The Geometrization of Physics
by Richard S. Palais
Publisher: University of California at Irvine 1981
Number of pages: 107
The major goal of these notes is to develop, in sufficient detail to be convincing, an observation that basically goes back to Kaluza and Klein in the early 1920's that not only can gauge fields of the "Yang-Mills" type be unified with the remarkable successful Einstein model of gravitation in a beautiful, simple, and natural manner, but also that when this unification is made they, like gravitational field, disappear as forces and are described by pure geometry, in the sense that particles simply move along geodesics of an appropriate Riemannian geometry.
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by Ingemar Bengtsson - Stockholms universitet, Fysikum
These are the lecture notes from a graduate course in the geometry of quantum mechanics. The idea was to introduce the mathematics in its own right, but not to introduce anything that is not directly relevant to the subject.
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 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.
by Gabriel Lugo - University of North Carolina at Wilmington
These notes were developed as a supplement to a course on Differential Geometry at the advanced undergraduate level, which the author has taught. This texts has an early introduction to differential forms and their applications to Physics.