Abstract The salient features of generalized second‐quantization representations for nonrelativistic systems of composite particles are reviewed and their application to a reformulation of the quantum theory of reactive collisions is discussed. Such representations allow the properties of the bound composite states to be built explicitly into the algebra of states and observables. A single unperturbed Hamiltonian simultaneously describes the free propagation of the various species of bound composites as well as of their unbound constituents, while the interaction Hamiltonian describes only true scattering and reaction processes. The inclusion of the binding of all composites in the unperturbed Hamiltonian cures the divergences in the Born series arising from bound‐state poles. Unstable composites can be included in a natural way, leading to an explicit representation for the kinematics and dynamics of their decay and their contribution to collision phenomena.
>An unstable particle capable of undergoing real decay - N + theta is considered in the nonrelativistic second quantization theory (Lee model). Perturbation theory and the expansion of an arbitrary state in eigen states are extended to the case of an unstable particle. The quantity which plays the role of the state norm of such a particle is determined. A new method is proposed for determining the fraction of time a stable particle V capable of undergoing the virtual transformation into N + theta stays in the state V and in the state N + theta . If the method is applied to an unstable particle V, one can find the time it is in each of the two states, but the answer is expressed in complex numbers. (auth)