We mathematically study the infrared catastrophe for the Hamiltonian of Nelson's model when it has the external potential in a general class. For the model, we prove the pull-through formula on ground states in operator theory first. Based on this formula, we show both non-existence of any ground state and divergence of the total number of soft bosons.
|Number of pages||26|
|Journal||Publications of the Research Institute for Mathematical Sciences|
|Publication status||Published - Dec 2006|
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