Journal of Mathematical Physics

Duality of observables and generators in classical and quantum mechnics

Emile Grgin, Aage Petersen

Published Jun 1, 1974• 29 citations

Abstract

In classical and in quantum mechanics physical variables play a dual role as observables and as generators of infinitesimal transformations in the invariance groups. We show that if the Lie algebra of generators is central simple, the observable-generator duality restricts the structure of the algebra of observables to two cases: a commutative, associative algebra as in classical mechanics, or a central simple special Jordan algebra as in quantum mechanics.

DOI: 10.1063/1.1666726

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