Abstract
The space of pure states of any physical system,classical or quantum, is identified as a Poisson spacewith a transition probability. These two structures areconnected through unitarity. Classical and quantum mechanics are each characterized by asimple axiom on the transition probability p. Unitaritythen determines the Poisson bracket of quantum mechanicsup to a multiplicative constant (identified with Planck's constant).
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Landsman, N.P. Simple New Axioms for Quantum Mechanics. International Journal of Theoretical Physics 37, 343–348 (1998). https://doi.org/10.1023/A:1026631221235
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DOI: https://doi.org/10.1023/A:1026631221235