Geodesic
Some properties of the Lee model. I
Teoretičeskaâ i matematičeskaâ fizika, Tome 8 (1971) no. 3, pp. 308-323 
L. A. Dadashev. Some properties of the Lee model. I. Teoretičeskaâ i matematičeskaâ fizika, Tome 8 (1971) no. 3, pp. 308-323. http://geodesic.mathdoc.fr/item/TMF_1971_8_3_a1/
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A study is made of Lee's quantum-field model with the Hamiltonian introduced in [2]. The explicit dependence of the resolvent on the $\tau$ matrices is found and it is shown that the expansion of the resolvent in a series in normal products reduces to the inversion of a certain operator that depends on the Bose operators. The formula obtained can be used to give qualitative information about the spectrum of the Hamiltonian.

[1] S. Shveber, Vvedenie v relyativistskuyu kvantovuyu teoriyu polya, IL, M., 1963

[2] E. Khenli, V. Tirring, Elementarnaya kvantovaya teoriya polya, IL, 1963

[3] S. G. Krein, Lineinye differentsialnye uravneniya v banakhovom prostranstve, «Nauka», 1967 | MR

[4] F. A. Berezin, Metod vtorichnogo kvantovaniya, «Nauka», 1965 | MR

[5] Yu. I. Lyubich, UMN, XXI:3 (1966)

[6] E. Khille, R. Fillips, Funktsionalnyi analiz i polugruppy, IL, 1962 | MR