The present paper starts from the Bethe-Salpeter equation for the bound states of a fermion and anti-fermion pair. Assuming that the interaction between the straton and anti-straton can be represented approximately by an instantaneous interaction in the center of mass system, we obtain the following main conclusions: (1) the solution of the Bethe-Salpeter equation may be carried out in ordinary three dimensional space and the numbers of components of the wave functions for the pseudo-scalar and vector mesons reduce respectively from 4 and 8 to 2 and 4; (2) If the interaction is spherically symmetrical in space and its spinor structure is of the diagonal coupling type, then it is seen from the equation for the pseudo-scalar mesons that the meson mass appears as a quadratic eigen value in the equation, without leading to the negative energy excitation usually encountered in the fourdimensional equation; (3) The structure wave function obtained in the instantaneous interaction may be used to study both the mass spectra of the bound states, and the processes involving only the center of mass system.
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