The convolution formula for a decay rate

The convolution formula is derived within the framework of the decay-chain method for decay channels with three and four particles in a final state. To get this formula exactly for unstable particles of any type one must modify the propagators of vector and spinor fields. In this work we suggest proper modifications and get the convolution formula by direct calculations. It was noted that this approach naturally arises in the model of unstable particles with random mass.