Skip to main content
SpringerLink
Log in

S Q E D 4 and Q E D 4 on the Null-Plane

  • Particles and Fields
  • Published:
Brazilian Journal of Physics Aims and scope Submit manuscript

Abstract

We study the scalar electrodynamics (S Q E D 4) and the spinor electrodynamics (Q E D 4) in the null-plane formalism. We follow Dirac’s technique for constrained systems to analyze the constraint structure in both theories in detail. We impose the appropriate boundary conditions on the fields to fix the hidden subset first class constraints that generate improper gauge transformations and obtain a unique inverse of the second-class constraint matrix. Finally, choosing the null-plane gauge condition, we determine the generalized Dirac brackets of the independent dynamical variables, which via the correspondence principle give the (anti)-commutators for posterior quantization.

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

Notes

  1. See the definitions in Appendix A.

References

  1. P.A.M. Dirac, Rev Mod Phys. 21(392) (1949)

  2. P.A.M. Dirac. Lectures in quantum mechanics (Benjamin, New York, 1964)

    Google Scholar 

  3. A. Hanson, T. Regge, C. Teitelboim. Constrained hamiltonian systems (Acc. Naz. dei Lincei, Roma, 1976)

    Google Scholar 

  4. P.P. Srivastava, ed. by A. N. Mitra. in quantum field theory: a 20th century profile (Indian National Science Academy, New Delhi, 2000), p. 437

  5. P.P. Srivastava, Lectures on light-front quantized field theory: Spontaneous symmetry breaking. Phase transition in ϕ 4 theory, Proc. XIV Encontro Nacional de Partculas e Campos, Caxambu, MG, pgs. 154-192, Sociedade Brasileira de FL.sica, Brasil, 1993 and the references cited therein (hep-th@xxx.lanl.gov/9312064)

  6. F. Rohrlich, Acta Phys Austriaca Suppl. VIII, 277 (1971). R. A. Neville and F. Rohrlich, Nuovo Cimento A1 , 625 (1971).

    Google Scholar 

  7. G. McCartor, Z. Phys. C41, 271 (1988)

    Google Scholar 

  8. P.J. Steinhardt, Ann Phys. 128, 425 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  9. R. Benguria, P. Cordero, C. Teitelboim. Nucl Phys. B122, 61 (1976)

    ADS  Google Scholar 

  10. K. Sundermeyer, in Constrained Dynamics, Vol. 169. Lectures Notes in Physics (Springer, New York, 1982)

  11. E. Tomboulis, Phys Rev. D8, 2736 (1971)

    ADS  Google Scholar 

  12. S.B. Pereslegin, V.A. Franke, Theor Math Phys. 59, 365 (1984)

    Article  MathSciNet  Google Scholar 

  13. R.A. Neville, F. Rohrlich, Phys Rev. 1692, D3 (1971)

    Google Scholar 

  14. P.N. Pyatov, A.V. Ruzanov, G.N. Rybkin, Classsical Mechanics on Superspace, IFVE-88-212 (1988)

  15. J.B. Kogut, D.E. Soper, Phys Rev. D1, 2901 (1970)

    ADS  Google Scholar 

  16. F.A. Berezin. The Method of Second Quantization (Academic Press, New York, 1966)

    MATH  Google Scholar 

  17. F.A. Berezin, in Introduction to Superanalysis, Vol. 9, ed. by A. A. Kirillov (Reidel Publishing Company, 1987)

  18. R. Casalbouni, Nuovo Cim. 33A, 115 (1976)

    Article  ADS  Google Scholar 

  19. R. Casalbouni, Nuovo Cim. 33A, 389 (1976)

    Article  ADS  Google Scholar 

  20. R. Casana, B.M. Pimentel, G.E.R. Zambrano. Int J Mod Phys. E16, 2993 (2007)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

BMP thanks CNPq for partial support. GERZ thanks CNPq (grant 142695/2005-0) for full support.

Author information

Authors and Affiliations

  1. Departamento de Física, Universidade Federal do Maranhão (UFMA) Campus Universitário do Bacanga, CEP 65085-580, São Luís, MA, Brazil

    R. Casana

  2. Instituto de Física Teórica (IFT/UNESP), UNESP - São Paulo State University, Rua Pamplona 145, CEP 01405-900, São Paulo, SP, Brazil

    B. M. Pimentel

  3. Departamento de Física, Universidad de Nariño Ciudad Universitaria Torobajo, Clle 18 Cr 50, San Juan de Pasto, Nariño, Colombia

    G. E. R. Zambrano

Authors
  1. R. Casana
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. M. Pimentel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. E. R. Zambrano
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. E. R. Zambrano.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Casana, R., Pimentel, B.M. & Zambrano, G.E.R. S Q E D 4 and Q E D 4 on the Null-Plane. Braz J Phys 44, 398–409 (2014). https://doi.org/10.1007/s13538-014-0237-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13538-014-0237-3

Keywords

Search

Navigation