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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {A. A. Arkhipov},
     title = {Equal-time reduction of~the {Bethe{\textendash}Salpeter} formalism for a~two-fermion system},
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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/

[1] Arbuzov B. A., EChAYa, 19:1 (1988), 5–50

[2] Gross D. I., Wilczek F., Phys. Rev. Lett., 30 (1973), 1343–1346 | DOI

[3] Politzer H. D., Phys. Rev. Lett., 30 (1973), 1346–1349 | DOI

[4] Andreev I. V., Khromodinamika i zhestkie protsessy pri vysokikh energiyakh, Nauka, M., 1981 | Zbl

[5] Bykov A. A., Dremin I. M., Leonidov A. V., UFN, 143 (1984), 3–32 | DOI | MR

[6] Quigg C., Rosner J. L., Phys. Rep., 56 (1979), 167 | DOI | MR

[7] Wilson K. Q., Phys. Rev., D10 (1974), 2445–2459

[8] Makeenko Yu. M., UFN, 143 (1984), 161–212 | DOI

[9] Fukugita M., Lattice Quantum Chromodynamics with Dynamical Quarks, Preprint RIEP-729, 1987

[10] Arkhipov A. A., Reports on Math. Phys., 23 (1986), 83–98 | DOI | MR

[11] Arkhipov A. A., TMF, 74 (1988), 69–81 | MR | Zbl

[12] Arkhipov A. A., Savrin V. I., EChAYa, 16:5 (1985), 1091–1125 | MR

[13] Bogolyubov N. N., Logunov A. A., Oksak A. I., Todorov I. T., Obschie printsipy kvantovoi teorii polya, Nauka, M., 1987 | MR

[14] Bogolyubov N. N., Shirkov D. V., Vvedenie v teoriyu kvantovannykh polei, Nauka, M., 1984 | MR

[15] Logunov A. A., Tavkhelidze A. N., Nuovo Cim., 29 (1963), 380–399 | DOI | MR

[16] Faustov R. N., TMF, 3 (1970), 240–254

[17] Macke W., Zs. f. Naturforsch., 8a (1953), 599–615 ; 8a, 615–620 | MR | Zbl | MR

[18] Dyson F., Phys. Rev., 91 (1953), 1543–1550 | DOI | MR | Zbl

[19] Zimmerman W., Nuovo Cim. Suppl., 11 (1954), 43–90 | DOI | MR | Zbl

[20] Krolikowski W., Rzewuski J., Nuovo Cim., 2 (1955), 203–219 | DOI | MR | Zbl

[21] Matveev V. A., Muradyan R. M., Tavkhelidze A. H., Relativistically covariant equations for two particles in quantum field theory, Preprint JINR E2-3498, JINR, Dubna, 1967

[22] Kadyshevski V. G., Nucl. Phys., B6 (1968), 125–148 | DOI

[23] Logunov A. A., Savrin V. I., Tyurin N. E., Khrustalev O. A., TMF, 6 (1971), 157–165

[24] Logunov A. A., Khrustalev O. A., Problemy teoreticheskoi fiziki, Sb., posvyaschennyi I. E. Tammu, Nauka, M., 1972, 96 | MR

[25] Faustov R. N., Ann. of Phys. (N. Y.), 78 (1973), 176–189 | DOI

[26] Blokhintsev D. I., Rizov V. A., Todorov I. T., TMF, 28 (1976), 3–26

[27] Logunov A. A., Khrustalev O. A., EChAYa, 1:1 (1970), 72–89

[28] Kadyshevskii V. G., Mir-Kasimov R. M., Skachkov N. B., EChAYa, 2:3 (1972), 637–690

[29] Faustov R. N., EChAYa, 3:1 (1972), 238–268

[30] Rizov V. A., Todorov I. T., EChAYa, 6:3 (1975), 669–742 | MR

[31] Skachkov N. B., Solovtsov I. D., EChAYa, 9:1 (1978), 5–47 | MR