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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Arik, M., Coon, D.: J. Math. Phys 17, 524 (1976)
Jackson, F.: Mess. Math. 38, 57 (1909)
Swamy, P.: Transformations of q-boson and q-fermion algebras, arXiv:0109062 (2001)
Daskaloyannis, C.: J.Phys.A:Math. Gen. 24, L789 (1991)
Odaka, K., Kishi, T., Kamefuchi, S.: J. Phys. A24, L591 (1991)
Manḱo, V., Mendes, R.: J. Phys. A31, 6037 (1998)
Macfarlane, A.J.: J. Phys. A 22, 4581 (1989)
Biedenharn, L.: J. Phys. A 22, L873 (1990)
Quesne, C., Vansteenkiste, N.: Phys. Lett. A 240, 21 (1998)
hung, W., Chung, K., Nam, S., Um, C.: Phys. Lett. A 183, 363 (1993)
Fu, H. -C., Sasaki, R.: J. Phys. A: Math. Gen. 29, 4049 (1996)
Quesne, C.: Phys. Lett. A 272, 313 (2000). Erratum Phys. Lett. A 275 (2000) 313
Lavagno, A., Narayana Swamy, P.: Physica A 389, 993 (2010)
Lee, C.R., Yu, J.P.: Phys. Lett. A 150, 63 (1990)
Su, G., Ge, M.: Phys. Lett. A 173, 17 (1993)
Tuszynski, J.A., et al.: Phys. Lett. A 175, 173 (1993)
Song, H.S., Ding, S.X., An, I.: J. Phys. A 26, 5197 (1993)
Narayana Swamy, P.: Phys. Int. J. Mod. B 10, 683 (1996)
Kaniadakis, G., Lavagno, A., Quarati, P.: Phys. Lett A 227, 227 (1997)
Vokos, S., Zachos, C.: Mod. Phys. Lett. A 9, 1 (1994)
Ubriaco, M.R.: Rev. Phys. E 57, 179 (1998)
Rego-Monteiro, M., Roditi, I., Rodrigues, L.: Phys. Lett. A 188, 11 (1994)
Polychronakos, A.P.: Lett. Phys. B 365, 202 (1996)
Wilczek, F.: Rev. Phys. Lett. 49, 957 (1982)
Mashkevich, S., Myrheim, J., Olaussen, K.: Phys. Lett. A 330, 142 (2004)
Ponomarenko, V.V., Averin, D.V.: Phys. Rev. B 205411, 82 (2010)
Martin-Delgado, M.A.: J. Phys. A24, L1285 (1991)
Martin-Delgado, M.A.: J. Phys. A24, 807 (1991)
Gavrilik, A., Kachurik, I.: Mod. Phys. Lett. A 27, 1250114 (2012)
Gavrilik, A., Kachurik, I.: SIGMA 12, 047 (2016)
Algin, A.: Commun Nonlinear Sci Numer Simulat 15, 1372 (2010)
Rebesh, A., Kachurik, I., Gavrilik, A.: Ukr. J. Phys. 58, 1182 (2013)
Jannussis, A.: J. Phys. A: Math. Gen. 26, L233 (1993)
Tsallis, C.: J. Stat. Phys. 52, 479 (1988)
Curado, E., Tsallis, C.: J.Phys. A 24, L69 (1991)
Tsallis, C.: Quimica Nova. 17, 468–471 (1994)
Abe, S.: Lett. Phys. A 224, 326 (1997)
Borges, E.: Physica A 340, 95 (2004)
Curado, E.M.F., Nobre, F.D.: Physica A 335, 94 (2004)
Nivanen, L., Le Mehaute, A., Wang, Q.: Rep. Math. Phys. 52, 437 (2003)
Borges, E.: Physica A 340, 95 (2004)
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Appendix
Appendix
From q-boson algebra we have
Hence we can set
Using the q-deformed inner product we have
or
or
which gives
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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