Skip to main content
SpringerLink
Log in

Faddeev–Jackiw canonical path integral quantization for a general scenario, its proper vertices and generating functionals

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal C Aims and scope Submit manuscript

Abstract

We generalize the Faddeev–Jackiw canonical path integral quantization for the scenario of a Jacobian with J=1 to that for the general scenario of non-unit Jacobian, give the representation of the quantum transition amplitude with symplectic variables and obtain the generating functionals of the Green function and connected Green function. We deduce the unified expression of the symplectic field variable functions in terms of the Green function or the connected Green function with external sources. Furthermore, we generally get generating functionals of the general proper vertices of any n-points cases under the conditions of considering and not considering Grassmann variables, respectively; they are regular and are the simplest forms relative to the usual field theory.

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. J.L. Anderson, P.G. Bergmann, Phys. Rev. 83, 1 018 (1951)

    MathSciNet  Google Scholar 

  2. P.G. Bergmann, J. Goldberg, Phys. Rev. 98, 531 (1955)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  3. P.A.M. Dirac, Lectures on Quantum Mechanics (Yeshiva University Press, New York, 1964)

    Google Scholar 

  4. M. Henneaux, C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, 1992)

    MATH  Google Scholar 

  5. Z.P. Li, J.H. Jiang, Symmetries in Constrained Canonical Systems (Science, New York, 2002)

    Google Scholar 

  6. R. Floreanini, R. Jackiw, Phys. Rev. Lett. 59, 1 873 (1987)

    Article  Google Scholar 

  7. L. Faddeev, R. Jackiw, Phys. Rev. Lett. 60, 1 692 (1988)

    Article  MathSciNet  Google Scholar 

  8. J. Barcelos-Neto, C. Wotzasek, Mod. Phys. Lett. A 7, 1 737 (1992)

    Article  MathSciNet  Google Scholar 

  9. J. Barcelos-Neto, C. Wotzasek, Int. J. Mod. Phys. A 7, 4 981 (1992)

    Article  MathSciNet  Google Scholar 

  10. H. Montani, C. Wotzasek, Mod. Phys. Lett. A 8, 3 387 (1993)

    Article  MathSciNet  Google Scholar 

  11. Y.C. Huang , Mod. Phys. Lett. A 21, 1 107 (2006)

    Google Scholar 

  12. C.X. Yu, Y.C. Huang, Phys. Lett. B 647, 49 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  13. Y.C. Huang, C.X. Yu, Phys. Rev. D 75, 044 011 (2007)

    MathSciNet  Google Scholar 

  14. L. Liao, Y.C. Huang, Ann. Phys. (N.Y.) 322, 2 469 (2007)

    Article  MathSciNet  Google Scholar 

  15. L. Liao, Y.C. Huang, Phys. Rev. D 75, 025 025 (2007)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, Beijing University of Technology, Beijing, 100022, China

    Yong-Chang Huang & Leng Liao

  2. Institute of Physics, Chinese Academy of Sciences, Beijing, 100080, China

    Leng Liao

  3. Institute of Modern Physics, Chinese Academy of Science, Lanzhou, 730000, China

    Xie-Guo Lee

  4. CCAST (World Lab.), P.O. Box 8730, Beijing, 100080, China

    Yong-Chang Huang

Authors
  1. Yong-Chang Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leng Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xie-Guo Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yong-Chang Huang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huang, YC., Liao, L. & Lee, XG. Faddeev–Jackiw canonical path integral quantization for a general scenario, its proper vertices and generating functionals. Eur. Phys. J. C 60, 481–487 (2009). https://doi.org/10.1140/epjc/s10052-009-0922-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjc/s10052-009-0922-5

PACS

Search

Navigation