Smooth manifolds and observables光滑的多头管和可测

书籍目录

Preface to the English Edition  Preface  1 Introduction 2 Cutoff and Other Special Smooth Functions on R[superscript n] 3 Algebras and Points 4 Smooth Manifolds (Algebraic Definition) 5 Charts and Atlases 6 Smooth Maps 7 Equivalence of Coordinate and Algebraic Definitions 8 Spectra and Ghosts 9 The Differential Calculus as a Part of Commutative Algebra 10 Smooth Bundles 11 Vector Bundles and Projective Modules Afterword Appendix Observability Principle, Set Theory and the "Foundations of Mathematics" References Index

作者简介

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.

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