Relativistic generalization of Feynman's path integral on the basis of extended Lagrangians
The paper introduces extended Lagrangians that treat physical time as a dependent variable, allowing classical dynamics to be parametrized by an evolution parameter $s$. These non-homogeneous extended Lagrangians are shown to be physically significant because they can reproduce the conventional relativistic Lagrangian. Using these extended forms, Feynman's path integral approach is successfully adapted to yield the Klein-Gordon equation for a charged spin-zero particle.