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arXiv · 1202.3969

Reduction of Lie-Jordan Banach algebras and quantum states

F. Falceto·L. Ferro·A. Ibort·G. Marmo
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Abstract

A theory of reduction of Lie-Jordan Banach algebras with respect to either a Jordan ideal or a Lie-Jordan subalgebra is presented. This theory is compared with the standard reduction of C*-algebras of observables of a quantum system in the presence of quantum constraints. It is shown that the later corresponds to the particular instance of the reduction of Lie-Jordan Banach algebras with respect to a Lie-Jordan subalgebra as described in this paper. The space of states of the reduced Lie-Jordan Banach algebras is described in terms of equivalence classes of extensions to the full algebra and their GNS representations are characterized in the same way. A few simple examples are discussed that illustrates some of the main results.

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F. Falceto, L. Ferro, A. Ibort, G. Marmo. 2012-02-17. Reduction of Lie-Jordan Banach algebras and quantum states. https://doi.org/10.1088/1751-8113/46/1/015201

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