No. Resonances are definitely not internal lines in a Feynmn diagram, since the latter have arbitrary real 4-momentum and no associated states, while resonances have complex 4-momentum and unnormalized states.Resonances are indeed states in the continuous-spectrum part of the Hamiltonian. [...]
In QFT it's an internal line in a Feynman diagram (in the case that the corresponding "particles" are described as an elementary field in the Lagrangian). As such it's as "virtual" as any internal line in a Feynman diagram.
There is no normalizable state directly corresponding to the resonance pole on the second sheet of the S-matrix's analytic continuation. But there are wave packets made from the energy eigenstates with energies in the region that approximate the resonance state. This shows in a modified short time behavior - unlike normalizable states, resonances decay purely exponentially at all times (which is impossible at times before preparation).I just want to understand this better. So if we take a reasonably long lived particle like a free neutron, ultimately it is still a resonance. What's going on during those ~15 minutes? Surely there is a state representing what is occurring in some manner. Or do you mean there is no state directly corresponding to the resonance pole on the second sheet of the S-matrix's analytic continuation.