AIP Digital Archive
In classical mechanics, the system of two coupled harmonic oscillators is shown to possess the symmetry of the Lorentz group O(3,3) or SL(4,r) in the four-dimensional phase space. In quantum mechanics, the symmetry is reduced to that of O(3,2) or Sp(4), which is a subgroup of O(3,3) or SL(4,r), respectively. It is shown that among the six Sp(4)-like subgroups, only one possesses the symmetry which can be translated into the group of unitary transformations in quantum mechanics. © 1995 American Institute of Physics.
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