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Abelian decomposition of Einstein’s theory: restricted gravity. (English) Zbl 1333.83008

Summary: Treating Einstein’s theory as the gauge theory of Lorentz group, we discuss the Abelian decomposition of Einstein’s theory and show that in restricted gravity the graviton is described by the spin-one gauge potential. This establishes the Abelian dominance in Einstein’s theory, that the core dynamics of Einstein’s theory is described by restricted gravity obtained by the abelian projection of Einstein’s theory. We discuss physical implications of our results.

MSC:

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83A05 Special relativity
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
22E10 General properties and structure of complex Lie groups
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[1] Cho, Y. M., No article title, Phys. Rev. D, 14, 3335 (1976) · doi:10.1103/PhysRevD.14.3335
[2] also, S.; Hehl, F.; McCrea, J.; Mielke, E.; Ne’eman, Y., No article title, Phys. Rep., 258, 1 (1995) · doi:10.1016/0370-1573(94)00111-F
[3] Cho, Y. M., No article title, Int. J. Mod. Phys. A, 24, 3327 (2009) · Zbl 1176.83063 · doi:10.1142/S0217751X09046928
[4] Cho, Y. M., No article title, Int. J. Mod. Phys. CS, 7, 116 (2012)
[5] Y. M. Cho, S. H. Oh, and Sangwoo Kim, Class. Quantum Grav.29, 205007 (2012).
[6] Feynman, R., No article title, Acta. Phys. Pol., 24, 697 (1963)
[7] Witt, B. D., No article title, Phys. Rev., 160, 1113 (1967) · Zbl 0158.46504 · doi:10.1103/PhysRev.160.1113
[8] Witt, B. D., No article title, Phys. Rev., 162, 1195 (1967) · Zbl 0161.46501 · doi:10.1103/PhysRev.162.1195
[9] Cho, Y. M., No article title, Phys. Rev. D, 21, 1080 (1980) · doi:10.1103/PhysRevD.21.1080
[10] Cho, Y. M., No article title, Phys. Rev. D, 62, 074009 (2000) · doi:10.1103/PhysRevD.62.074009
[11] Cho, Y. M., No article title, Phys. Rev. Lett., 46, 302 (1981) · doi:10.1103/PhysRevLett.46.302
[12] Cho, Y. M., No article title, Phys. Rev. D, 23, 2415 (1981) · doi:10.1103/PhysRevD.23.2415
[13] Bae, W. S.; Cho, Y. M.; Kimm, S. W., No article title, Phys. Rev. D, 65, 025005 (2002) · doi:10.1103/PhysRevD.65.025005
[14] Cho, Y. M.; Cho, F. H.; Yoon, J. H., No article title, Phys. Rev. D, 87, 085025 (2013) · doi:10.1103/PhysRevD.87.085025
[15] Cundy, N.; Cho, Y. M.; Lee, W., No article title, PoS LATTICE, 2012, 212 (2012)
[16] Cundy, N.; Cho, Y. M.; Lee, W.; Leem, J., No article title, Phys. Lett. B, 729, 192 (2014) · Zbl 1331.81302 · doi:10.1016/j.physletb.2014.01.009
[17] Cho, Y. M., No article title, J. Math. Phys., 20, 2605 (1979) · doi:10.1063/1.524022
[18] Bondi, H., No article title, Nature, 179, 1072 (1957) · Zbl 0082.21203 · doi:10.1038/1791072a0
[19] Bondi, H.; Pirani, F.; Robinson, I., No article title, Proc. Roy. Soc. (London) A, 125, 519 (1959) · Zbl 0084.44002 · doi:10.1098/rspa.1959.0124
[20] Cho, Y. M., No article title, Phys. Rev. Lett., 44, 1115 (1980) · doi:10.1103/PhysRevLett.44.1115
[21] Hooft, G. t., No article title, Phys. Rev. Lett., 37, 8 (1976) · doi:10.1103/PhysRevLett.37.8
[22] Jackiw, R.; Rebbi, C., No article title, Phys. Rev. Lett., 37, 172 (1976) · doi:10.1103/PhysRevLett.37.172
[23] Callan, C.; Dashen, R.; Gross, D. G., No article title, Phys. Lett. B, 63, 334 (1976) · doi:10.1016/0370-2693(76)90277-X
[24] Belavin, A.; Polyakov, A.; Schwartz, A.; Tyupkin, Y., No article title, Phys. Lett. B, 59, 85 (1975) · doi:10.1016/0370-2693(75)90163-X
[25] Cho, Y. M., No article title, Phys. Lett. B, 81, 25 (1979) · doi:10.1016/0370-2693(79)90708-1
[26] Cho, Y. M., No article title, Phys. Lett. B, 644, 208 (2007) · Zbl 1248.81264 · doi:10.1016/j.physletb.2006.11.040
[27] Cho, Y. M.; Cho, F. H.; Yoon, J. H., No article title, Class. Quantum Grav., 30, 055003 (2013) · Zbl 1263.83028 · doi:10.1088/0264-9381/30/5/055003
[28] Zee, A., No article title, Phys. Rev. Lett., 55, 2379 (1985) · doi:10.1103/PhysRevLett.55.2379
[29] Y. M. Cho, in Proceedings of XXV International Conference on High Energy Physics, Ed. by Y. Yamaguchi and K. K. Phua (World Scientific, Singapore, 1991).
[30] Newman, E.; Tamburino, L.; Unti, No article title, J. Math. Phys., 4, 915 (1963) · Zbl 0115.43305 · doi:10.1063/1.1704018
[31] Misner, C., No article title, J. Math. Phys., 4, 924 (1963) · doi:10.1063/1.1704019
[32] Dowker, J., No article title, Gen. Rel. Grav., 5, 603 (1974) · doi:10.1007/BF02451402
[33] Ramaswamy, S.; Sen, A., No article title, J. Math. Phys., 22, 2612 (1981) · doi:10.1063/1.524839
[34] Hawking, S., No article title, Phys. Lett. A, 60, 81 (1977) · doi:10.1016/0375-9601(77)90386-3
[35] Eguchi, T.; Hanson, A., No article title, Phys. Lett. B, 74, 249 (1978) · doi:10.1016/0370-2693(78)90566-X
[36] Gibbons, G.; Hawking, S., No article title, Phys. Lett. B, 78, 430 (1978) · doi:10.1016/0370-2693(78)90478-1
[37] Eguchi, T.; Gilkey, P.; Hanson, A., No article title, Phys. Rep., 66, 213 (1980) · doi:10.1016/0370-1573(80)90130-1
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