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Physics Letters A

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

Antonio Boulhosa Nassar, F.L.A. Machado

Published Jul 1, 1987• 8 citations
Publisher
DOI
10.1016/0375-9601(87)90750-x

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

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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.

Physica Scripta•Jul 1, 1990•5 citations
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.