Smooth Manifolds and Observables
Gewicht:
391 g
Format:
235x155x0 mm
Beschreibung:
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 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.
* 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