Hermitean with respect to $g_{ij}$, i.e. $g_{ik}h^k_j= h^k_ig_{kj}$.

It is easy to show that the eigenoperators are $\co_\a (x) =
v^i_\a \co_i(x)$ and have diagonal 2-point functions: \[eigop\] \_(x) \_(y) &=& [\_ (x-y)\^[2J+4]{}]{} \[1 - \_(x-y)\^2M\^2\]\
&\~& [ \_ (x-y)\^[2\_]{}]{}, from which one can read the scale dimension $\D_\a = J+2+\g_\a$.

A simpler method for field theory computations was developed in [@golm1]. It is a method to compute $h^i_j$ directly with no need for the complicated combinatorics of Feynman diagrams required in earlier work. The resulting effective Hamiltonian has a quite simple and striking structure. The method applies to 2-point functions of the operators of (\[ops\]) and has recently been extended [@golm2] to a wider class of scalar operators.

We refer readers to [@golm1] for an explanation of the method, and we begin our discussion with (11) of that paper. Certain “end-point terms” and other terms which vanish in the BMN limit are neglected in (11), and we note that the omitted terms actually vanish in the channel which is symmetric under exchange $\phi \leftrightarrow \psi$ of the two impurities, so (11) is exact in this channel. Although the BMN limit is taken at an early stage in [@golm1], we 