Lorentz covariance of three-dimensional equations

V. Pascalutsa; J. A. Tjon

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arXiv · nucl-th/9905062

Lorentz covariance of three-dimensional equations

V. Pascalutsa·J. A. Tjon

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Abstract

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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V. Pascalutsa, J. A. Tjon. 1999-05-28. Lorentz covariance of three-dimensional equations. https://arxiv.org/abs/nucl-th/9905062

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