Quantum mechanics and geometric analysis on manifolds

A central idea of modern geometric analysis is the assignment of a geometric structure, usually called the symbol, to a differential operator. It is known that this operation is closely related to quantum mechanics. For a class of linear operators, including the Dirac operator, a geometric structure, called a co-Riemannian metric, is assigned to such symbols. Certain other topics related to the geometric structure of quantum mechanics, e.g., the symplectic structure of the projective space of Hilbert space, are briefly treated. (author)