The unstable system in relativistic quantum mechanics

AbstractA soluble model for the relativistically covariant description of an unstable system is given in terms of relativistic quantum field theory, with a structure similar to Van Hove's generalization of the Lee model in the nonrelativistic theory. Since the Fock space for this model can be decomposed to sectors, it can be embedded in a one-particle Hilbert space in a spectral form similar to the Friedrichs model in the nonrelativistic theory. Several types of spectral models result, corresponding to physically motivated assumptions made in the framework of the field theory. For example, the continuous spectrum of the unperturbed problem may be (−∞, ∞) or semibounded. In the decay V → N+θ, the θ may have negative energy. In this case, the reaction corresponds to the crossed channel process V+ $$\bar \theta $$ → N.