A soluble model in field theory - I

Abstract

Examining a model presented earlier we performed a calculation of unstable particle production and decay without separating these two processes. The usual separation of production and decay is seen to be valid for a timet, such that\(\frac{\hbar }{{\mu _3 c^2 }} \ll t \ll 2\tau ln 2\pi \tau t^2 Q^3 \), whereQ is the energy above threshold for unstable particle production andτ is the lifetime. When the above conditions are valid the unstable states possess a simple enough time development to be characterized with a particle label. Our model also predicts bound state production for suitable cut-off functions. The Nishijima-Zimmermann formalism for handling bound states in conjunction with dispersion relations reproduces direct calculations.