Question

Bound states and the meaning of 'off shell'?

Answer 1

there are a couple of similar posts here on Stack Exchange about bound particles being off shell in QFT. From posts on other sites, I've been told that the idea of off shell particles doesn't apply to bound states - but I still see this language in many places.

Answer 2

The meanings of the words "off-shell" and "on-shell" just describe the contribution of the states to the propagators. There is known the so-called spectral representation of the propagator, which reads
Dab(p)=∫0∞dm2ρ(m2)Dab(p,m)
Here, ρ(m2) is the so-called state spectral density depending on details of interacting theory, while Dab(p,m2) is the free propagator depending on the squared mass m2.