Differential Calculus on Manifolds with a Boundary. Applications

Abstract

This paper contains a set of lecture notes on manifolds with boundary and corners, with particular attention to the space of quantum states. A geometrically inspired way of dealing with these kind of manifolds is presented,and explicit examples are given in order to clearly illustrate the main ideas.

42 pages, 6 figures, accepted for publication in International Journal of Geometric Methods in Modern Physics

References in corpus (2)

• Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics
• Geometry of quantum systems: density states and entanglement

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• Covariant Jacobi Brackets for Test Particles
• Geometrical Structures for Classical and Quantum Probability Spaces
• Covariant Variational Evolution and Jacobi Brackets: Fields
• Covariant Variational Evolution and Jacobi Brackets: Particles
• Lagrangian description of Heisenberg and Landau-von Neumann equations of motion
• Differential Geometry of Quantum States, Observables and Evolution