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Bogolyubov group variables in relativistic field theory. (English. Russian original) Zbl 0978.81516

Theor. Math. Phys. 111, No. 2, 583-591 (1997); translation from Teor. Mat. Fiz. 111, No. 2, 242-251 (1997).
Summary: We define the Bogolyubov variables for strongly coupled systems that are invariant under the Poincaré group in \((1+1)\)-dimensional space-time. This allows us to achieve a compatibility between taking the conservation laws into account exactly and developing a regular perturbation theory. We perform the secondary quantization in terms of the Bogolyubov variables and discuss the problem of reducing the number of states of the field. We also discuss the conditions for validity of the perturbation theory.

MSC:

81T70 Quantization in field theory; cohomological methods
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References:

[1] N. N. Bogoliubov,Ukr. Mat. Zh.,2, 3–24 (1950).
[2] E. P. Solodovnikova, A. N. Tavkhelidze, and O. A. Khrustalev,Theor. Math. Phys.,10, 105 (1972);11, 537 (1972);12, 731 (1973).
[3] E. P. Solodovnikova and A. N. Tavkhelidze,Theor. Math. Phys.,21, 935 (1974).
[4] S. V. Semenov,Theor. Math. Phys.,18, 251 (1974).
[5] A. N. Tolstenkov, N. E. Tyurin, and A. V. Shurgaya,Theor. Math. Phys.,19, 459 (1974).
[6] A. V. Shurgaya,Theor. Math. Phys.,28, 745 (1976).
[7] O. D. Timofeevskaya,Theor. Math. Phys.,37, 1051 (1978).
[8] S. T. Zavtrak, L. I. Komarov, and I. D. Feranchuk,Theor. Math. Phys.,47, 313 (1981).
[9] R. V. Jolos, V. G. Kartavenko, and V. Rybarska,Theor. Math. Phys.,20, 873 (1974).
[10] K. A. Sveshnikov, P. K. Silaev, and O. A. Khrustalev,Theor. Math. Phys.,80, 790 (1989). · Zbl 0699.53088
[11] S. V. Tyablikov,Zh. Eksp. Teor. Fiz.,21, 377–383 (1951);Fiz. Tverdogo Tela,3, 3445–3460 (1961).
[12] V. A. Moskalenko,Sov. Phys. JETP,34, 241 (1958).
[13] P. N. Bogolyubov and A. E. Dorokhov,Theor. Math. Phys.,51, 462 (1982).
[14] O. D. Timofeevskaya,Theor. Math. Phys.,54, 303 (1983).
[15] V. G. Bornyakov and O. D. Timofeevskaya,Theor. Math. Phys.,55, 451 (1983).
[16] N. H. Christ and T. D. Lee,Phys. Rev. D,12, 1606 (1975).
[17] E. Tomboulis,Phys. Rev. D,12, 1678 (1975).
[18] M. Greutz,Phys. Rev. D,12, 3126 (1975).
[19] K. A. Sveshnikov,Theor. Math. Phys.,55, 553 (1983);74, 251 (1988).
[20] O. D. Timofeevskaya, in:Problems of High-Energy Physics and Quantum Field Theory (Proc. Vth International Seminar) [in Russian], Vol. 1, Inst. High Energy Phys., Protvino (1982).
[21] K. A. Sveshnikov,Theor. Math. Phys.,75, 482 (1988).
[22] V. A. Matveev,Nucl. Phys. B.,121, 403–415 (1977).
[23] O. A. Khrustalev, A. V. Razumov, and A. Yu. Taranov,Nucl. Phys. B,172, 44–58 (1980).
[24] A. V. Razumov and A. Yu. Taranov,Theor. Math. Phys.,52, 641 (1982);57, 1106 (1983). · Zbl 0513.58024
[25] A. V. Razumov,J. Math. Phys.,31, 1416–1421 (1990). · Zbl 0762.53019
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