Lectures on the Geometry of Quantization
by Sean Bates, Alan Weinstein
Publisher: University of California at Berkeley 1997
Number of pages: 134
This is an introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role which these ideas play in formalizing the transition between the mathematics of classical dynamics (hamiltonian flows on symplectic manifolds) and that of quantum mechanics (unitary flows on Hilbert spaces).
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by Michael Atiyah - arXiv
These notes are based on a set of six lectures that the author gave in Edinburgh and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and they may stimulate readers to investigate them.
by C. Nash - arXiv
In this essay we wish to embark on the telling of a story which, almost certainly, stands only at its beginning. We shall discuss the links and the interaction between one very old subject, physics, and a much newer one, topology.
by Alexander Altland
Contents: Exterior Calculus (Exterior Algebra, Differential forms in Rn, Metric, Gauge theory); Manifolds (Basic structures, Tangent space); Lie groups (Lie group actions, Lie algebras, Lie algebra actions, From Lie algebras to Lie groups).
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.