Abstract
An analysis in phase space of the behavior of a relativistic four-dimensional harmonic oscillator undergoing stochastic interactions shows that the group of linear canonical transformations in phase space which leaves invariant the Poisson brackets is anSp(12,4) group, withSp(12,4)⊃U(6,2)⊃SU(1,1)⊗SO(6,2). The application of Cartan's treatment to its behavior implies a classification of its stable states characterized by a set of discrete numbers.
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Gueret, P., Merat, P., Moles, M. et al. Stable states of a relativistic harmonic oscillator imbedded in a random stochastic thermostat. Lett Math Phys 3, 47–56 (1979). https://doi.org/10.1007/BF00959538
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DOI: https://doi.org/10.1007/BF00959538