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Quantum Algebras and Quantum Physics

E. Celeghini·M. A. del Olmo
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Abstract

In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum algebra operators is suggested by extending the definition of matrix elements of a physical observable, including the eventual projection on the appropriate symmetric space. This allows to build in the Lie space of representations one-parameter families of operators belonging to the enveloping Lie algebra that satisfy an approximate symmetry and have the properties required by physics.

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E. Celeghini, M. A. del Olmo. 2001-09-04. Quantum Algebras and Quantum Physics. https://doi.org/10.1209/epl%2Fi2003-00326-y

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