Integration within an ordered product for q-deformed bosons

Paweł Błasiak, A. Horzela, K. A. Penson +1 more

Hong-Yi Fan, Sicong Jing

We extend the newly developed technique of integration with an ordered product (IWOP) of operators to q -deformed boson case. The ambiguity arising from defining the normal ordering of q -deformed boson operators, which satisfy aa † - qa † a = 1, can be eliminated by following the q -deformed IWOP technique. Some new q-integration formulas and new qboson operator identities are obtained, and the P -representation of q -analogue of the chaotic state of radiation field is derived.

Jack A. Tuszyński, Jacques L. Rubin, J. Meyer +1 more

G. Kaniadakis, A. Lavagno, P. Quarati

Ye‐Jun Xu, Jun Song, Hong‐Chun Yuan +1 more

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.

Hong-Yi Fan

We construct q -deformed displaced number state, q -deformed two-mode squeezed state and q -deformed two-mode single-complex-variable state by making use of the q -deformed inverse field operators. Their completeness relations are investigated by virtue of the technique of integration within an ordered product of operators. Some new operator identities in q -deformed Fock space are also derived.