Smooth Manifolds and Observables: 220 (Graduate Texts in Mathematics, 220) - Hardcover

Nestruev, Jet

Hardcover

ISBN 10: 0387955437 ISBN 13: 9780387955438

Publisher: Springer, 2002

Synopsis

This book is a self-contained introduction to fiber spaces and differential operators on smooth manifolds that is accessible to graduate students specializing in mathematics and physics. The authors offer an algebraic approach which is based on the fundamential notion of "observable" used by physicists, and which will further the understanding of the mathematics underlying quantum field theory. The prerequisites for this book are a standard advanced calculus course as well as courses in linear algebra and algebraic structures.

About this title

Review

From the reviews:

"Main themes of the book are manifolds, fibre bundles and differential operators acting on sections of vector bundles. ... A classical treatment of these topics starts with a coordinate description of a manifold M ... . The present book is based on an alternative point of view, where calculus on manifolds is treated as a part of commutative algebra. ... The book contains quite a few exercises and many useful illustrations." (EMS, September, 2004)

"The book provides a self-contained introduction to the theory of smooth manifolds and fibre bundles, oriented towards graduate students in mathematics and physics. The approach followed here, however, substantially differs from most textbooks on manifold theory. ... This book is certainly quite interesting and may appeal even to people who merely want to study algebraic geometry, in the sense that they will gain extra insight here by the attention which is paid to making certain constructions in algebraic geometry physically or intuitively acceptable." (Willy Sarlet, Zentralblatt MATH, Vol. 1021, 2003)

Synopsis

This book is a self-contained introduction to fiber spaces and differential operators on smooth manifolds that is accessible to graduate students specializing in mathematics and physics. Over the last 20 years the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be considered as an aspect of commutative algebra. This new approach is based on the fundamential notion of "observable" which is used by physicists and it will further the understanding of the mathematics underlying quantum field theory. The prerequisites for this book are a standard advanced calculus course as well as courses in linear algebra and algebraic structures.

Edition details

• Publisher: Springer
• Publication date: 2002
• Language: English
• ISBN 10: 0387955437
• ISBN 13: 9780387955438
• Binding: Hardcover
• Number of pages: 236