Relativistic Klein-Gordon Equation Research Articles

Quantum Mechanics, Stochasticity and Space-Time

An extended and more rigorous version of a recent proposal for an objective stochastic formulation of quantum mechanics along with its extension to the relativistic case without spin is presented. The relativistic Klein-Gordon equation is shown to be a particular form of the relativistic Kolmogorov-Fokker-Planck equation which is derived from a covariant formulation of the Chapman-Kolmogorov condition. Complexification of probability amplitudes is again achieved only through a conformal rotation of Minkowski space-time M4.

Particle trajectories in relativistic quantum mechanics

The causal stochastic approach to the relativistic scalar Klein-Gordon equation is shown to preserve the time-like character of particle trajectories provided additional physical assumptions are introduced. A proposed “counterexample” reveals the essential necessary restrictions on the set of mathematical solutions of the quantum relativistic scalar equation.