O(3,3)-like Symmetries of Coupled Harmonic Oscillators

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dc.creatorHan, D.
dc.creatorKim, Y. S.
dc.creatorNoz, Marilyn E.
dc.date1997-04-03
dc.date.accessioned2026-07-07T06:14:13Z
dc.date.available2026-07-07T06:14:13Z
dc.descriptionIn classical mechanics, the system of two coupled harmonic oscillators is shown to possess the symmetry of the Lorentz group O(3,3) applicable to a six-dimensional space consisting of three space-like and three time-like coordinates, or SL(4,r) in the four-dimensional phase space consisting of two position and two momentum variables. 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. In quantum mechanics, there is the lower bound in the size of phase space for each mode determined by the uncertainty principle while there are no restriction on the phase-space size in classical mechanics. This is the reason why the symmetry is smaller in quantum mechanics.
dc.descriptionRevTeX, 24 pages, no figures, preliminary version in J. Math. Phys. {\bf 36}, 3940 (1995)
dc.identifierhttps://arxiv.org/abs/quant-ph/9704005
dc.identifierhttp://arxiv.org/abs/quant-ph/9704005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/93381
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.titleO(3,3)-like Symmetries of Coupled Harmonic Oscillators
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