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General Interaction Picture from Action Principle for Mechanics
Garrido, L. (Luis), 1930-
Universitat de Barcelona
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.
Àlgebres de Lie
Pertorbació (Dinàmica quàntica)
Teoria quàntica
Lie algebras
Perturbation (Quantum dynamics)
Quantum theory
(c) American Institute of Physics, 1969
American Institute of Physics

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