and the discussion above it[^5]. Of course, the principal value derived here to resolve the divergence in the last term is not present in conventional perturbation theory. The physical interpretation of our result is that the pole of the resolvent operator $1/(H_0-E)$ at $E=E_n$ due to the discrete state $|n \ra$ is shifted to $E = E_n + \D\o_n - i\G/2$ in the complex plane by the interaction in $1/(H_0+V-E)$. The state $|n
\ra$ is unstable in the full theory.

The goal of the Hamiltonian formulation of [@golm1] was the calculation of anomalous dimensions of BMN operators. In our opinion the calculations undertaken for this purpose should be revised to incorporate degenerate rather than non-degenerate perturbation theory. One may note that the various contributions to our energy shift (\[eshif\]) agree exactly with those of (25) of [@golm1]. So the result there should be interpreted as the real part of the shift of a pole rather than the anomalous dimension of an eigenstate of the dilatation operator.

It is interesting that the present time-dependent treatment provides justification for the recent suggestion in [@sv] of an $S$-matrix approach to the BMN system (see also [@sj]) which would require an $i\e$ prescription in 