Skip to main content
SpringerLink
Log in

Q-Deformed determinants and a unified realization of boson, fermion and quon algebras

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

A new mathematical concept, theq-deformation of the determinant is proposed. By using theq-deformed Slater determinant, a unified realization of boson, fermion and quon algebras is presented. The quon algebra is characterized by the qumutation relationa j a ° k -qa δ k a j = δ jk , which interpolates between Fermi anticommutation and Bose commutation relations. It turns out that for allq∈(−1, 1), the Fock-like spaces are the same, that is the direct sum of all tensor product powers of the single particle spaceh,. This state vector space describes systems of identical particles obeying Boltzmann statistics.

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. Gentile G.,Nuovo Cimento,17 (1940) 493.

    Article  MathSciNet  MATH  Google Scholar 

  2. Green H. S.,Phys. Rev.,90 (1953) 270.

    Article  ADS  MATH  Google Scholar 

  3. Volkov D. V.,Sov. Phys. JETP,9 (1959) 1107;11 (1960) 375.

    MATH  Google Scholar 

  4. Wilczek F. andZee A.,Phys. Rev. Lett.,51 (1983) 2250.

    Article  MathSciNet  ADS  Google Scholar 

  5. Greenberg O. W.,Phys. Rev. Lett.,64 (1990) 705.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Greenberg O. W.,Phys. Rev. D,43 (1991) 4111.

    Article  MathSciNet  ADS  Google Scholar 

  7. Greenberg O. W.,Physica A,180 (1992) 419.

    Article  MathSciNet  ADS  Google Scholar 

  8. Mohapatra R. N.,Phys. Lett. B,242 (1990) 407.

    Article  MathSciNet  ADS  Google Scholar 

  9. Govorkov A. B.,Phys. Lett. A,137 (1989) 1.

    Article  MathSciNet  ADS  Google Scholar 

  10. Ramberg E. andSnow G. A.,Phys. Lett. B,238 (1990) 438.

    Article  ADS  Google Scholar 

  11. Miljanić D. et al., Phys. Lett. B,252 (1990) 487.

    Article  ADS  Google Scholar 

  12. Bożjeko M. andSpeicher R.,Commun. Math. Phys.,137 (1991) 519.

    Article  ADS  Google Scholar 

  13. Fivel D. I.,Phys. Rev. Lett.,65 (1990) 3361;69 (1992) 2020 (E).

    Article  MathSciNet  ADS  Google Scholar 

  14. Zagier D. B.,Commun. Math. Phys.,147 (1992) 199.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Yu T. andWu Z. inProceedings of the XXI International Conference on Differential Geometry Methods in Theoretical Physics (World Scientific, Singapore) 1993.

    Google Scholar 

  16. Yu T. andWu Z. Sci. China A,37 (1994) 1472.

    MathSciNet  Google Scholar 

  17. Wu Z. andYu T.,Phys. Lett. A,179 (1993) 266.

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Theoretical Physics, Jilin University, 130023, Changchun, Jilin, PRC

    Zhaoyan Wu

Authors
  1. Zhaoyan Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by the National Natural Science Foundation of China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, Z. Q-Deformed determinants and a unified realization of boson, fermion and quon algebras. Nuov Cim B 110, 1269–1276 (1995). https://doi.org/10.1007/BF02723111

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02723111

PACS

PACS

PACS

Search

Navigation