Analysis, Manifolds and Physics, Part 1: Basics by Yvonne Choquet-Bruhat (PDF)

Description

This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled “Connections on Principle Fibre Bundles” which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.

User’s Reviews

Editorial Reviews: Review Barry Simon..This book belongs on the shelf of every mathematically inclined physicist and every mathematician who is interested in physics… The high quality of French mathematics, combined in this volume with the wide professional expertise of the authors in mathematical physics, has resulted in a work of great value. … I can wholeheartedly recommend it to anyone who aspires to participate in the exciting developments in modern elementary particle physics and relativity.Physics Today… The scope of the coverage is unusually wide and the material treated with more rigour than is customary in a mathematical physics text, because only then can the results be used correctly and fruitfully…Physikalische Berichte

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

⭐The binding and paper used of this print batch are very poor, much worse than the last print one that I borrowed from the library. Disappointed.

⭐Writing a review for something that everybody knows its high quality would be a waste of time, but perhaps not anymore – younger people should know the ‘standard candles’.Unless you are in a place where all this material you can attend from lectures, this is the book that if you are (or want to be) a mathematical physicist must try to read ‘a little every day’, hoping that eventually things will start focusing and you will catch up.It should be considered in a sense as THE modern analogue of Synge & Schild’s Tensor Calculus – it has the same selection of topics but now all on manifolds: Analysis on Manifolds, Riemannian geometry, Integration, Connections, plus distributions and aplications to PDEs and selected topics of infinite-dim geometry.So you have here a source-book that will not only allow you to formulate, in a modern way, physical laws (differential geometry) but also help you to study them (PDEs).It is a profitable reading for someone who is somewhat versatile with elementary abstract mathematics, say at the level of Geroch’s Mathematical Physics (algebra, topology, measure theory, functional analysis), but once you get going, you never stop!Start off from chapter 3 and get back (or look up Geroch) if you need an explanation of a word you don’t understand or have forgotten.After you have a basic understanding a Riemannian geometry from this book you’ll hopefully be able to reach Mme Choquet’s new book on GR and the Einstein Equations, it is a continuation and uses the same notation, or volume 2 of the book under review on various topics in mathematical physics.Most importantly, keep your cool and don’t get intimidated!

⭐This is the book that inspired me as an undergraduate to learn and appreciate, to a large extent, how physics and mathematics cohabit so beautifully. I continue to see, to this day, as a graduate student, how many of the recent developments in theoretical physics have been inspired by new mathematics and conversely. I still refer to this book on occasion, since it is laid out in a style that is amenable to mathematicians (such as myself!). It’s an excellent read, and I highly recommend it (even as bed time reading!) Best regards, A.

⭐I use this book constantly. At first I thought it was good only as a reference, but now I know it is possible to actually LEARN any of its subjects from scratch. I particularly like its chapters on manifolds, Lie Groups and bundles. Connections on a principal bundle is extremely well done, with a translation to physics (gauge theories) performed in detail in an exercise (so to speak). Some time ago David Ruelle said that the physicists needed a presentation of recent mathematics in the form of Bourbaki’s “Fascicule des resultats”, a synthesis of the subject with complete definitions, examples and theorems clearly stated, but with the proofs ommited. This is it, except that in this book most demonstrations are not ommited, only those too complicated. The whole book is extremely readable, if you concentrate, turn out the TV, etc. A precious book.

⭐Este es una referencia enciclopédica sobre física matemática. Con una influencia francesa centrada en el análisis y una claridad extraordinaria en la exposición, está es una pieza de consulta deseable en toda biblioteca matemática personal. Sin embargo, no es una lectura suave y requiere dominio previo de las nociones básicas de análisis, física y geometría para poder emplearla adecuadamente.I have been looking for a good book to learn more about geometrical concepts without going the full blown pure math route. This is exactly what this book allows me to do and for a bonus the authors always mention how the math is applied to physical situations as is routinely shown in the problems they created.

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