Geodesic
Investigation of systems with quadratic interaction by the method of functional derivatives
Teoretičeskaâ i matematičeskaâ fizika, Tome 41 (1979) no. 2, pp. 273-284

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For a fermion-boson system with quadratic interaction in the boson field in which the transition matrix element depends on the boson variables, a method is proposed for calculating the many-time statistical Green's functions on the basis of the method of functional derivatives. In the limit of a fixed fermion, the explicit form of the exact many-time Green's functions is found. For the case of a moving fermion, an iterative procedure is proposed for calculating the Green's functions with allowance for indirect interaction in the boson subsystem. 
@article{TMF_1979_41_2_a9,
     author = {A. I. Ivanov and G. S. Lomakin and O. A. Ponomarev},
     title = {Investigation of systems with quadratic interaction by the method of functional derivatives},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {273--284},
     publisher = {mathdoc},
     volume = {41},
     number = {2},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_41_2_a9/}
}
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A. I. Ivanov; G. S. Lomakin; O. A. Ponomarev. Investigation of systems with quadratic interaction by the method of functional derivatives. Teoretičeskaâ i matematičeskaâ fizika, Tome 41 (1979) no. 2, pp. 273-284. http://geodesic.mathdoc.fr/item/TMF_1979_41_2_a9/