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arXiv 2001.077812020-01-21hep-phquant-ph

The Lee model: a tool to study decays

Francesco Giacosa

备注：: 25 pages, 1 figure. Prepared for the proceedings of the symposium Symmetries in Science, 4-9/8/2019, Bregenz, Austria
DOI：: 10.1088/1742-6596/1612/1/012012

英文摘要：

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.

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