The author treats the Dirac-Proca equations (D-P eqs.):
, , with , , , where is an integer. The unique local existence of a smooth solution is standard. Let and .
Main results: (1) If satisfies the estimation for a sufficiently small , and if holds at , then there exists a unique global solution of the Cauchy problem of the D-P eqs.
(2) has a unique free profile such that as , where are the solutions of the linear D-P eqs.
A priori estimates , , with the norm given by prove the results.