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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Pascalutsa, V., Tjon, J.A. (1999). Lorentz covariance of three-dimensional equations. In: Desplanques, B., Protasov, K., Silvestre-Brac, B., Carbonell, J. (eds) Few-Body Problems in Physics ’98. Few-Body Systems, vol 10. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6798-4_18
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DOI: https://doi.org/10.1007/978-3-7091-6798-4_18
Publisher Name: Springer, Vienna
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