Skip to main content
SpringerLink
Log in

The Behavior of Quantum Particles at Very Low Scale

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

In this paper, we propose that the behavior of quantum particles assuming discreteness of the spacetime at very low scale is similar to the behavior of Anyons.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kempf, A.: Spacetime could be simultaneously continuous and discrete, in the same way that information can be, New Journal of Physics vol. 12 (2010)

  2. Farrelly, T.C., Short, A.J.: Discrete spacetime and relativistic quantum particles. Phys. Rev. A 89, 062109 (2014)

    Article  ADS  Google Scholar 

  3. Creutz, M.: Quarks, Gluons and Lattice, Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge (1983)

    Google Scholar 

  4. Marks, R.J.: Introduction to shannon sampling and interpolation theory. Springer, Berlin (1991)

    Book  Google Scholar 

  5. Hilger, S.: Ein MaXkettenkalkul Mit Anwendung Auf Zentrumsmannigfaltigkeiten. Ph.D. thesis, Universit Wurzburg (1988)

  6. Hilger, S.: Analysis on measure chains: a unified approach to continuous and discrete calculus. Results Math. 18, 18–56 (1990)

    Article  MathSciNet  Google Scholar 

  7. Agarwal, R., Bohner, M.: Basic calculus on time scales and some of its applications. Results Math. 35, 3–22 (1999)

    Article  MathSciNet  Google Scholar 

  8. Bohner, M., Peterson, A.: Dynamic Equations on Time Scales: an Introduction with Applications. Birkhauser, Boston (2001)

    Book  Google Scholar 

  9. Agarwal, R., Bohner, M., Oregan, D., Peterson, A.: Dynamic equations on time scales: a survey. J. Comput. Appl. Math. 141, 1–26 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  10. Bohner, M., Peterson, A.: Advances in Dynamic Equations on Time Scales. Birkhauser, Boston (2003)

    Book  Google Scholar 

  11. Mandelbrot, B.: The Fractal Geometry of Nature. Freeman, San Francisco (1982)

    MATH  Google Scholar 

  12. Ahmed, E., Hegazi, A.S.: Infinitesimally deformed field and string theories. J. Math. Phys. 33, 379–381 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  13. Ali, A.F., Das, S., Vagenas, E.C.: Discreteness of space from the generalized uncertainty principle. Phys. Lett. B 678, 497–499 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  14. Das, S., Vagenas, E.C., Ali, A.F.: Discreteness of space from GUP II: relativistic wave equations. Phys. Lett. B 690, 407–412 (2010)

    Article  ADS  Google Scholar 

  15. Abutaleb, A.A.: Discreteness of Curved Spacetime from GUP. Adv High Energy Phy 2013, 124543 (2013)

    MATH  Google Scholar 

  16. Agarwal, R., Bohner, M., Wong, P.J.Y.: Sturm-Liouville eigenvalue problems on time scales. Appl. Math. Comput. 99, 153–166 (1999)

    MathSciNet  MATH  Google Scholar 

  17. Ahlbrandt, D.C., Bohner, M., Ridenhour, J.: Hamiltonian systems on time scales. J. Math. Anal. Applic. 250, 561–578 (2000)

    Article  MathSciNet  Google Scholar 

  18. Bohner, M., Peterson, A.: Laplace transform and Z-transform: unification and extension. Methods Applic. Anal. 9, 151–158 (2002)

    MathSciNet  MATH  Google Scholar 

  19. Hilscher, R.: Linear Hamiltonian systems on time scales: Positivity of quadratic funetionals. Math. Comput. Modelling 32, 507–527 (2000)

    Article  MathSciNet  Google Scholar 

  20. Agarwal, R., Regan, D.O., Saker, S.H.: Dynamic inequalities on time scales. Springer, Berlin (2014)

    Book  Google Scholar 

  21. Greenberg, O.W., Mohaparta, R.N.: Phenomenology of small violations of Fermi and Bose statistics. Phys. Rev. D 39, 2032 (1989)

    Article  ADS  Google Scholar 

  22. Gentile, G.: Itosservazioni sopra le statistiche intermedie. Nuovo cimento 17, 493 (1940)

    Article  Google Scholar 

  23. Pauli, W.: ber den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren. Zeitschrift für physik 31, 765–783 (1925)

    Article  ADS  Google Scholar 

  24. Wu, Y.S.: Statistical distribution for generalized ideal gas of Fractional-Statistics particles. Phys. Rev. Lett 73, 922–925 (1994)

    Article  ADS  Google Scholar 

  25. Medvedev, M.V.: Properties of particles obeying ambiguous statistics. Phys. Rev.Lett 78, 4174–4150 (1997)

    Google Scholar 

  26. Abutaleb, A.A.: Unified statistical distribution of quantum particles and symmetry. Int. J. Theor. Phys 53, 3893–3900 (2014)

    Article  Google Scholar 

  27. Higgins, R.J., Peterson, A.: Cauchy functions and Taylor’s formula for time scales T. In: Proceedings of the Sixth International Conference on Difference Equations, pp. 299-308 (2004)

  28. Hilger, S.: Matrix lie theory and measure chains. J. Comp. Appl. Math 141, 197–217 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  29. Herrmann, R.: common aspects of q- deformed Lie algebras and fractional calculus. Physica A 389, 4613–4622 (2010)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Mansoura, Mansoura, Egypt

    A. A. Abutaleb, E. Ahmed & A. I. Elmahdy

Authors
  1. A. A. Abutaleb
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. I. Elmahdy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Abutaleb.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abutaleb, A.A., Ahmed, E. & Elmahdy, A.I. The Behavior of Quantum Particles at Very Low Scale. Int J Theor Phys 59, 3888–3896 (2020). https://doi.org/10.1007/s10773-020-04640-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-020-04640-9

Search

Navigation