1996/04/10 by N. P. Landsman, Landsman, N. P.
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9604008
LaTeX, 4 pages
arxiv created 1996/04/10 · arxiv updated 2009/12/01
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.