Geodesic
Nonstationary perturbation theory for the energy shifts of a~degenerate level
Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 2, pp. 219-229

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The asymptotic (when $T\equiv t_1-t_2\to\infty$ ) representation for the operator $PS(t_1,t_2)P$ where $P$ is the projector on some degenerate subspace of the nonperturbed energy level and $S(t_1,t_2)$ is the operator of the time development in the interaction picture is obtained. The asymptotic formula is the following: $$PS(t_1,t_2)P=R_0\exp (-iQT)=(\exp\{-iQ^+T\})R_0=R_0^{1/2}(\exp\{-i\bar QT\})R_0^{1/2},$$ where $Q$ is the nonhermitian secular operator [3], $R_0$ and $\bar Q$ are the hermitian operators. 
@article{TMF_1975_24_2_a7,
     author = {A. N. Vasil'ev and A. L. Kitanin},
     title = {Nonstationary perturbation theory for the energy shifts of a~degenerate level},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {219--229},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1975_24_2_a7/}
}
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A. N. Vasil'ev; A. L. Kitanin. Nonstationary perturbation theory for the energy shifts of a~degenerate level. Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 2, pp. 219-229. http://geodesic.mathdoc.fr/item/TMF_1975_24_2_a7/