Lorentz covariance of three-dimensional equations

  • V. Pascalutsa
  • J. A. Tjon
Part of the Few-Body Systems book series (FEWBODY, volume 10)


We show how the invariance under the charge conjugation and CPT symmetry, present in the Bethe-Salpeter equation, is lost in the reduction to certain relativistic three-dimensional equations. This in particular leads to the breakdown of the standard Lorentz structure and renormalization procedures for the resulting single-particle propagators. We formulate the equal-time approximation of the Bethe-Salpeter equation in the form which manifestly satisfies the above symmetries, and apply it to the description of the pion-nucleon interaction in a dynamical model based on hadron exchanges. We also consider the one-body limit of various three-dimensional equations for the case of t- and u-channel one-particle-exchange potential.


Charge Conjugation Lorentz Covariance Nucleon Spectator Charge Conjugation Symmetry Bind State Problem 
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Copyright information

© Springer-Verlag/Wien 1999

Authors and Affiliations

  • V. Pascalutsa
    • 1
  • J. A. Tjon
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of UtrechtUtrechtThe Netherlands

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