symmetric channel in the $J\to\infty$ limit. Another thing to note here is that working at finite $J$ does not resolve the degeneracy problem. For example, single- and double-trace operators are degenerate when $\frac {n}{J+1} = \pm
\frac {m}{J_0+1}$, and there is a similar degeneracy condition for $(k+1)$-trace operators. One may also observe that $ A(n,m,J')$ does not vanish at degeneracy for finite $J$, although it does vanish as $J \to \infty$. In principle, one should apply degenerate perturbation theory to the calculation of eigenvalues of $H$ even before triple-trace operators are included. However, we will ignore this complication, which very likely disappears in the large $J$ limit.

Our primary goal is to apply time-dependent perturbation theory to study the time evolution of a state which is purely single-trace at time $t=0$. We will calculate the decay rate of such a state into degenerate triple-trace states. We have found it useful to illustrate the essential physics in quantum mechanical toy models and then adapt the results in the models to the BMN limit of the Hamiltonian (\[heff\]).

Quantum Mechanical Models
=========================

Our calculation of the decay rate is based on the treatment of the decay of a discrete state embedded in 