Document type
ArticleVersion
Published versionPublication date
All rights reserved
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/24548
General Interaction Picture from Action Principle for Mechanics
Journal Title
Authors
Director/Tutor
Journal ISSN
Volume Title
Related resource
Abstract
In this paper we consider a general action principle for mechanics written by means of the elements of a Lie algebra. We study the physical reasons why we have to choose precisely a Lie algebra to write the action principle. By means of such an action principle we work out the equations of motion and a technique to evaluate perturbations in a general mechanics that is equivalent to a general interaction picture. Classical or quantum mechanics come out as particular cases when we make realizations of the Lie algebra by derivations into the algebra of products of functions or operators, respectively. Later on we develop in particular the applications of the action principle to classical and quantum mechanics, seeing that in this last case it agrees with Schwinger's action principle. The main contribution of this paper is to introduce a perturbation theory and an interaction picture of classical mechanics on the same footing as in quantum mechanics.
Subject (English)
Citation
Citation
GARRIDO, L. (Luis). General Interaction Picture from Action Principle for Mechanics. Journal of Mathematical Physics. 1969. Vol. 10, num. 1045. ISSN 0022-2488. [consulted: 9 of June of 2026]. Available at: https://hdl.handle.net/2445/24548