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.
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Book 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.
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Editorial Reviews
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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
..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
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Most Helpful Customer Reviews
17 of 18 people found the following review helpful:
5.0 out of 5 stars
an inspiration,
By
This review is from: Analysis, Manifolds and Physics Part I: Basics (Hardcover)
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.
19 of 21 people found the following review helpful:
5.0 out of 5 stars
A treasure for physicists,
This review is from: Analysis, Manifolds and Physics Part I: Basics (Hardcover)
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.
14 of 15 people found the following review helpful:
5.0 out of 5 stars
A must have desk reference and educational tool,
By A Customer
This review is from: Analysis, Manifolds and Physics Part I: Basics (Hardcover)
This was the most reliable (and compact) source of mathematical information that I could find. I used it (almost exclusively) to teach myself what I needed to know to do my PhD thesis in General Relativity with Torsion fields. It is very overwhelming to look at the book the first time. But give it time. It is well written and inviting. The only draw back for me was the very small print.
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