Geodesic
Equal-time reduction of~the Bethe--Salpeter formalism for a~two-fermion system
Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 2, pp. 247-267

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The method of equal-time reduction proposed by the author [10, 11] for a system of two scalar particles is generalized to a system of two fermions. A self-consistent procedure for equal-time reduction is constructed both in terms of Bethe–Salpeter wave functions and in terms of Green's functions of the two-fermion system. Three-dimensional dynamical equations are obtained for the equal-time wave functions and the two-time Green's functions of the system of two fermions, and it is shown that the Schrödinger structure of the obtained equations is a consequence of the causal structure of local quantum field theory. 
@article{TMF_1990_83_2_a7,
     author = {A. A. Arkhipov},
     title = {Equal-time reduction of~the {Bethe--Salpeter} formalism for a~two-fermion system},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {247--267},
     publisher = {mathdoc},
     volume = {83},
     number = {2},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_83_2_a7/}
}
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A. A. Arkhipov. Equal-time reduction of~the Bethe--Salpeter formalism for a~two-fermion system. Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 2, pp. 247-267. http://geodesic.mathdoc.fr/item/TMF_1990_83_2_a7/