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 Barney Bramham, Helmut Hofer - arXiv
Both dynamical systems and symplectic geometry have rich theories and the time seems ripe to develop the common core with integrated ideas from both fields. We discuss problems which show how dynamical systems and symplectic ideas come together.
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 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.
by Shahn Majid - arXiv
Systematic introduction to the geometry of linear braided spaces. These are versions of Rn in which the coordinates xi have braid-statistics described by an R-matrix. From this starting point we survey the author's braided-approach to q-deformation.