非交換微分幾何及其在物理學(xué)中的應(yīng)用導(dǎo)論

內(nèi)容概要

本書主要內(nèi)容包括：Differential forms I、Differential forms II、Tensor products、Metrics、Yang-Mills connections、Linear connections、Curvature等。

作者簡(jiǎn)介

作者：(法國(guó))馬多雷(J.Madore)

書籍目錄

1 Introduction2 Differential Geometry　2.1 Diiferential manifolds　2.2 Metrics and connections　2.3 Cohomology3 Matrix Geometry　3.1 Differential forms I　3.2 Differential forms II　3.3 Tensor products　3.4 Metrics　3.5 Yang-Mills connections　3.6 Linear connections　3.7 Curvature4 Noncommutative Geometry　4.1 General algebras　4.2 Poisson structures　4.3 Topological algebras　4.4 Quantum groups5 Vector Bundles　5.1 K-theory　5.2 A matrix analogue　5.3 Predholm modules6 Cyclic Homology　6.1 The universal calculus　6.2 Cyclic homology　6.3 Morita equivalence　6.4 The Loday-QuiUen theorem7 Modifications of Space-Time　7.1 Noncommutative space-time　7.2 A finite model 　7.3 Fuzzy physics8 Extensions of Space-Time　8.1 The spinning particle　8.2 Noncommutative electrodynamics　8.3 Modified Kaluza-Klein theory

章節(jié)摘錄

插圖：If V is a smooth manifold then the algebra of smooth functions C（V） definedon it is of course a commutative algebra and in this case also there is an intrinsiccharacterization of the set of all such algebras, an additional structure which can beadded to an arbitrary commutative algebra .A which would insure that ,4 = C（V）for some V. The manifold V can always be considered as embedded in a euclideanspace Rn of sufficiently high dimension. The coordinates of the embedding spaceare generators of an algebra of polynomials which is dense in the algebra C（Rn）of smooth functions and the equations which define the manifold are relations inC（Rn）. The quotient of C（Rn） by the ideal generated by the relations is equal to thealgebra of smooth functions C（V） on V.

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