The aim of this paper is to suggest a general approach to Poisson brackets, based on the study of the Lie algebra of potential operators with respect to closed skew-symmetric bilinear forms. This approach allows to extend easily to infinite-dimensional spaces the classical Cartan geometrical approach developed in the phase space. It supplies a simple, unified, and general formalism to deal with such brackets, which contains, as particular cases, the classical and the quantum treatments. © 1976.

Magri, F. (1976). An operator approach to Poisson brackets. ANNALS OF PHYSICS, 99(1), 196-228 [10.1016/0003-4916(76)90090-7].

An operator approach to Poisson brackets

Magri, F
1976

Abstract

The aim of this paper is to suggest a general approach to Poisson brackets, based on the study of the Lie algebra of potential operators with respect to closed skew-symmetric bilinear forms. This approach allows to extend easily to infinite-dimensional spaces the classical Cartan geometrical approach developed in the phase space. It supplies a simple, unified, and general formalism to deal with such brackets, which contains, as particular cases, the classical and the quantum treatments. © 1976.
Articolo in rivista - Articolo scientifico
Poisson brackets
English
196
228
Magri, F. (1976). An operator approach to Poisson brackets. ANNALS OF PHYSICS, 99(1), 196-228 [10.1016/0003-4916(76)90090-7].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/18492
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