General relativistic analogue solutions for the Yang–Mills theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 117 (1998) no. 2, pp. 308-324 Cet article a éte moissonné depuis la source Math-Net.Ru

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We discuss several solutions to the Yang–Mills equations that can be found using the connection between general relativity and the Yang–Mills theory. Some comments about the possible physical meaning of these solutions are made. In particular, it is argued that some of these analogue solutions of the Yang–Mills theory may have some connection with the confinement phenomenon. To this end, we briefly look at the motion of test particles moving in the background potential of the Schwarzschild analogue solution.
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D. Singleton. General relativistic analogue solutions for the Yang–Mills theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 117 (1998) no. 2, pp. 308-324. http://geodesic.mathdoc.fr/item/TMF_1998_117_2_a9/

[1] C. N. Yang, R. L. Mills, Phys. Rev., 96 (1954), 191 | DOI | Zbl

[2] J. D. Jackson, Classical Electrodynamics, $2^{\mathrm{nd}}$ Edition, John Wiley, New York, 1975 | MR

[3] G. 't Hooft, Nucl. Phys. B, 79 (1974), 276 ; А. М. Поляков, ЖЭТФ, 68:6 (1975), 1975 | DOI

[4] B. Julia, A. Zee, Phys. Rev. D, 11 (1975), 2227 | DOI

[5] E. B. Bogomolnyi, YaF, 24 (1976), 861 | MR

[6] M. K. Prasad, C. M. Sommerfield, Phys. Rev. Lett., 35 (1975), 760 | DOI

[7] A. A. Belavin, A. M. Polyakov, A. S. Schwartz, Yu. S. Tyupkin, Phys. Lett. B, 59 (1975), 85 | DOI | MR

[8] R. Utiyama, Phys. Rev., 101 (1956), 1597 | DOI | MR | Zbl

[9] M. Carmeli, Classical fields: General relativity and gauge theory, Wiley, New York, 1982 | MR | Zbl

[10] F. A. Lunev, Phys. Lett. B, 295 (1992), 99 ; Ф. А. Лунев, ТМФ, 94 (1993), 66 | DOI | MR | MR | Zbl

[11] F. A. Lunev, J. Math. Phys., 37 (1996), 5351 | DOI | MR | Zbl

[12] C. N. Yang, T. T. Wu, Properties of Matter under Unusual Conditions, eds. H. Mark, S. Fernbach, Interscience, New York, 1968

[13] E. Witten, Phys. Rev. Lett., 38 (1977), 121 | DOI

[14] G. Rosen, J. Math. Phys., 13 (1972), 595 | DOI | MR

[15] J. H. Swank, L. J. Swank, T. Dereli, Phys. Rev. D, 12 (1975), 1096 | DOI

[16] A. P. Protogenov, Phys. Lett. B, 67 (1977), 62 | DOI | MR

[17] S. M. Mahajan, P. M. Valanju, Phys. Rev. D, 35 (1987), 2543 ; 36, 1500 | DOI | MR | DOI

[18] F. A. Lunev, Phys. Lett. B, 311 (1993), 273 | DOI | MR

[19] D. Singleton, Phys. Rev. D, 51 (1995), 5911 ; Nuovo Cimento A, 109 (1996), 169 | DOI | MR | DOI | MR

[20] D. Singleton, A. Yoshida, A general relativistic model for confinement in $SU(2)$ Yang–Mills theory, E-print hep-th/9505160

[21] F. A. Lunev, O. Pavlovsky, Singular solutions of Yang–Mills equations and Bag model, E-print hep-ph/9609452

[22] V. De Alfaro, S. Fubini, G. Furlan, Phys. Lett. B, 65 (1976), 163 | DOI | MR

[23] J. P. Hsu, E. Mac, J. Math. Phys., 18 (1977), 100 | DOI | MR

[24] D. Singleton, Int. J Theor. Phys., 36 (1997), 1857 | DOI | MR | Zbl

[25] H. Ohanian, Gravitation and Space-time, W. W. Norton Company, 1976

[26] D. Singleton, A. Yoshida, Int. J. Mod. Phys. A, 12 (1997), 4823 | DOI | MR | Zbl

[27] E. Eichten et al., Phys. Rev. D, 17 (1978), 3090 | DOI

[28] K. Wilson, Phys. Rev. D, 10 (1974), 2445 | DOI

[29] D. Sivers, J. Ralston, Phys. Rev. D, 28 (1983), 953 | DOI

[30] D. Singleton, Z. Phys. C, 72 (1996), 525 | DOI | MR

[31] V. Dzhunushaliev, Confining properties of the classical $SU(3)$ Yang–Mills theory, E-print hep-th/9611096

[32] A. C. T. Wu, T. T. Wu, J. Math. Phys., 15 (1974), 53 | DOI

[33] W. J. Marciano, H. Pagels, Phys. Rev. D, 12 (1975), 1093 | DOI

[34] D. V. Gal'tsov, M. S. Volkov, Phys. Lett. B, 274 (1992), 173 | DOI | MR

[35] J. Arafune, P. G. O. Freund, C. J. Goebel, J. Math. Phys., 16 (1975), 433 | DOI | MR

[36] J. J. Thomson, Elements of the Mathematical Theory of Electricity and Magnetism, $3^{rd}$ Ed., Cambridge University Press, Cambridge, 1904

[37] M. N. Saha, Ind. J Phys., 10 (1936), 145; Phys. Rev., 75 (1949), 1968 ; H. A. Wilson, Phys. Rev., 75 (1949), 309 | DOI | DOI

[38] R. Jackiw, C. Rebbi, Phys. Rev. Lett., 36 (1976), 1116 | DOI

[39] J. Dittrich, P. Exner, J. Math. Phys., 26 (1985), 2000 ; В. Б. Гостев, А. Р. Френкин, ТМФ, 974 (1988), 247 | DOI | MR | Zbl | MR

[40] C. Goebel, D. LaCourse, M. G. Olsson, Phys. Rev. D, 41 (1990), 2917 | DOI

[41] Y. Shibata, H. Tezuka, Z. Phys. C, 62 (1994), 533 | DOI

[42] B. Ram, Amer. J. Phys., 50 (1982), 549 | DOI

[43] Z. Flyugge, Zadachi po kvantovoi mekhanike, T. 1, Mir, M., 1974

[44] J. Ashman et al., Phys. Lett. B, 206 (1988), 364 ; Nucl. Phys. B, 328 (1989), 1 | DOI | DOI

[45] D. Singleton, J. Math. Phys., 37 (1996), 4574 | DOI | MR | Zbl

[46] D. Singleton, Phys. Lett. A, 223 (1996), 12 | DOI | MR | Zbl