Wave Equation with Mass and Spin Spectrum Based on O(3,3) Group for Relativistic Deformable Model

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Abstract
On the basis of the fact that the group SL(4,R) of relativistic linear deformation and rotation is isomorphic to SO(3,3), new transformation properties under the physical Lorentz transformation is assigned to the internal coordinate in the bilocal-type model, which is adopted as a simple relativistic example having internal movement. The new viewpoint leads to both integer and half-integer spin states and also to the first order wave equation, which contains a mass spectrum corresponding to infinite-dimensional representations of the inner Lorentz group. On the other hand several versions of bilocal model which belong to the conventional identification of inner Lorentz group and represent oscillator or rotator type internal motion are successively discussed in the Appendix.

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