Abstract
It is shown that classical and quantum equations of motion of a relativistic spinless particle (the Lorentz and Klein-Gordon equations) allow for a geometrization on the same manifold\(\begin{array}{*{20}c} * \\ V \\ \end{array}\)4. A classical particle on\(\begin{array}{*{20}c} * \\ V \\ \end{array}\)4 is described as a free particle (\(\mathop \Delta \limits^*\)pμ=0), while the quantum particle, as a free wave (\(\begin{array}{*{20}c} * \\ \nabla \\ \end{array}\)s=0).
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