Lifetime and Decay of Unstable Particles inS-Matrix Theory

An investigation is made of the possible time dependence of decay laws for unstable particles. The probability $P\left(t\right)\mathrm{}$ that an unstable particle has not decayed at time $t$ is expressed in terms of $S$-matrix quantities. It is concluded that, contrary to popular belief, the exponential decay law $P=e^{-\Gamma t}$ is only one of a discrete set of possible decay laws.