# Bound states and corresponding elementary fields

+ 4 like - 0 dislike
404 views

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]

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOverflo$\varnothing$Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). Please complete the anti-spam verification