Lorentz covariance of three-dimensional equations

Details Lorentz covariance of three-dimensional equations Lorentz covariance of three-dimensional equations

1999-05-28

arxiv.org/abs/nucl-th/9905062v1

Few Body Syst.Suppl.10:105-114,1999

Physics

Nuclear Physics

Nuclear Theory

10 pages, 6 figures, invited paper at 16th European Conference on Few-Body Problems in Physics (FB 98), Autrans, Grenoble, Fra

Scientific paper

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.

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