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);
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.
|Uncontrolled Keywords:||canonical commutation relation, weak Weyl representation, Weyl representation,
Hamiltonian, time operator, spectrum.
|Subjects:||81-xx QUANTUM THEORY|