Asao Arai and Yasumichi Matsuzawa Construction of a Weyl Representation from a Weak Weyl Representation of the Canonical Commutation Relation (25K, LaTex2e) ABSTRACT. Some aspects of weak Weyl representations of the canonical commutation relation (CCR) with one degree of freedom is considered in relation to the theory of time operator in quantum mechanics. It is shown that there exists a general structure in which a Weyl representation of the CCR can be constructed from a weak Weyl representation of the CCR.