A geometric approach to the canonical reformulation of quantum mechanics

The measure of distinguishability between two neighboring preparations of a physical system by a measurement device naturally defines a line element on the preparation space of the system. We show that quantum mechanics can be derived from the invariance of this line element in the canonical formulation. We also discuss the canonical formulation of quantum statistical mechanics. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 3, pp. 479–486, June, 2006.