Skip to main content
SpringerLink
Log in

Vector Schwinger Model with a Photon Mass Term with Faddeevian Regularization

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

In this talk, we consider the vector Schwinger model with a photon mass term with Faddeevian Regularization, describing two-dimensional (2D) electrodynamics with mass-less fermions and study its Hamiltonian and path integral quantization. This theory is seen to be gauge-non-invariant (GNI). We then construct a gauge-invariant (GI) theory corresponding to this GNI theory using the Stueckelberg mechanism and then recover the physical content of the original GNI theory from the newly constructed GI theory under some special gauge-fixing conditions.

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. Schwinger J.: Gauge invariance and mass. Phys. Rev. 125, 397–398 (1962)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Schwinger J.: Gauge invariance and mass 2. Phys. Rev. 128, 2425–2429 (1962)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Lowenstein J.H., Swieca J.A.: Quantum electrodynamics in two-dimensions. Ann. Phys. 68, 172–195 (1971)

    Article  MathSciNet  ADS  Google Scholar 

  4. Casher A., Kogut J., Susskind L.: Vacuum polarization and the absence of free quarks. Phys. Rev. D10, 732–745 (1974) and references therein

  5. Kogut J., Susskind L.: Hamiltonian formulation of Wilson’s lattice gauge theories. Phys. Rev. D11, 395–408 (1975) and references therein

    ADS  Google Scholar 

  6. Boyanovsky D.: Complete solution of the chiral Schwinger model Hilbert space, constraints and Wess-Zumino terms. Nucl. Phys. B294, 223 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  7. Boyanovsky D., Schmidt I., Golterman M.F.L.: The physics of the chiral Schwinger model: taming an anomalous theory. Ann. Phys. 185, 111 (1988)

    Article  ADS  Google Scholar 

  8. Kulshreshtha U., Kulshreshtha D.S., Mueller-Kirsten H.J.W.: Hamiltonian and BRST formulations of a gauge-invariant chiral Schwinger model. Can. J. Phys. 72, 639 (1994)

    Article  ADS  MATH  Google Scholar 

  9. Kulshreshtha U., Kulshreshtha D.S., Mueller-Kirsten H.J.W.: BRST formulation of a gauge-invariant chiral Schwinger model. Nuovo Cim. A107, 569 (1994)

    Article  ADS  Google Scholar 

  10. Kulshreshtha U., Kulshreshtha D.S.: The front-form Hamiltonian and BRST formulations of the Jackiw-Rajaraman chiral Schwinger model. Can. J. Phys. 80, 791 (2002)

    Article  ADS  Google Scholar 

  11. Kulshreshtha, U., Kulshreshtha, D.S.: Generalized Schwinger model in the light-front frame. “Contributed Paper” at the 8th international workshop on light-cone QCD and non-perturbative hadronic physics, held at Lutsen, University of Minnesota at Duluth, USA, August 11–22, (1997)

  12. Kulshreshtha U., Kulshreshtha D.S., Mueller-Kirsten H.J.W.: Hamiltonian and BRST formulations of the Schwinger model. Helv. Phys. Acta 66, 743–757 (1993)

    Google Scholar 

  13. Kulshreshtha U., Kulshreshtha D.S.: Front-form Hamiltonian and BRST formulations of the Schwinger model. Int. J. Theor. Phys. 37, 2539 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kulshreshtha U.: Vector Schwinger model with a photon mass term: gauge-invariant reformulation, operator solutions and Hamiltonian and path integral formulations. Mod. Phys. Lett. A22, 2993–3001 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  15. Kulshreshtha U., Kulshreshtha D.S.: Gauge-invariant reformulation of the vector Schwinger model with a photon mass term and its Hamiltonian, path integral and BRST formulations. Int. J. Mod. Phys. A22, 6183–6201 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  16. Kulshreshtha U.: Vector Schwinger model with a photon mass term on the light-front. “Invited Contributed Talk” at the International conference on light cone 2008: relativistic nuclear and particle physics (LC2008), Mulhouse, France, July 07–11, 2008, arXiv:0809.1042, Published in PoS LC2008, 008 (2008)

  17. Kulshreshtha U.: Light-front Hamiltonian and path integral formulations of the vector Schwinger model with a photon mass term. Int. J. Mod. Phys. A22, 6183–6201 (2012)

    MathSciNet  ADS  Google Scholar 

  18. Kulshreshtha U., Kulshreshtha D.S., Vary J.P., Sharma L.K.: Light-front BRST quantization of the vector Schwinger model with a photon mass term. Int. J. Theor. Phys. 53(12), 4230–4243 (2014)

    Article  MATH  Google Scholar 

  19. Kulshreshtha U., Kulshreshtha D.S., Vary J.P.: Hamiltonian, path integral and BRST quantization of vector Schwinger model with a photon mass term under Faddeevian regularization. Int. J. Theor. Phys. D10, 26 (2015). doi:10.1007/s10773-015-2665-4

    Google Scholar 

  20. Mitra P.: Chiral Schwinger model with a Faddeevian regularization. Phys. Lett. B284, 23–26 (1992)

    Article  ADS  Google Scholar 

  21. Mukhopadhyay S., Mitra P.: Chiral Schwinger model with new regularization. Zeit. Phys. C67, 525–530 (1995)

    ADS  Google Scholar 

  22. Mitra P., Rahaman A.: The nonconfining Schwinger model. Ann. Phys. 249, 34–43 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  23. Rahaman, A.: A note on the vector Schwinger Model with the photon mass term: gauge invariant reformulation, operator solution and path integral formulation. arXiv:1011.2392 (2 Sept 2012)

  24. Dirac P.A.M.: Generalized Hamiltonian dynamics. Can. J. Math 2, 129 (1950)

    Article  MathSciNet  MATH  Google Scholar 

  25. Kulshreshtha U., Kulshreshtha D.S., Vary J.P.: Light-front Hamiltonian and path integral formulations of large N scalar QCD(2). Phys. Lett. B708, 195–198 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  26. Dirac P.A.M.: Forms of relativistic dynamics. Rev. Mod. Phys. 21, 392–399 (1949)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. Brodsky S.J., Pauli H.C., Pinsky S.S.: Quantum chromodynamics and other field theories on the light-cone. Phys. Rep. 301, 299–486 (1998)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, Iowa State University, Ames, IA, 50011, USA

    Usha Kulshreshtha, Daya Shankar Kulshreshtha & James P. Vary

  2. Department of Physics, Kirori Mal College, University of Delhi, Delhi, 110007, India

    Usha Kulshreshtha

  3. Department of Physics and Astrophysics, University of Delhi, Delhi, 110007, India

    Daya Shankar Kulshreshtha

Authors
  1. Usha Kulshreshtha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daya Shankar Kulshreshtha
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. James P. Vary
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Usha Kulshreshtha.

Additional information

Presented by Usha Kulshreshtha at LIGHTCONE2014, 24–30 May, 2014, North Carolina State University, Raleigh, USA.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kulshreshtha, U., Kulshreshtha, D.S. & Vary, J.P. Vector Schwinger Model with a Photon Mass Term with Faddeevian Regularization. Few-Body Syst 56, 559–563 (2015). https://doi.org/10.1007/s00601-015-1015-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00601-015-1015-7

Keywords

Search

Navigation