Nonlinear Schroedinger Solitons in Massive Yang-Mills Theory and Partial Localization of Dirac Matter

Xanthos N. Maintas, Charilaos E. Tsagkarakis, Fotios K. Diakonos, Dimitrios J. Frantzeskakis

Department of Physics, University of Athens, GR-15771 Athens, Greece.

DOI: 10.4236/jmp.2012.38087                

Abstract

We investigate the classical dynamics of the massive SU(2) Yang-Mills field in the framework of multiple scale perturbation theory. We show analytically that there exists a subset of solutions having the form of a kink soliton, modulated by a plane wave, in a linear subspace transverse to the direction of free propagation. Subsequently, we explore how these solutions affect the dynamics of a Dirac field possessing an SU(2) charge. We find that this class of Yang- Mills configurations, when regarded as an external field, leads to the localization of the fermion along a line in the transverse space. Our analysis reveals a mechanism for trapping SU(2) charged fermions in the presence of an external Yang-Mills field indicating the non-abelian analogue of Landau localization in electrodynamics.

Keywords

Yang-Mills Solitons; Non-Linear Schroedinger Equation; Dirac Fermions; Localization

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. Smilga, “Lectures on Quantum Chromodynamics,” World Scientific, Singapore, 2001. HUdoi:10.1142/9789812810595U
[2]	S. G. Matinyan, G. K. Savvidy and N. G. Ter-Arutyunyan -Savvidy, “Classical Yang—Mills Mechanics. Nonlinear Color Oscillations (in Russian),” Journal of Experimental and Theoretical Physics, Vol. 80, 1981, pp. 830-838.
[3]	B. V. Chirikov and D. L. Shepelyanskii, “Stochastic Oscillations of Classical Yang-Mills Fields (in Russian),” Journal of Experimental and Theoretical Physics Letters, Vol. 34, No. 4, 1981, pp. 171-175.
[4]	S. G. Matinyan, G. K. Savvidy and N. G. Ter-Arutyunyan -Savvidy, “Stochasticity of Classical Yang-Mills Mechanics and Its Elimination by Using the Higgs Mechanism (in Russian),” Journal of Experimental and Theo- retical Physics Letters, Vol. 34, No. 11, 1981, pp. 613- 616.
[5]	S. G. Matinyan, “Dynamical Chaos of Nonabelian Gauge Fields (in Russian),” Fizika Elementarnykh Chastits I Atomnoya Yadra, Vol. 16, 1985, pp. 522-570.
[6]	S. G. Matinyan, E. P. Prokhorenko and G. K. Savvidy, “Non-Integrability of Time Dependent Spherically Sym- metric Yang-Mills Equations,” Nuclear Physics B, Vol. 258, No. 2, 1988, pp. 414-428. HUdoi:10.1016/0550-3213(88)90273-8U
[7]	S. Coleman, “There Are No Classical Glueballs,” Communications in Mathematical Physics, Vol. 55, No. 2, 1977, pp. 113-116. HUdoi:10.1007/BF01626513U
[8]	M. Wellner, “Evidence for a Yang-Mills Fractal,” Physi- cal Review Letters, Vol. 68, No. 12, 1992, pp. 1811-1813. doi:10.1103/PhysRevLett.68.1811U
[9]	M. Wellner, “The Road to Fractals in a Yang-Mills Sys- tem,” Physical Review E, Vol. 50, No. 2, 1994, pp. 780- 789. HUdoi:10.1103/PhysRevE.50.780U
[10]	M. Frasca, “Strongly Coupled Quantum Field Theory,” Physical Review D, Vol. 73, No. 4, 2006, Article ID 027701. HUdoi:10.1103/PhysRevD.73.049902U
[11]	M. Frasca, “Infrared Gluon and Ghost Propagators,” Physics Letters B, Vol. 670, No. 1, 2008, pp. 73-77. HUdoi:10.1016/j.physletb.2008.10.022U
[12]	M. Frasca, “Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical Case,” Modern Physics Letters A, Vol. 24, No. 30, 2009, pp. 2425-2432. doi:10.1142/S021773230903165XU
[13]	V. Achilleos, F. K. Diakonos, D. J. Frantzeskakis, G. C. Katsimiga, X. N. Maintas, C. E. Tsagkarakis and A. Tsapalis, “A Multi-Scale Perturbative Approach to SU(2)- Higgs Classical Dynamics: Stability of Nonlinear Plane Waves And Bounds of the Higgs Field Mass,” Physical Review D, Vol. 85, No. 2, Article ID 027702. HUdoi:10.1103/PhysRevD.85.027702U
[14]	A. Jeffrey and T. Kawahara, “Asymptotic Methods in Nonlinear Wave Theory,” Pitman, London, 1982.
[15]	Yu. S. Kivshar and B. Luther-Davies, “Dark Optical Soli- tons: Physics and Applications,” Physics Reports, Vol. 298, No. 2-3, 1998, pp. 81-197. doi:10.1016/S0370-1573(97)00073-2U
[16]	D. J. Frantzeskakis, “Dark Solitons in Atomic Bose-Ein- stein Condensates: From Theory to Experiments,” Journal of Physics A-mathematical and Theoretical, Vol. 43, No. 21, 2010.
[17]	V. E. Zakharov and A. B. Shabat, “Interaction between Solitons in a Stable Medium (in Russian),” Journal of Experimental and Theoretical Physics, Vol. 64, No. 5, 1973, pp. 1627-1639.
[18]	J. D. Bjorken and S. D. Drell, “Relativistic Quantum Mechanics,” McGraw-Hill, New York, 1978
[19]	L. D. Landau and E. M. Lifshitz, “Quantum Mechanics,” Pergamon Press, Oxford, 1991.