Enhanced binding of an \(N\)-particle system interacting with a scalar field. II: Relativistic version (Q899103)

Stability and instability have been the subject of many investigations over the years, in particular in situations when a quantum mechanical particle -- be it relativistic or nonrelativistic -- is coupled to some quantized scalar or non-scalar field. Often with zero coupling, the bottom of the energy spectrum is embedded in the continuous spectrum. Therefore, for non-zero coupling the spectral analysis needs to solve a perturbation problem of an embedded eigenvalue. It is shown that the interaction with a scalar field enhances the binding energy, so that for a sufficiently large coupling constant there is a ground state, even if there is no ground state for zero coupling. In the present article, \(N\) relativistic particles are assumed to be coupled to a massless scalar field. The stability condition is checked for an infrared-regularized ground state.