Unstable Particles in a General Field Theory

The problem of unstable particles in quantum field theory is treated as one of the interpretation of complex singularities appearing in the analytic continuation of scattering amplitudes into unphysical sheets of their Lorentz invariant variables. Suitable continuations are shown to hold under certain restrictive assumptions in a general field theory, making use of unitarity and causality of the $S$ matrix. The extra singularities appearing in the continuation are fixed isolated poles, in accordance with a conjecture of Peierls.