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Whenever the Breit-Wigner amplitude appears in a calculation,there are manyinstances (e.g., Fermi's two-level system and the Weisskopf-Wignerapproximation) where energy integrations are extended from the scatteringspectrum of the Hamiltonian to the whole real line. Such extensions areperformed in order to obtain a desirable, causal result. In this paper, werecall several of those instances and show that substituting the Breit-Wigneramplitude by the complex delta function allows us to recover such desirableresults without having to extend energy integrations outside of the scatteringspectrum.

Replacing the Breit-Wigner amplitude by the complex delta function to describe resonances