We present the construction of an infinite dimensional Banach manifold of quantum mechanical states on a Hilbert space H using different types of small perturbations of a given Hamiltonian. We provide the manifold with a flat connection, called the exponential connection, and comment on the possibility of introducing the dual mixture connection.

Proceedings of the Disordered and Complex Systems, King's College, London, 10-14 July 2000 (satellite meeting of the ICMP2000)