Poincare Group and the Relativistic Wave Equation of the Extended Particle Model

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Abstract
The relativistic wave equation of a point-like system with space-like extension is studied. The divergence difficulty of the norm of the wave functions satisfying the constraints is solved by modifying the invariant volume element. We have also shown that the generators of Lorentz transformations are hermitian with respect to the modified norm. It can be explicitly shown that the constraints imposed on physical states suppress the redundant variables. After eliminating the constraints, we obtain Poincaré generators written in terms of true dynamical variables. From the procedure of the elimination of the redundant variables, it is obvious that our wave equation with the characteristic constraints is obtained from the canonical representation of Poincaré group.

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