Space-time-transformation technique in connection with the Schwinger action principle

Abstract

We show that, by using a convenient space-time transformation, we can considerably simplify the evaluation of the exact transformation function (or propagator) for a time-dependent mass, subject to a time-varying, forced harmonic oscillator potential, obtained through the Schwinger action principle. Overall, we demonstrate that such a transformation function can be obtained from that for a free particle (with unit mass) in the new space-time coordinate system.