Abstract
A notion of Quantum Motion Algebra (QMA) allows to construct quantum state spaces for various physical systems moving under a given group of motion. The main idea of QMA is a construction of a group algebra with involution generated by a group of motion G. After defining a linear and nonnegative functional on this algebra one can construct the appropriate quantum state space by means of the Gelfand-Naimark-Segal theorem. The QMA method can be also applied in the modeling of physical systems requiring additional degrees of freedom or additional constraints.The presented paper gives a brief description of the QMA method. As an example of the QMA application, we present a model of nuclear collective pairing where the nonnegative functional is generated by a temperature dependent quantum density operator.
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