Functional Solution Scheme for Relativistic Strong - coupling Theory III

The graph scheme developed in 1 is further investigated. The structure of the coefficients aais determined in terms of a0 and the projections of the splitting graphs. This allows a formal sum­ mation of the /c-series. The first few terms of the strong coupling series for the lowest mass eigen­ value are computed for the X <}r4 theory. The leading term for large /. is complex. This restricts physically acceptable solutions to /. below some critical value. By including a bare mass m in the I.agrangian. the a/.become dependent on it. Consideration of one a/,e.g. a0(m, X) should then be sufficient for the determination of physical mass eigen­