Probabilistic Treatment of Relativistic Scattering of Scalar Particles and Their Mass Spectrum.

The physical legitimacy of Stuckelberg's manifestly covariant wave equation describing relativistic spin zero particles, the four-space formalism (FSF), is assessed through specific physical applications. To this end two things are done. (1) Starting with the coordinate representation of the FSF a machinery for performing scattering calculations is developed. The solutions incorporate the Stuckelberg -Feynman interpretation for particle-antiparticle pairs. The probability interpretation for relativistic scattering of scalar particles results. Application to low-order Coulomb scattering of (pi)('+) mesons is discussed in detail. The resulting cross-section agrees with that of the Klein-Gordon formalism (KGF). It is shown that for all orders of -independent potentials, cross sections obtained from the FSF agree with their counterparts in the KGF. Calculational and conceptual expediencies of this approach is emphasized. An additional advantage is that the rest mass as well as the energy is now allowed to go "off-shell" during an interaction. Therefore, the FSF approach may be used to directly investigate problems involving particles of finite width in an interacting medium. (2) For the first time, via the mass representation of the FSF, we have obtained the exact solutions for the mass spectrum of scalar particles in a static uniform electric field perpendicular to a static uniform magnetic field. The nonrelativistic limit of these solutions correctly reduce to "the Landau levels". The magnitude of the quantum of mass arising from the spectrum is determined for various field strengths. This result is in principle measurable; thus, providing a test of the theory. By directly calculating the average and the most probable mass, the correspondence principle as well as the Ehrenfest theorem are shown to be upheld, independent of the field strengths. Advantages of the FSF operator language, such as the hermiticity in the usual sense of the evolution operator, is emphasized.