Symplectic formulation of relativistic quantum mechanics

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Abstract
It is shown that the covariant harmonic oscillator formalism in the light-cone coordinate system discussed in previous papers is a realization of the symplectic group. It is shown in particular that the Lorentz transformation of the wave function along a given direction corresponds to a one-parameter subgroup of Sp(4). The diagonal form in the light-cone coordinate system is discussed in detail. The oscillator formalism is known to represent the Poincaré group for relativistic extended hadrons, while serving as a simple calculational device for basic high-energy hadronic phenomena. Likewise, the symplectic formulation given in the present paper may serve as the basic spacetime/momentum-energy symmetry for a relativistic quantum mechanics of bound-state quarks.

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