Skip to main content
Log in

Is Pseudo-Hermitian Quantum Mechanics an Indefinite-Metric Quantum Theory?

  • Published:
Czechoslovak Journal of Physics Aims and scope

Abstract

With a view to eliminate an important misconception in some recent publications, we give a brief review of the notion of a pseudo-Hermitian operator, outline pseudo-Hermitian quantum mechanics, and discuss its basic difference with the indefinite-metric quantum mechanics. In particular, we show that the answer to the question posed in the title is a definite No.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. Mostafazadeh: J. Math. Phys. 43 (2002) 205.

    Google Scholar 

  2. A. Mostafazadeh: J. Math. Phys. 43 (2002) 2814; 3944. Czech. J. Phys. 53 (2003) 1083 A. Mostafazadeh: Pseudo-Hermitian and inde.nite-metric QM

    Google Scholar 

  3. A. Mostafazadeh: Nucl. Phys. B 640 (2002) 419; J. Math. Phys. 44 (2003) 974.

    Google Scholar 

  4. A. Mostafazadeh: J. Math. Phys. 43 (2002) 6343; Erratum: 44 (2003) 943.

    Google Scholar 

  5. C.M. Bender and S. Boettcher: Phys. Rev. Lett. 80 (1998) 5243.

    Google Scholar 

  6. A. Mostafazadeh: J. Phys. A: Math. Gen. 36 (2003) 7081.

    Google Scholar 

  7. A. Mostafazadeh: Class. Quantum Grav. 20 (2003) 155.

    Google Scholar 

  8. A. Mostafazadeh: Preprint: gr-qc/0306003; Ann. Phys. (NY), to appear.

  9. A. Mostafazadeh: Preprint: quant-ph/0307059.

  10. S.M. Klishevich and M.S. Plyushchay: Nucl. Phys. B 628 (2002) 217. H. Fakhri and A. Imaanpur: JHEP 03 (2003) 003.

    Google Scholar 

  11. Z. Ahmed: Phys. Lett. A 308 (2003) 140. Z. Ahmed and S.R. Jain: Phys. Rev. E 67 (2003) 045106; J. Phys. A 36 (2003) 3349.

    Google Scholar 

  12. L. Solombrino: J. Math. Phys. 43 (2002) 5439. G. Scolarici: J. Phys. A 34 (2002) 7493. T.V. Fityo: J. Phys. A 35 (2002) 5893. Z. Ahmed: Phys. Lett. A 310 (2003) 139. U. G¨unther and F. Stefani: J. Math. Phys. 44 (2003) 3097.

    Google Scholar 

  13. P.A.M. Dirac: Proc. Roy. Soc. London A 180 (1942) 1. W. Pauli: Rev. Mod. Phys., 15 (1943) 175. S.N. Gupta: Proc. Phys. Soc. London 63 (1950) 681. K. Bleuler: Helv. Phys. Acta 23 (1950) 567. E.C.G. Sudarshan: Phys. Rev. 123 (1961) 2183. T.D. Lee and G.C. Wick: Nucl. Phys B 9 (1969) 209.

    Google Scholar 

  14. J. Bognár: Inde.nite Inner Product Spaces, Springer, Berlin, 1974. T. Ya. Azizov and I.S. Iokhvidov: Linear Operators in Spaces with Inde.nite Metric, Wiley, Chichester, 1989.

    Google Scholar 

  15. A. Mostafazadeh: Preprint: math-ph/0302050.

  16. F.G. Scholtz, H.B. Geyer, and F.J.W. Hahne: Ann. Phys. 213 (1992) 74.

    Google Scholar 

  17. B.S. DeWitt: Phys. Rev. 160 (1967) 1113. S. Carlip: Rep. Prog. Phys. 64 (2001) 885.

    Google Scholar 

  18. H. Feshbach and F. Villars: Rev. Mod. Phys. 30 (1958) 24.

    Google Scholar 

  19. M. Reed and B. Simon: Functional Analysis, Vol. 1, Academic Press, San Diego, 1980. pp1084 Czech. J. Phys. 53 (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mostafazadeh, A. Is Pseudo-Hermitian Quantum Mechanics an Indefinite-Metric Quantum Theory?. Czechoslovak Journal of Physics 53, 1079–1084 (2003). https://doi.org/10.1023/B:CJOP.0000010537.23790.8c

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:CJOP.0000010537.23790.8c

Navigation