Geometry in Physics
by Alexander Altland
Number of pages: 79
From the table of contents: Exterior Calculus (Exterior Algebra, Differential forms in Rn, Metric, Gauge theory, Summary and outlook); Manifolds (Basic structures, Tangent space, Summary and outlook); Lie groups (Generalities, Lie group actions, Lie algebras, Lie algebra actions, From Lie algebras to Lie groups).
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by Raffaele Resta - University of Trieste
From the table of contents: Introduction; Early discoveries; Berry-ology (geometry in nonrelativistic quantum mechanics); Manifestations of the Berry phase; Modern theory of polarization; Quantum metric and the theory of the insulating state.
by Alain Connes - Academic Press
The definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics. Ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics.
by Alain Connes, Matilde Marcolli - American Mathematical Society
The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role.
by Maximilian Kreuzer - Technische Universitat Wien
From the table of contents: Topology (Homotopy, Manifolds, Surfaces, Homology, Intersection numbers and the mapping class group); Differentiable manifolds; Riemannian geometry; Vector bundles; Lie algebras and representations; Complex manifolds.