in the discrete sector at time $t=0$ undergoes irreversible decay to the continuum of states which are degenerate in energy. This phenomenon can be derived using time-dependent perturbation theory [@cotan]. The standard derivation must be generalized in the present case because the relevant process is composite. We make this generalization and compute the order $g_2^4$ contributions to the energy shift and decay width of single trace states with $n \ge 2.$ The energy shift is the less significant datum when there is instability, but it agrees with the principal value calculation of [@golm1]. The value we find for the decay width would also emerge from the formalism of [@golm1] if an $i\e$ prescription had been used rather than principal value (as suggested recently in [@sv]). We show that the decay amplitude is invariant under the basis change discussed above. It should therefore agree with the amplitude computed in string theory.

The development of the continuous spectrum in the string theory is intimately connected with the Penrose limit which produces the pp-wave spacetime from ${\rm AdS}_5\times {\rm S}_5$. For finite radius $R$ of ${\rm S}_5$, the null circle in $x^-$ is compact [@nas] and there is a discrete spectrum of stable 