A quantum action principle for open systems
Schwinger's remarkable contributions to the various areas of theoretical physics are quite well known. Particularly, his quantum action principle (QAP) leads to a nice, compact formulation of quantum mechanics. It is of great value as a powerful tool for computational physics apart from its intrinsic interest in general. However, in its original form QAP is limited to closed systems. It is now sought to be generalized to the open systems as well, through the present rather long letter under review. Starting with the essentials of QAP of Schwinger, the principle in Hilbert space is re-formulated in the Liouville space. An extension of QAP to open systems with time evolution via Markovian dynamics is given. It is then illustrated by means of a driven, damped harmonic oscillator. The new action principle provides for a differential characterization of the Green's function for the master equation as against Schrödinger equation. A short heuristic derivation of the extended QAP, following Schwinger's original method, is also added. On the whole, the work breaks fresh and useful ground which must have far-reaching consequences.
scientific article; zbMATH DE number 922364