Quantum Theory, Groups and Representations: An Introduction by Peter Woit | (PDF) Free Download

Description

This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader’s understanding of and facility in quantum-theoretical concepts and calculations.

User’s Reviews

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

⭐When I started studying group theory, I wondered to get a book which provided both a rigor mathematical background and an application on physics. So, I found it out o/. This is the most brilliant book that I have ever seen. Try it and you will realize that you would not wish to stop studying!

⭐Many thanks to Peter Woit for this beautiful and engaging work.A model of clarity, it is one of the best I’ve seen on the topics at hand.

⭐One can learn a lot from this book, but the experience can be excruciating. As observed by another reviewer this is an unusual math book. More like a narrative. Definitions are frequently omitted, and even when provided are incomplete. For example, there is a definition of the tangent space of a matrix Lie group but there is no proof that the sum of two elements of that set is also an element of it. In the unnumbered Theorem on p. 65 there is no proof that π’ is a linear map, which was the whole point. I could sketch a proof using the Campbell-Baker-Hausdorff formula, which was not introduced at that point in the book. The biggest problem is lack of clear definitions. Here are some examples: defining representation, vector representation, representation isomorphism, spin representation (there is a definition of spinor representation).Having said that, there is a lot to learn from the book. Reading it one gets many useful pieces of information that maybe some day will be unified in a coherent way. But for that a more rigorous book will be needed.The author has a YouTube channel that follows the book. He is not a good lecturer and skims over the material. There is no area for comments, so one cannot get answers through this channel.

⭐Excellent approach that doesn’t require an entire math degree to understand. Every graduate program should require a course using at least in part this book.

⭐I have been spending my time under lockdown working my way through this wonderful introduction to group theory in quantum mechanics. The book has just enough mathematical rigour to avoid the problems with Zee’s book without letting the math get in the way of the physics. If you are a physics student who wants to learn about the role of Lie theory in QM I cannot recommend this book highly enough. Buy it, read it and enjoy the new perspectives it will open for you.

⭐I am a ‚hobby mathematician‘ only, so my comments should be read with this in mind.The mathematical prerequisites seem modest to me, surely an undergraduate degree should be enough.The book is not written in the ‚normal‘ style of a math book, that is ‚definition‘, ‚some motivation‘, ‚theorem‘, ‚proof‘. Rather is looks like a narrative on the subject. (Richard Courant‘s books come to mind). There are very few theorems, they are not numbered, and sometimes not even a proof, but just some reference.This made it very difficult for me to read: when I did not understand some statement in the narrative, I never knew whether I should understand it form previous statements in the book, or whether it was not to be understood at this level.After about 250 pages (out of 600 total) is gave up.The book has very few typos, I have seen much worse.

⭐Quantum mechanics is an extremely rich source of group representations and yet most introductory courses and texts avoid the language and concepts of representation theory as they are more suited to an advanced treatment of the subject.This book emphasises the algebraic aspects of quantum theory and as such is an excellent complement to any of the other QM texts which emphasise the analytic material necessary to cover the Stone – Von Neumann and spectral theorems.It is highly readable and well suited to self study. An excellent book on a rewarding subject.

⭐Great book, like new, prompt delivery and good value

⭐i bought that book as somebody who is pretty fluent in quantum mechanics when i didnt knew anything about group theory, and i have loved absolutely everything about this book. in parts its very short, so you have to connect the given equations which is sometimes not that easy, but in general it is a good read, and i learned a ton. 10/10 would buy again.

⭐Pour mon usage personnel ; je veux savoir comment les physiciens théoriciens traitent de la théorie des représentations ; beaucoup d’ouvrages tous en Anglais hélas existent et se complétent ; l’ouvrage de P Voit est de façon ouverte une INTRODUCTION ; comme tel et à ce stade je n’en ai pas tout lu , il s’en faut , cet ouvrage est des plus utiles à la fois à des Étudiants en Physique Théorique et à des Étudiants en Mathématiques dont la culture dans les questions de Physique Théorique est le plus souvent lacunaire pour ne pas dire pire . C’est le premier Objectif de l’Ouvrage ; il est certain qu’il peut servir avec d’autres à des Chercheurs confirmés dans l’une ou l’autre des disciplines ; l’accés est original , clair et porte loin en dépit de sa modestie ; de l’auteur de ” Not even Wrong” cet Ouvrage était attendu ; il ne saurait se substituer à des monuments tels que ” QFTIN” de A Zee ( référencé ) ni à “A tourist guide for mathematicians ” de G Folland mais le tryptique forme un panorama impressionnant et très remarquable qu’en France on devrait mettre entre toutes les mains .

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