# Construction of a Weyl Representation from a Weak Weyl Representation of the Canonical Commutation Relation

Preprint Series # 888
Arai, Asao and Matsuzawa, Yasumichi Construction of a Weyl Representation from a Weak Weyl Representation of the Canonical Commutation Relation. (2008);

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## Abstract

Weak Weyl representations of the canonical commutation relation (CCR) with one degree of freedom are considered in relation to the theory of time operator in quantum mechanics. It is proven that there exists a general structure through which a weak Weyl representation can be constructed from a given weak Weyl representation. As a corollary, it is shown that a Weyl representation of the CCR can be constructed from a weak Weyl representation which satisfies some additional property. Some examples are given.

Item Type: Preprint 10 canonical commutation relation, weak Weyl representation, Weyl representation, Hamiltonian, time operator, spectrum. 81-xx QUANTUM THEORY 1811