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
|Publications of the Research Institute for Mathematical Sciences
|Published - Dec 2006
All Science Journal Classification (ASJC) codes
- General Mathematics