Lorentz covariance of three-dimensional equations

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.

Note:

10 pages, 6 figures, invited paper at 16th European Conference on Few-Body Problems in Physics (FB 98), Autrans, Grenoble, France, 1-6 Jun 1998 Report-no: THU-98/40 Journal-ref: Few-Body Systems Suppl. 10 (1999) 105-114

talk: Autrans 1998/06/01
Bethe-Salpeter equation
dimension: 3
invariance: Lorentz
renormalization
propagator
approximation: quasipotential
pi nucleon: interaction
hadron: exchange
charge conjugation

References(14)

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