. To give more of an idea of what the author was up to, here are a couple of excerpts from the book's preface. "... In practice I have imagined the reader as a mathematics student taking a third-year undergraduate course in quantum mechanics such as is commonly offered as part of the mathematics degree course in British universities. Only a minority of such students will be intending to pursue the subject further, and it seems more appropriate to aim for a wide survey of the interesting bits than to try to provide a sound basis for a training as a quantum mechanic. ... this book might be found difficult by students who have not taken a first course on quantum mechanics based on wave functions. Formally, however, it requires no knowledge of any physics. Formally, also, the only mathematics required is vector algebra and vector calculus; but the reader with no knowledge of linear algebra will probably find it heavy going, and an acquaintance with the idea of a group and the elements of analytical mechanics will be helpful in places." Unfortunately, this excellent book is out of print; I don't know if its available at any used book on-line sites. Good luck with whatever book (or books) that you choose! Regards, George ============================================================================== From: George Jones Subject: Re: Self-learning quantum mechanics Date: Mon, 1 Jan 2001 05:39:49 GMT Newsgroups: sci.physics.research In article , John Baez wrote: > In article <3A4D220E.170D51CD@uvi.edu>, George Jones wrote: > > >I only brought up quantum field theory because Sudbery is the only > >book of its kind that I know of, i.e., it starts at the beginning, > >ends with quantum field theory, and gives a (I think masterful) > >quantitative overview of these topics and everything in between. > > Sounds interesting. I've always thought there was no really good > introduction to quantum field theory - there are a lot of books worth > reading, but most of them make sense *after* you've learned quantum > field theory. So I never know what to recommend... especially to > my math department colleagues who are curious about QFT, but > unwilling to submit themselves to years of confusion and struggle > (as I had to, when I learned the stuff). I'll have a look at this book! > > A question: what's Sudbery's first name? I would be really pleased > if it were Anthony. Anthony ("Tony") Sudbery is one of the physicists > who has done the most to understand the possible applications of > octonions to physics. But I somehow can't imagine him writing the > book you describe, so it's probably some other Sudbery. Yes, your friend Tony Sudbery authored this book. In the spring of 96 (or was it 95),I met Sudbery (who was one of the speakers) at a day of invited talks sponsored by the philosophy of science group at the University of Western Ontario. I talked to him during the lunch break and at the end of the day, and he was pleased when I expressed interest in his book. When he got back to Britain, he mailed an errata collection for the book to a then colleague of mine, and I still have a copy. Nice guy. I'm not sure if his treatment of quantum field theory is comprehensive enough for your math colleagues; it's only about 35 pages long. Also, I have a bit of a problem with the way he talks about "second quantization." I, too, would like to see a good introduction to quantum field theory. There is also "Quantum Field Theory for Mathematicians," by R. Ticciati. Again, I don't like the title. This is a physics book (as opposed to a math book), but many physicists will be immediately turned off by the title. This book contains virtually no functional analysis and worries little about things like convergence, etc. The book is about the same size as Peskin/Schroeder, and covers much of the same material. However, the math is a little more formal and a little tighter. In particular, the finite-dimensional representation theory is presented better. For example, he at least makes the distinction between a real Lie algebra and its complexification. Unfortunately, he doesn't touch on unitary, infinite-dimensional representations of the (covering of the) Poincare group and their relation to wave equations. I don't know how many people are reading this deeply in this thread, but I've always meant to ask the whole news group what they thought of this book. Don't be put off by the university that he was at when he wrote the book! His presentation was heavily influenced by a grad course he took from Sidney Coleman, but I wonder whether Ticciatti's "feel" for the physics is good enough. Regards, George