On the proper symmetry theoretical formulation of the theory of Lorentz covariant, or ‘relativistic’, quantum particle dynamics, we illustrate the inadequacy of the Poincare symmetry for the purpose and present a fully conceptually consistent formulation from a larger symmetry which also admits a noncommutative geometric interpretation as an exact analog of that of the standard quantum mechanics as its ‘nonrelativistic’ limit, to be retrieved from a symmetry contraction procedure. Our approach emphasizes how such a formulation gives essentially all aspects of the theory from a full representation picture, including the dynamics from the natural symplectic geometry.

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Lorentz Covariant Quantum Particle Dynamics from the Proper Symmetry Theoretical Formulation

  • Otto C. W. Kong

摘要

On the proper symmetry theoretical formulation of the theory of Lorentz covariant, or ‘relativistic’, quantum particle dynamics, we illustrate the inadequacy of the Poincare symmetry for the purpose and present a fully conceptually consistent formulation from a larger symmetry which also admits a noncommutative geometric interpretation as an exact analog of that of the standard quantum mechanics as its ‘nonrelativistic’ limit, to be retrieved from a symmetry contraction procedure. Our approach emphasizes how such a formulation gives essentially all aspects of the theory from a full representation picture, including the dynamics from the natural symplectic geometry.