Smooth Manifolds and Observables
Seiten
2002
|
2003 ed.
Springer-Verlag New York Inc.
978-0-387-95543-8 (ISBN)
Springer-Verlag New York Inc.
978-0-387-95543-8 (ISBN)
An introduction to fiber spaces and differential operators on smooth manifolds. It explains why differential calculus on manifolds can be considered as an aspect of commutative algebra.
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.
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.
Cutoff and Other Special Smooth Functions on ?n.- Algebras and Points.- Smooth Manifolds (Algebraic Definition).- Charts and Atlases.- Smooth Maps.- Equivalence of Coordinate and Algebraic Definitions.- Spectra and Ghosts.- The Differential Calculus as a Part of Commutative Algebra.- Smooth Bundles.- Vector Bundles and Projective Modules.
| Erscheint lt. Verlag | 4.10.2002 |
|---|---|
| Reihe/Serie | Graduate Texts in Mathematics ; 220 |
| Zusatzinfo | XIV, 222 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Naturwissenschaften ► Physik / Astronomie ► Quantenphysik | |
| ISBN-10 | 0-387-95543-7 / 0387955437 |
| ISBN-13 | 978-0-387-95543-8 / 9780387955438 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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