Microcausality, Kramers' theorem and the bound-state Bethe-Salpeter equation

Abstract

The explicit role of microcausality in exact bound-state Bethe-Salpeter schemes is examined. It is found to lead to covariant analyticity properties of Bethe-Salpeter momentum-space amplitudes which, it is suggested, can be used to judge the structural consistency of approximate schemes. It is argued ingeneral that the structure of the exact scheme is retained by those approximations obtained by finite order truncation of graphical series. The additional implications of time-reversal invariance are also considered and a relativistic extension of the configuration-space Kramers theorem is established. Finally, explicit examination of the Wick-Cutkosky model solutions is made: all such solutions, both normal and abnormal, are shown to display the requisite analyticity, microcausality, and time-reversal properties.