Smooth Manifolds and Observables

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.

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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.