Geometry and Physics

verfasst von: Jürgen Jost

Verlag: Springer Berlin Heidelberg

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Geometry

Abstract

We collect here some basic facts and principles of differential geometry as the foundation for the sequel. For a more penetrating discussion and for the proofs of various results, we refer to J. Jost (Riemannian Geometry and Geometric Analysis, 5th edn., Springer, Berlin, 2008). Classical differential geometry as expressed through the tensor calculus is about coordinate representations of geometric objects and the transformations of those representations under coordinate changes. The geometric objects are invariantly defined, but their coordinate representations are not, and resolving this contradiction is the content of the tensor calculus.

Jürgen Jost

Chapter 2. Physics

Abstract

In this section, we will describe some important principles at a heuristic level. We hope this will be useful as a guide to some of the sequel which is more formal, but whenever the meaning of this section appears unclear, the reader should proceed to the more formal treatment below. There are many textbooks available on the mathematical aspects of quantum mechanics, for instance (Gustafson and Sigal, Mathematical Concepts of Quantum Mechanics, Springer, Berlin, 2003).

Jürgen Jost

Backmatter

Titel: Geometry and Physics
verfasst von: Jürgen Jost
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-642-00541-1
Print ISBN: 978-3-642-00540-4
DOI: https://doi.org/10.1007/978-3-642-00541-1