Wong’s equations in Yang-Mills theory

• Autorzy: Sergey Storchak
• Języki publikacji: EN

Abstrakty

EN

Wong’s equations for the finite-dimensional dynamical system representing the motion of a scalar particle on a compact Riemannian manifold with a given free isometric smooth action of a compact semi-simple Lie group are derived. The equations obtained are written in terms of dependent coordinates which are typically used in an implicit description of the local dynamics given on the orbit space of the principal fiber bundle. Using these equations, we obtain Wong’s equations in a pure Yang-Mills gauge theory with Coulomb gauge fixing. This result is based on the existing analogy between the reduction procedures performed in a finite-dimensional dynamical system and the reduction procedure in Yang-Mills gauge fields.

Słowa kluczowe

EN

Yang-Mills theory; Marsden-Weinstein reduction; Kaluza-Klein theories; Wong’s equation

• Czasopismo: Open Physics
• Rocznik: 2014
• Tom: 12
• Numer: 4
• Strony: 233-244

Daty

wydano

2014-04-01

online

2014-04-23

Twórcy

autor

Sergey Storchak

• Institute for High Energy Physics, Protvino, Moscow Region, 142284, Russia,

Bibliografia

• [1] S. K. Wong, Il Nuovo Cimento A 65, 689 (1970) http://dx.doi.org/10.1007/BF02892134[Crossref]
• [2] L. S. Brown, W. I. Weisberger, Nucl. Phys. B 157, 285 (1979) http://dx.doi.org/10.1016/0550-3213(79)90508-X[Crossref]
• [3] B. P. Kosyakov, Phys. Rev. D 57, 5032 (1998) http://dx.doi.org/10.1103/PhysRevD.57.5032[Crossref]
• [4] J. Jalilian-Marian, S. Jeon, R. Venugopalan, Phys. Rev. D 63, 036004 (2001) http://dx.doi.org/10.1103/PhysRevD.63.036004[Crossref]
• [5] J. F. Dawson, B. Mihaila, F. Cooper, Phys. Rev. D 81, 054026 (2010) http://dx.doi.org/10.1103/PhysRevD.81.054026[Crossref]
• [6] Z. Haba, Mod. Phys. Lett. A28, 1350091 (2013) http://dx.doi.org/10.1142/S0217732313500910[Crossref]
• [7] R. Kerner, Ann. Inst. H. Poincaré 9, 143 (1968)
• [8] R. Montgomery, Lett. Math. Phys. 8, 59 (1984) http://dx.doi.org/10.1007/BF00420042[Crossref]
• [9] R. Montgomery, Ph. D. thesis, University of California, (Berkeley, USA, 1986)
• [10] C. Duval, P. Horvathy, Ann. Phys. (N.Y.) 142, 10 (1982) http://dx.doi.org/10.1016/0003-4916(82)90226-3[Crossref]
• [11] J. E. Marsden, Lecture on Mechanics, London Math. Soc. Lect. Notes Series 174 (Cambridge University Press, Cambridge, 1992) http://dx.doi.org/10.1017/CBO9780511624001[Crossref]
• [12] J. E. Marsden, T. S. Ratiu, J. Scheurle, J. Math. Phys. 41, 3379 (2000) http://dx.doi.org/10.1063/1.533317[Crossref]
• [13] S. N. Storchak, J. Phys. A: Math. Gen. 34, 9329 (2001) http://dx.doi.org/10.1088/0305-4470/34/43/315[Crossref]
• [14] S. N. Storchak, Bogolubov transformation in path integral on manifold with a group action (IHEP Preprint 98-1, Protvino, 1998)
• [15] S. N. Storchak, Phys. Atom. Nucl. 64, 2199 (2001) http://dx.doi.org/10.1134/1.1432926[Crossref]
• [16] S. N. Storchak, J. Phys. A: Math. Gen. 37, 7019 (2004) http://dx.doi.org/10.1088/0305-4470/37/27/011[Crossref]
• [17] S. N. Storchak, J. Geom. Phys. 59, 1155 (2009) http://dx.doi.org/10.1016/j.geomphys.2009.05.001[Crossref]
• [18] Y. M. Cho, D. S. Kimm, J. Math. Phys. 30, 1571 (1989)
• [19] Y. M. Cho, Phys. Rev. D 35, 2628 (1987) http://dx.doi.org/10.1103/PhysRevD.35.2628[Crossref]
• [20] R. G. Littlejohn, M. Reinsch, Rev. Mod. Phys. 69, 213 (1997) http://dx.doi.org/10.1103/RevModPhys.69.213[Crossref]
• [21] A. Z. Jadczyk, Class. Quant. Grav. 1, 517 (1984) http://dx.doi.org/10.1088/0264-9381/1/5/006[Crossref]
• [22] O. Babelon, C. M. Viallet, Phys. Lett. B 85, 246 (1979) http://dx.doi.org/10.1016/0370-2693(79)90589-6[Crossref]
• [23] O. Babelon, C. M. Viallet, Commun. Math. Phys. 81, 515 (1981) http://dx.doi.org/10.1007/BF01208272[Crossref]
• [24] P. K. Mitter, C. M. Viallet, Commun. Math. Phys. 79, 43 (1981) http://dx.doi.org/10.1007/BF01209307[Crossref]
• [25] I. M. Singer, Phisica Scripta 24, 817 (1981) http://dx.doi.org/10.1088/0031-8949/24/5/002[Crossref]
• [26] I. M. Singer, Commun. Math. Phys. 60, 7 (1978) http://dx.doi.org/10.1007/BF01609471[Crossref]
• [27] M. S. Narasimhan, T. R. Ramadas, Commun. Math. Phys. 67, 121 (1979) http://dx.doi.org/10.1007/BF01221361[Crossref]
• [28] D. Groisser, T. H. Parker, J. Diff. Geom. 29, 499 (1989)
• [29] Yu. P. Soloviev, Geometrical structures on a manifold of interacting gauge fields, In: Global analysis and mathematical physics (Voronezh, Voronezh State University, 1987) 110 (in Russian).
• [30] G. C. Rossi, M. Testa, Nucl. Phys. B 163, 109 (1980) http://dx.doi.org/10.1016/0550-3213(80)90393-4[Crossref]
• [31] G. C. Rossi, M. Testa, B 176, 477 (1980)
• [32] S. N. Storchak, arXiv: 0711.2910 [hep-th]
• [33] G. Kunstatter, Class. Quant. Grav. 9, 1466 (1992) http://dx.doi.org/10.1088/0264-9381/9/6/005[Crossref]
• [34] J. Harnad, J. P. Pareé, Class. Quant. Grav. 8, 1427 (1991) http://dx.doi.org/10.1088/0264-9381/8/8/009[Crossref]
• [35] D. Lukman, N. S. Mankoč Borštink and H. B. Nielsen, New J. Phys. 13, 103027 (2011) http://dx.doi.org/10.1088/1367-2630/13/10/103027[Crossref]
• [36] T. Mestdag, A Lie algebroid approach to Lagrangian systems with symmetry, In: J. Bures et al. (Eds.), Differential Geometry and its Applications, Proc. Conf. (Prague, Czech Republic, 2005) 523–535.
• [37] T. Guhr, S. Keppeler, Annals Phys. 322, 287 (2007) http://dx.doi.org/10.1016/j.aop.2006.09.010[Crossref]
• [38] S. Fabi, G. S. Karatheodoris, arXiv:1104.3970. [WoS]
• [39] S. Fabi, B. Harms, S. Hou, arXiv:1302.0795. [WoS]

Identyfikatory

DOI

10.2478/s11534-014-0439-x