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.
Cite this article
Masao Hirokawa, Infrared Catastrophe for Nelson’s Model—Non-Existence of Ground State and Soft-Boson Divergence. Publ. Res. Inst. Math. Sci. 42 (2006), no. 4, pp. 897–922DOI 10.2977/PRIMS/1166642191