Differential Manifolds: A Basic Approach For Experimental Physicists

Paul Baillon (Autor)

Buch | Hardcover

592 Seiten

2013
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-4449-56-4 (ISBN)

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Differential Manifold is the framework of particle physics and astrophysics nowadays. It is important for all research physicists to be well accustomed to it and even experimental physicists should be able to manipulate equations and expressions in that framework.This book gives a comprehensive description of the basics of differential manifold with a full proof of any element. A large part of the book is devoted to the basic mathematical concepts in which all necessary for the development of the differential manifold is expounded and fully proved.This book is self-consistent: it starts from first principles. The mathematical framework is the set theory with its axioms and its formal logic. No special knowledge is needed.

Manifold: Differentiable Manifold; Smooth Maps; Vector Fields on a Differentiable Manifold; Conventions; Tangent Spaces and Tangent Vectors; Coordinate Changes; Metric on a Differentiable Manifold; One-Form Field and Differential; Tensorial Field; Wedge Product of 1-Linear Forms (versus Vector Fields); Exterior Differential; Volume and Integral in Differential Manifold, Stokes Kelvin - Thomson Theorem; Lie Bracket; Bundles and Differentiable Manifold; Parallel Transport; Curvature; Lagrangian of the Electro-Weak Interactions (Left Handed); General Relativity; Notations; Some Basic Mathematics Needed for Manifolds: General Concepts; Real Numbers, Set ℛ; Euclidean Metric; Metric and Topology on ℛ; Behavior at a Point; Some Properties of Continuous Maps from ℛ to ℛ; Continuous Maps from Topological Sets to ℛ; Derivable Function; Group; Module Over a Commutative Ring; Vector Spaces; Complex Numbers; ℛn; Convex Subset; Topology on ℛn; Continuous Map on ℛn to ℛp; Sequence; Sequence in ℛ∞; Sequence of Maps; Partial Derivative; Topology on Convex Subsets; Path Connected Sets; Riemann Integral of Maps with Compact Support; Volume in ℛn; Integral of a Continuous Map; Differential Equations; Lebesgue Integral; Taylor Expansion of Functions with Derivatives; Exponentials; Polynomials; Useful Smooth Maps Built with Exponentials; Eigenvectors of a Linear Transformation; Conventions, Basic Relations and Symbols: Logical Theory; Specifics Terms; Quantificators; Specifics Relations; Sets; Relations and Operations on Sets; Zermolo Theorem; Cardinals; Integers; Rational Numbers; Conventions.

Verlagsort	Singapore
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik
	Naturwissenschaften ► Physik / Astronomie ► Hochenergiephysik / Teilchenphysik
ISBN-10	981-4449-56-3 / 9814449563
ISBN-13	978-981-4449-56-4 / 9789814449564
Zustand	Neuware