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Communications in Theoretical Physics

Some New Expressions for Vacuum Projection Operators of q -Deformed Boson Oscillators

Hong-Yi Fan, Sicong Jing

Published Oct 1, 1993• 1 citation
Publisher

Abstract

We derive some new expressions for the vacuum projection operator of q-deformed boson oscillators. A recursion method is essential to our derivation of the power series expansion of the vacuum projection operator in terms of the q-creation and q-annihilation operators.
DOI
10.1088/0253-6102/20/3/381

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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.
The q-deformed entangled states are introduced by using deformation quantization methods and new normal ordering of the vacuum projection operator for q-deformed boson oscillator. In similar way, by virtue of the technique of integration within an ordered product (IWOP) of operators, the new completeness and orthogonality relations composed of the bra and ket, which are not mutually Hermitian conjugates are obtained. Furthermore, the property of squeezing operator represented by the q-deformed entangled states is exhibited. Lastly, the nonclassical properties of the q-deformed two-mode squeezed vacuum state are studied.