A new derivation of the quantum stochastic differential equation for the evolution operator in the low density limit is presented. We use the distribution approach and derive a new algebra for quadratic master fields in the low density limit by using the energy representation. We formulate the stochastic golden rule in the low density limit case for a system coupling with a Bose field via quadratic interaction. In particular, the vacuum expectation value of the evolution operator is computed and its exponential decay is shown.A new derivation of the quantum stochastic differential equation for the evolution operator in the low density limit is presented. We use the distribution approach and derive a new algebra for quadratic master fields in the low density limit by using the energy representation. We formulate the stochastic golden rule in the low density limit case for a system coupling with a Bose field via quadratic interaction. In particular, the vacuum expectation value of the evolution operator is computed and its exponential decay is shown.

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