Smooth Manifolds and Observables
Seiten
2002
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 gives an introduction to fiber spaces and differential operators on smooth manifolds. 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 fundamental notion of observable which is used by physicists and will further the understanding of the mathematics underlying quantum field theory.
This book gives an introduction to fiber spaces and differential operators on smooth manifolds. 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 fundamental notion of observable which is used by physicists and will further the understanding of the mathematics underlying quantum field theory.
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 |
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