| 书目名称 | Smooth Manifolds and Observables |
| 编辑 | Jet Nestruev |
| 视频video | |
| 概述 | Motivates the algebraic study of smooth manifolds by looking at them from the point of view of physics, in particular by using the observability principle.Bridges between ideas from physics, geometry, |
| 丛书名称 | Graduate Texts in Mathematics |
| 图书封面 |  |
| 描述 | This textbook demonstrates how differential calculus, smooth manifolds, and commutative algebra constitute a unified whole, despite having arisen at different times and under different circumstances. Motivating this synthesis is the mathematical formalization of the process of observation from classical physics. A broad audience will appreciate this unique approach for the insight it gives into the underlying connections between geometry, physics, and commutative algebra..The main objective of this book is to explain how differential calculus is a natural part of commutative algebra. This is achieved by studying the corresponding algebras of smooth functions that result in a general construction of the differential calculus on various categories of modules over the given commutative algebra. It is shown in detail that the ordinary differential calculus and differential geometry on smooth manifolds turns out to be precisely the particular case that corresponds to the category of geometric modules over smooth algebras. This approach opens the way to numerous applications, ranging from delicate questions of algebraic geometry to the theory of elementary particles..Smooth Manifolds and |
| 出版日期 | Textbook 2020Latest edition |
| 关键词 | Smooth manifolds; Smooth manifold theory; Observables; Observability; differential geometry smooth manif |
| 版次 | 2 |
| doi | https://doi.org/10.1007/978-3-030-45650-4 |
| isbn_softcover | 978-3-030-45652-8 |
| isbn_ebook | 978-3-030-45650-4Series ISSN 0072-5285 Series E-ISSN 2197-5612 |
| issn_series | 0072-5285 |
| copyright | Springer Nature Switzerland AG 2020 |
发表于 2025-3-21 18:21:24
