Abstract

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.

中文翻译：

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广义相干状态表示

摘要

针对创生算符与湮灭算符非经典对易关系的情况，研究了湮灭算符特征向量系统的性质。证明了在湮灭算子的特征值集上的测度的存在性，关于该测度，相干态形成了广义拥挤系统。得到了广义相干态表示中向量和算子的协变符号公式。结果表明，与经典玻色子情况类似，广义相干态是具有最小不确定性的状态。