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New deformed Heisenberg algebra with reflection operator

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Abstract

In this paper, a new generalization of Dunkl derivative with three parameters is proposed. With a help of the generalized Dunkl derivative, a new deformed Heisenberg algebra with reflection operator is proposed. The Hilbert space and inner product are well defined for the new deformed Heisenberg algebra, and some physical examples are discussed.

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References

  1. E. Wigner, Phys. Rev. 77, 711 (1950)

    Article  ADS  MathSciNet  Google Scholar 

  2. L. Yang, Phys. Rev. 84, 788 (1951)

    Article  ADS  MathSciNet  Google Scholar 

  3. C. Dunkl, Trans. Am. Math. Soc. 311, 167 (1989)

    Article  Google Scholar 

  4. V. Genest, M. Ismail, L. Vinet, A. Zhedanov, J. Phys. A 46, 145201 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  5. V. Genest, M. Ismail, L. Vinet, A. Zhedanov, Commun. Math. Phys. 329, 999 (2014)

    Article  ADS  Google Scholar 

  6. V. Genest, L. Vinet, A. Zhedanov, J. Phys, Conf. Ser. 512, 012010 (2014)

    Article  Google Scholar 

  7. H. Carrion, R. Rodrigues, Mod. Phys. Lett. A 25, 2507 (2010)

    Article  ADS  Google Scholar 

  8. W. Chung, H. Hassanabadi, Mod. Phys. Lett. A 34, 1950190 (2019)

    Article  ADS  Google Scholar 

  9. M. Salazar-Ramírez, D. Ojeda-Guillén, R.D. Mota, V.D. Granados, Eur. Phys. J. Plus 132, 39 (2017)

    Article  Google Scholar 

  10. M. Salazar-Ramírez, D. Ojeda-Guillén, R.D. Mota, V.D. Granados, Mod. Phys. Lett. A 33, 1850112 (2018)

    Article  ADS  Google Scholar 

  11. F. Chouchane, M. Muli, K. Trimeche, Anal. Appl. 1, 387 (2003)

    Article  MathSciNet  Google Scholar 

  12. B. Basu-Mallick, F. Finkel, A. González-López, Nucl. Phys. B 21, 391 (2013)

    Article  ADS  Google Scholar 

  13. S. Sontz, Infinite dimensional analysis. Quant. Probab. Related Top. 12, 269 (2009)

    MathSciNet  Google Scholar 

  14. R.D. Mota, D. Ojeda-Guillén, M. Salazar-Ramírez, V. D. Granados (2020). arXiv preprint arXiv:2008.13204

  15. V.X. Genest, L. Vinet, A. Zhedanov, J. Phys.: Conf. Ser. 512(1), 012010 (2014)

    Google Scholar 

  16. S. Tsujimoto, L. Vinet, A. Zhedanov, From slq(2) to a parabosonic Hopf algebra. SIGMA 7, 93–105 (2011)

    MATH  Google Scholar 

Download references

Acknowledgements

The authors thank the referees for a thorough reading of our paper and constructive suggestions.

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Authors and Affiliations

  1. Department of Physics and Research Institute of Natural Science, College of Natural Science, Gyeongsang National University, Jinju, 660-701, Korea

    Won Sang Chung

  2. Faculty of physics, Shahrood University of Technology, Shahrood, Iran

    Hassan Hassanabadi

Authors
  1. Won Sang Chung
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  2. Hassan Hassanabadi
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Correspondence to Hassan Hassanabadi.

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Chung, W.S., Hassanabadi, H. New deformed Heisenberg algebra with reflection operator. Eur. Phys. J. Plus 136, 239 (2021). https://doi.org/10.1140/epjp/s13360-021-01186-5

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  • DOI: https://doi.org/10.1140/epjp/s13360-021-01186-5

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