The Lee model: a tool to study decays

Abstract

We describe -- in a didactical and detailed way -- the so-called Lee model (which shares similarities with the Jaynes-Cummings and Friedrichs models) as a tool to study unstable quantum states/particles. This Lee model is based on Quantum Mechanics (QM) but possesses some of the features of Quantum Field Theory (QFT). The decay process can be studied in great detail and typical QFT quantities such as propagator, one-loop resummation, and Feynman rules can be introduced. Deviations from the exponential decay law as well as the Quantum Zeno effects can be studied within this framework. The survival probability amplitude as a Fourier transform of the energy distribution, the normalization of the latter, and the Breit-Wigner limit can be obtained in a rigorous mathematical approach.

25 pages, 1 figure. Prepared for the proceedings of the symposium Symmetries in Science, 4-9/8/2019, Bregenz, Austria

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Cited by in corpus (3)

• A simple alternative to the Breit-Wigner distribution
• Multichannel decay law
• The self-energy of Friedrichs-Lee models and its application to bound states and resonances