Abstract
We review papers on a new method for quantizing the Yang-Mills field applicable both in perturbation theory and beyond it. We show that in the modified formulation of the Yang-Mills theory leading to a formal perturbation theory that coincides with the standard one, there exist soliton solutions of the classical equations of motion.
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C. N. Yang and R. L. Mills, Phys. Rev., 96, 191–195 (1954).
L. D. Faddeev and V. N. Popov, Phys. Lett. B, 25, 29–30 (1967).
B. S. DeWitt, Phys. Rev., 160, 1113–1148 (1967); 162, 1195–1239 (1967).
G. Gursi and F. Ferrari, Nuovo Cimento A Ser. 11, 35, 273–279 (1976).
T. Kugo and I. Ojima, Progr. Theoret. Phys. Suppl., 66, 1–130 (1979).
R. Brout and F. Englert, Phys. Rev. Lett., 13, 321–323 (1964).
P. W. Higgs, Phys. Lett., 12, 132–133 (1964).
T. W. B. Kibble, Phys. Rev., 155, 1554–1561 (1967).
V. N. Gribov, Nucl. Phys. B, 139, 1–19 (1978).
I. Singer, Commun. Math. Phys., 60, 7–12 (1978).
D. Zwanziger, Nucl. Phys. B, 321, 591–604 (1989); 323, 513–544 (1989).
G. ’t Hooft, Nucl. Phys. B, 79, 276–284 (1974).
A. M. Polyakov, JETP Lett., 20, 194–195 (1974).
A. A. Slavnov, JHEP, 0808, 047 (2008); arXiv:0807.1795v1 [hep-th] (2008).
A. A. Slavnov, Theor. Math. Phys., 161, 1497–1502 (2009).
A. A. Slavnov, Proc. Steklov Inst. Math., 272, 235–245 (2011).
A. Quadri and A. A. Slavnov, JHEP, 1007, 087 (2010); arXiv:1002.2490v2 [hep-th] (2010).
A. A. Slavnov, Theor. Math. Phys., 181, 1302–1306 (2014).
S. Coleman, Commun. Math. Phys., 55, 113–116 (1977).
S. Deser, Phys. Lett. B, 64, 463–464 (1976).
H. Pagels, Phys. Lett. B, 68, 466 (1977).
A. A. Slavnov, “Solitons in the modified Yang–Mills theory,” arXiv:1406.7724v2 [hep-th] (2014).
B. Julia and A. Zee, Phys. Rev. D, 11, 2227–2232 (1975).
M. K. Prasad and C. M. Sommerfield, Phys. Rev. Lett., 35, 760–762 (1975).
E. B. Bogomol’nyi, Soviet J. Nuclear Phys., 24, 449–454 (1976).
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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 183, No. 2, pp. 163–176, May, 2015.
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Slavnov, A.A. New approach to the quantization of the Yang-Mills field. Theor Math Phys 183, 585–596 (2015). https://doi.org/10.1007/s11232-015-0286-y
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DOI: https://doi.org/10.1007/s11232-015-0286-y