ON DEFORMED BOSON ALGEBRA AND VACUUM PROJECTION OPERATOR ON NONCOMMUTATIVE PLANE

In the noncommutative phase space, a new mapping is proposed to express the noncommutative coordinate and momentum operators in terms of the ordinary coordinate and momentum operators under the case of large noncommutativity parameters (μν>1). Using this mapping matrix, the deformed boson operators can be expressed in terms of the ordinary boson operators. Thus, the normal ordering expansion form of vacuum projection operator is obtained. As an application, the completeness relation of the two-mode deformed coherent states is verified by using the vacuum projection operator.