Let's have some bound state, like positronium or meson. I need to

calculate an amplitude of a process which involves the bound state in an

in- or out-state. Is it necessary to introduce the corresponding

elementary field (for example, elementary "positronium" field) and its

interaction lagrangian for using perturbation theory? Or there are some

other methods for calculating amplitudes?

I.e., consider the matrix element $\langle\gamma\gamma|\hat S|Ps\rangle$

for process positronium decay, $Ps\to\gamma\gamma$.

Is it possible to use lagrangian $L_{int}=\bar\psi\gamma_\mu\psi A^\mu$

(i.e., positronium creation operator is simple $a_s^+(p)b_{s′}^+(k)$,

where $\hat a$, $\hat b$ correspond to electron and positron

destruction operators), or do I need to introduce a positronium field

$\phi_{Ps}$ and its interaction lagrangian to calculate such an amplitude?

[edited upon import]