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International Journal of Theoretical Physics

, Volume 53, Issue 2, pp 685–693 | Cite as

Nonlinear Spin and Pseudo-Spin Symmetric Dirac Equations

  • A. D. AlhaidariEmail author
Article

Abstract

Nonlinear Dirac equations are obtained by variation of the spinor action whose Lagrangian components have the same conformal degree and the coupling parameter of the self-interaction term is dimensionless. In 1+1 space-time, we show that these requirements result in the “conventional” quartic form of the nonlinear interaction and present the general equation for various coupling modes. These include, but not limited to, the Thirring and Gross-Neveu models. We consider the spin and pseudo-spin symmetric models and obtain a numerical solution. We also propose a two-component “minimal” pseudo-scalar coupling model.

Keywords

Nonlinear interaction Dirac equation Conformal degree Thirring model Gross-Neveu model Spin pseudo-spin symmetry 

Notes

Acknowledgements

The Author is grateful for the support provided by the Saudi Center for Theoretical Physics (SCTP). We also appreciate the help in computations offered by S. Al-Marzoug, especially in producing some of the material in footnote 2.

Supplementary material

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Saudi Center for Theoretical PhysicsJeddahSaudi Arabia
  2. 2.Danat Al-Khan Tower #5006SharjahUnited Arab Emirates

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