Schwinger action principle, eikonal theory and two-time rotation-translation of coordinates

Abstract

Via the Schwinger action principle, we derive a formula for the transformation function (or propagator) of time-dependent systems that can be expressed into a quadratic form. We present also a new type of two-time rotation-translation of coordinates which makes it possible to evaluate the exact transformation function of the three-dimensional time-dependent charged harmonic oscillator in cross time-varying, arbitrary magnetic and laser fields. We demonstrate that such a transformation function can be obtained from that for a free-particle in the new two-time and space coordinate system, whereby the scalar and vector (quadratic) potentials are transformed away from the quantum-mechanical motion. We also show how the quantum-mechanical eikonal theory of this problem arises in a natural way from the Schwinger action principle.