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Conceptual foundations of soliton versus particle dualities toward a topological model for matter. (English) Zbl 1342.81241

Summary: The idea that fermions could be solitons was actually confirmed in theoretical models in 1975 in the case when the space-time is two-dimensional and with the sine-Gordon model. More precisely S. Coleman showed that two different classical models end up describing the same fermions particle, when the quantum theory is constructed. But in one model the fermion is a quantum excitation of the field and in the other model the particle is a soliton. Hence both points of view can be reconciliated. The principal aim in this paper is to exhibit a solutions of topological type for the fermions in the wave zone, where the equations of motion are non-linear field equations, i.e. using a model generalizing sine-Gordon model to four dimensions, and describe the solutions for linear and circular polarized waves. In other words, the paper treat fermions as topological excitations of a bosonic field.

MSC:

81T10 Model quantum field theories
81V25 Other elementary particle theory in quantum theory
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[1] Pietrzyk, M.; Kanatchikov, I.; Bandelow, U., No article title, Journal of Nonlinear Mathematical Physics, 15, 162 (2008) · Zbl 1172.35502 · doi:10.2991/jnmp.2008.15.2.4
[2] Skyrme, T.H.R.: A nonlinear theory of strong interactions. Proc. Roy. Soc. A 247, 260 (1958) · doi:10.1098/rspa.1958.0183
[3] Kouneiher, J., Hélein, F.: On the soliton-particle dualities. In: Boi, L. (ed.) Geometries of Nature Living Systems and Human Cognition - New Interactions of Mathematics with Natural Sciences and Humanities. World Scientific (2005) · Zbl 1139.81367
[4] Hooft, G’t, No article title, Nucl. Phys., B79, 276 (1974) · doi:10.1016/0550-3213(74)90486-6
[5] Polyakov, AM, No article title, JET P Lett., 20, 194 (1974)
[6] Perring, J.K., Skyrme, T.H.R.: A model unified field equation. Nucl. Phys. 31, 550-555 (1962) · Zbl 0106.20105 · doi:10.1016/0029-5582(62)90774-5
[7] Kouneiher, J., Sidharth, B.: Mass generation without the Higgs mechanism. Int. Jour. of Theo. Phys. (2015). doi:10.1007/s10773-015-2542-1 · Zbl 1325.81184
[8] Thirring, W.: A soluble relativistic field theory. Ann. Phys. (N.Y.) 3, 91 (1958) · Zbl 0078.44303 · doi:10.1016/0003-4916(58)90015-0
[9] Coleman, S., No article title, Phys. Rev., D11, 2088 (1975)
[10] Mandelstam, S., No article title, Phys. Rev., D11, 3026 (1975)
[11] Faber, M.: Particles as stable topological solitons. Few Body Syst. 30, 149-186 (2001) · doi:10.1007/s006010170009
[12] Steenrod, N.: The topology of fibre bundles. Princeton University Press, Princeton (1951) · Zbl 0054.07103
[13] Gross, DJ; Pisarski, RD; Yaffe, LG, No article title, Rev. Mod. Phys., 53, 43 (1981) · doi:10.1103/RevModPhys.53.43
[14] Belavin, AA; Polyakov, AM; Schwartz, AS; Tyupkin, YuS, No article title, Phys. Lett., 59B, 85 (1975) · doi:10.1016/0370-2693(75)90163-X
[15] Jackson, J.D. Classical electrodynamics, 2nd edn. Wiley, New York (1975) · Zbl 0997.78500
[16] Hong-Mo, C., Sheung Tsun, T.: Some elementary gauge theory concepts, world scientific lecture notes in physics - Fol 47. World Scientific, Singapore (1993) · Zbl 0862.53054
[17] Makhankov, V.G., Rybakov, Y.P., Sanyuk, V.I.: The Skyrme model. Springer, Berlin, and referenced therin (1994)
[18] Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. Freeman and Company, San Francisco (1973)
[19] Faber, R. L.: Differential Geometry and Relativity Theory: An Introduction; Monographs and Textbooks in Pure and Applied Mathematics, vol. 76 (1983) · Zbl 0521.53002
[20] Makhankov, V.G., Rybakov, Y.P., Sanyuk, V.I.: The Skyrme Model. Springer (1993)
[21] de Broglie, L., No article title, Comp. Rend., 77, 506, 548, 630 (1923)
[22] Freed, D.: Five lectures on supersymmetry A.M.S. (1999) · Zbl 0937.81001
[23] Adkins, GS; Nappi, CR; Witten, E., No article title, Nucl. Phys., B 228, 552 (1983) · doi:10.1016/0550-3213(83)90559-X
[24] Faber, M.; Kobushkin, AP, No article title, Phys. Rev., D69, 116002 (2004)
[25] Partical Data Group, No article title, Phys. Lett., 592, 94 (2004)
[26] Skyrme, THR, No article title, Roy, Proc. Soc., A260, 127 (1961) · Zbl 0102.22605 · doi:10.1098/rspa.1961.0018
[27] Coleman, S.: Quantum sine-Gordon equation as the massive Thirring model. Phys. Rev. D 11, 2088 (1975)
[28] Dirac, PAM, No article title, Proc. R. Soc. London, A133, 60 (1931) · JFM 57.1581.06 · doi:10.1098/rspa.1931.0130
[29] Witten, E.: Nucl. Phys. B 160 (1979). 57; ibid B 223, p.433. (1983)
[30] Dirac, PAM, No article title, Phys. Rev., 74, 817 (1948) · Zbl 0034.27604 · doi:10.1103/PhysRev.74.817
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