Abstract
A general theory of representations of canonical commutation relations (CCR) with finite degrees of freedom is presented. For each N = 1, 2, …, the representations of the CCR with N degrees of freedom have some sub-classes. Fundamental properties of each of them are derived. Some examples of representations are given, including Schrodinger and Born–Heisenberg–Jordan representations. Physical correspondences of representations of CCR are discussed.
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