  The space P of pure states of any physical system, classical or quantum, is
identified as a Poisson space with a transition probability. The latter is a
function p: PxP -> [0,1]; in addition, a Poisson bracket is defined for
functions on P. These two structures are connected through unitarity. Classical
and quantum mechanics are each characterized by a simple axiom on the
transition probability p. Unitarity then determines the Poisson bracket of
quantum mechanics up to a multiplicative constant (identified with Planck's
constant). Superselection rules are naturally incorporated.

Quantum Physics