Generalized Coherent States Representation

The properties of the system of eigenvectors of the annihilation operator are investigated for the case of non-classical commutation relations between the operators of creation and annihilation. The existence of a measure on the set of eigenvalues of the annihilation operator is proved, with respect to which coherent states form a generalized crowded system. Formulas of covariant symbols of vectors and operators in the representation of generalized coherent states are obtained. It is shown that, similarly to the classical boson case, generalized coherent states are states with minimal uncertainty.