Smooth manifolds and observables
著者
書誌事項
Smooth manifolds and observables
（Graduate texts in mathematics, 220）
Springer, c2003
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注記
"First published in Russian in 2000 by MCCME Publishers"--P. [v]
Bibliography: p. [217]-218
Includes index
内容説明・目次
内容説明
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.
目次
* Preface to English Edition * Preface * Introduction * Cutoff and Other Special Smooth Functions on R^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 * Afterword * Appendix * References * Index
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