It is shown that the geometry of quantum theory can be derived fromgeometrical structure that may be considered more fundamental. The basicelements of this reconstruction of quantum theory are the natural metric on thespace of probabilities (information geometry), the description of dynamicsusing a Hamiltonian formalism (symplectic geometry), and requirements ofconsistency (K\"{a}hler geometry). The theory that results is standard quantummechanics, but in a geometrical formulation that includes also a particularcase of a family of nonlinear gauge transformations introduced by Doebner andGoldin. The analysis is carried out for the case of discrete quantum mechanics.The work presented here relies heavily on, and extends, previous work done incollaboration with M. J. W. Hall.
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