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The logical inference approach to quantum theory, proposed earlier [Ann. Phys. 347 (2014) 45-73], is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space-time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds.
The dynamical symmetries of the two-dimensional Klein-Gordon equations with equal scalar and vector potentials (ESVP) are studied. The dynamical symmetries are considered in the plane and the sphere respectively. The generators of the SO(3) group cor
We present a new axially symmetric monochromatic free-space solution to the Klein-Gordon equation propagating with a superluminal group velocity and show that it gives rise to an imaginary part of the causal propagator outside the light cone. We addr
We present an elementary proof based on a direct calculation of the property of completeness at constant time of the solutions of the Klein-Gordon equation for a charged particle in a plane wave electromagnetic field. We also review different forms o
A rigorous textit{ab initio} derivation of the (square of) Diracs equation for a single particle with spin is presented. The general Hamilton-Jacobi equation for the particle expressed in terms of a background Weyls conformal geometry is found to be
We consider the spectral problem associated with the Klein-Gordon equation for unbounded electric potentials. If the spectrum of this problem is contained in two disjoint real intervals and the two inner boundary points are eigenvalues, we show that