Abstract
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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References
C. N. Yang and R. L. Mills,Phys. Rev. 96, 191 (1954).
J. D. Jackson,Classical Electrodynamics (2nd ed.), Wiley, New York (1975), p. 251.
G. 't Hooft,Nucl. Phys. B,79, 276 (1974); A. M. Polyakov,JETP,41, 988 (1975).
B. Julia and A. Zee,Phys. Rev. D,11, 2227 (1975).
E. B. Bogomolnyi,Sov. J. Nucl. Phys.,24, 449 (1976).
M. K. Prasad and C. M. Sommerfield,Phys. Rev. Lett.,35, 760 (1975).
A. A. Belavin, A. M. Polyakov, A. S. Schwartz, and Yu. S. Tyupkin,Phys. Lett. B,59, 85 (1975).
R. Utiyama,Phys. Rev.,101, 1597 (1956).
M. Carmeli,Classical Fields: General Relativity and Gauge Theory, Wiley, New York (1982).
F. A. Lunev,Phys. Lett. B,295, 99 (1992);Theor. Math. Phys.,94, 48 (1993).
F. A. Lunev,J. Math. Phys.,37, 5351 (1996).
C. N. Yang and T. T. Wu, in.Properties of Matter under Unusual Conditions (H. Mark and S. Fernbach, eds.). Interscience, New York (1969).
E. Witten,Phys. Rev. Lett.,38, 121 (1977).
G. Rosen,J. Math. Phys.,13, 595 (1972).
J. H. Swank, L. J. Swank, and T. Dereli,Phys. Rev. D,12, 1096 (1975).
A. P. Protogenov,Phys. Lett. B,67, 62 (1977).
S. M. Mahajan and P. M. Valanju,Phys. Rev. D,35, 2543 (1987);36, 1500 (1987).
F. A. Lunev,Phys. Lett. B,311, 273 (1993).
D. Singleton,Phys. Rev. D,51, 5911 (1995);Nuovo Cimento A,109, 169 (1996).
D. Singleton and A. Yoshida, “A general relativistic model for confinement inSU (2) Yang-Mills theory,” hep-th/9505160 (1995).
F. A. Lunev and O. Pavlovsky, “Singular solutions of Yang-Mills equations and bag model,” hep-ph/9609452 (1996).
V. De Alfaro, S. Fubini, and G. Furlan,Phys. Lett. B,65, 163 (1976).
J. P. Hsu and E. Mac,J. Math. Phys.,18, 100 (1977).
D. Singleton,Int. J. Theor. Phys.,36, 1857 (1997).
H. Ohanian,Gravitation and Space-Time, Norton (1976), p. 286.
D. Singleton and A. Yoshida,Int. J. Mod. Phys. A,12, 4823 (1997).
E. Eichten, et al.,Phys. Rev. D,17, 3090 (1978).
K. Wilson,Phys. Rev. D,10, 2445 (1974).
D. Sivers and J. Ralston,Phys. Rev. D,28, 953 (1983).
D. Singleton,Z. Phys. C,72, 525 (1996).
V. Dzhunushaliev, “Confining properties of the classicalSU (3) Yang-Mills theory,” hep-th/9611096 (1996); “A single classical quark,” hep-th/9707039 (1997).
A. C. T. Wu and T. T. Wu,J. Math. Phys.,15, 53 (1974).
W. J. Marciano and H. Pagels,Phys. Rev. D,12, 1093 (1975).
D. V. Gal'tsov and M. S. Volkov,Phys. Lett. B,274, 173 (1992).
J. Arfune, P. G. O. Freund, and C. J. Goebel,J. Math. Phys.,16, 433 (1975).
J. J. Thomson,Elements of the Mathematical Theory of Electricity and Magnetism (3rd ed.), Cambridge Univ. Press, Cambridge (1904), Sec. 284.
M. N. Saha,Ind. J. Phys.,10, 145 (1936); M. N. Saha,Phys. Rev.,75, 1968 (1949); H. A. Wilson,Phys. Rev.,75, 309 (1949).
R. Jackiw and C. Rebbi,Phys. Rev. Lett.,36, 1116 (1976); P. Hasenfratz and G. 't Hooft,Phys. Rev. Lett.,36, 1119 (1976).
J. Dittrich and P. Exner,J. Math. Phys.,26, 2000 (1985); V. B. Gostev and A. R. Frenkin,Theor. Math. Phys.,74, 161 (1988).
C. Goebel, D. LaCourse, and M. G. Olsson,Phys. Rev. D,41, 2917 (1990).
Y. Shibata and H. Tezuka,Z. Phys. C,62, 533 (1994).
B. Ram,Am. J. Phys.,50, 549 (1982).
S. Flügge,Practical Quantum Mechanics I, Springer (1971), p. 89.
J. Ashman et al.,Phys. Lett. B,206, 364 (1988);Nucl. Phys. B,328, 1 (1989).
D. Singleton,J. Math. Phys.,37, 4574 (1996).
D. Singleton,Phys. Lett. A,223, 12 (1996).
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Dedication This articls is dedicated to the memory of Professor Fedor Lunev.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 2, pp, 308–324, November, 1998.
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Singleton, D. General relativistic analogue solutions for the Yang-Mills theory. Theor Math Phys 117, 1351–1363 (1998). https://doi.org/10.1007/BF02557173
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DOI: https://doi.org/10.1007/BF02557173