# Having difficulty comprehending a problem in Peskin's text

1. Dec 14, 2011

### kof9595995

In his "an introduction to quantum field theory", problem 5.4 (c), he describes a bound state of positronium as $$|B(k)\rangle=\sqrt{2M}\int{\frac{d^{3}p}{(2\pi)^{3}}\psi_{i}(p)a^{\dagger}_{p+\frac{k}{2}}\Sigma^{i}b^{\dagger}_{-p+\frac{k}{2}}|0\rangle}$$
where $\psi_{i}(p)$ are the p-orbtal wavefunctions in momentum space(i=1,2,3), $a^{\dagger}$and $b^{\dagger}$ are electron and positron creation operator, $\Sigma^{i}$ is some 2 by 2 matrix. I don't understand where this $\Sigma^{i}$ comes from. LHS of the equation is just a ket, in this case shouldn't RHS be a superposition of kets? What should I make of $\Sigma^{i}$?