Infrared Catastrophe for Nelson's Model

Details Infrared Catastrophe for Nelson's Model Infrared Catastrophe for Nelson's Model

2002-11-21

arxiv.org/abs/math-ph/0211051v6

Physics

Mathematical Physics

22 pages. This manuscript is the final version and it appears in Publ. RIMS

Scientific paper

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.

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