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The q-boson Algebra and suq(2) Algebra Based on q-deformed Binary Operations

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Abstract

In this paper we use the q-deformed binary operations to discuss q-derivative, q-integral, q-exponential function, q-Gamma function and q-logarithm and q-deformed complex number. We define the q-binary operation of q-matrix. Using these, we construct the q-boson algebra and suq(2) algebra based on the q-deformed binary operations.

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Acknowledgements

We acknowledge to reviewer for helpful comments.

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Correspondence to Hassan Hassanabadi.

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Appendix

Appendix

From q-boson algebra we have

$$ N_{q} \otimes ( a^{\dagger}_{q} \otimes \phi^{q}_{n}) = ( n+1)_{q} \otimes ( a^{\dagger}_{q} \otimes \phi^{q}_{n}) $$
(121)

Hence we can set

$$ a^{\dagger}_{q} \otimes \phi^{q}_{n} = c_{n} \otimes \phi^{q}_{n+1} $$
(122)

Using the q-deformed inner product we have

$$ ( a^{\dagger}_{q} \otimes \phi^{q}_{n}, a^{\dagger}_{q} \otimes \phi^{q}_{n})_{q} = c_{n} \otimes c_{n} $$
(123)

or

$$ ( \phi^{q}_{n}, a_{q} \otimes a^{\dagger}_{q} \otimes \phi^{q}_{n})_{q} = c_{n} \otimes c_{n} $$
(124)

or

$$ (n+1)_{q} = c_{n} \otimes c_{n} $$
(125)

which gives

$$ c_{n} = ( \sqrt{n})_{q} $$
(126)

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Chung, W.S., Hassanabadi, H. The q-boson Algebra and suq(2) Algebra Based on q-deformed Binary Operations. Int J Theor Phys 60, 2102–2114 (2021). https://doi.org/10.1007/s10773-021-04828-7

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  • DOI: https://doi.org/10.1007/s10773-021-04828-7

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