Title:
|
Distinguished Riemann-Hamilton geometry in the polymomentum electrodynamics (English) |
Author:
|
Oană, Alexandru |
Author:
|
Neagu, Mircea |
Language:
|
English |
Journal:
|
Communications in Mathematics |
ISSN:
|
1804-1388 |
Volume:
|
20 |
Issue:
|
2 |
Year:
|
2012 |
Pages:
|
137-145 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
In this paper we develop the distinguished (d-) Riemannian differential geometry (in the sense of d-connections, d-torsions, d-curvatures and some geometrical Maxwell-like and Einstein-like equations) for the polymomentum Hamiltonian which governs the multi-time electrodynamics. (English) |
Keyword:
|
jet polymomentum Hamiltonian of electrodynamics |
Keyword:
|
Cartan canonical connection |
Keyword:
|
Maxwell-like and Einstein-like equations |
MSC:
|
53C07 |
MSC:
|
53C80 |
MSC:
|
70S05 |
idZBL:
|
Zbl 06165040 |
idMR:
|
MR3032809 |
. |
Date available:
|
2013-01-28T10:55:32Z |
Last updated:
|
2013-10-22 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143144 |
. |
Reference:
|
[1] Asanov, G. S.: Jet extension of Finslerian gauge approach.Fortschr. Phys., 38, 8, 1990, 571-610, Zbl 0744.53035, MR 1076500, 10.1002/prop.2190380802 |
Reference:
|
[2] Atanasiu, Gh., Neagu, M.: Canonical nonlinear connections in the multi-time Hamilton geometry.Balkan J. Geom. Appl., 14, 2, 2009, 1-12, Zbl 1186.53038, MR 2539737 |
Reference:
|
[3] Christodoulou, D., Francaviglia, M., Tulczyjew, W. M.: General relativity as a generalized Hamiltonian system.J. Gen. Relativ. Gravit., 10, 1979, 567-579, Zbl 0448.58006, MR 0541653, 10.1007/BF00757208 |
Reference:
|
[4] Chruściński, D.: Hamiltonian structure for classical electrodynamics of a point particle.Rep. Math. Phys., 41, 1, 1998, 13-48, Zbl 0932.70016, MR 1617898, 10.1016/S0034-4877(98)80181-X |
Reference:
|
[5] Coriasco, S., Ferraris, M., Francaviglia, M.: Non linear relativistic electrodynamics.Geometria, Fisica-Matematica e outros Ensaios -- volume in honour of A. Ribeiro Gomes, 1998, 101-118, Coimbra, |
Reference:
|
[6] Dickey, L. A.: Solitons Equations and Hamiltonian systems.1991, Advanced Series in Mathematical Physics 12, World Scientific, Singapore, Chapter 17: Multi-Time Lagrangian and Hamiltonian Formalism.. MR 1147643 |
Reference:
|
[7] Eells, J., Lemaire, L.: A report on harmonic maps.Bull. London Math. Soc., 10, 1978, 1-68, Zbl 0401.58003, MR 0495450, 10.1112/blms/10.1.1 |
Reference:
|
[8] Francaviglia, M., Palese, M., Winterroth, E.: A new geometric proposal for the Hamiltonian description of classical field theories.Proc. of the 8th Int. Conf. ``DGA 2001 -- Differential Geometry and Its Applications", 2002, 415-423, Silesian University, MR 1978795 |
Reference:
|
[9] Giachetta, G., Mangiarotti, L., Sardanashvily, G.: Covariant Hamiltonian field theory.1999, arXiv:hep-th/9904062v1. |
Reference:
|
[10] Gotay, M., Isenberg, J., Marsden, J. E., Montgomery, R.: Momentum maps and classical fields. Part I. Covariant field theory.2004, arXiv:physics/9801019v2 [math-ph]. MR 1188431 |
Reference:
|
[11] Kanatchikov, I. V.: On quantization of field theories in polymomentum variables.AIP Conf. Proc., 453, 1, 1998, 356-367, Zbl 0982.81028, MR 1765516, 10.1063/1.57105 |
Reference:
|
[12] Krupková, O.: Hamiltonian field theory.J. Geom. Phys., 43, 2002, 93-132, Zbl 1016.37033, MR 1919207, 10.1016/S0393-0440(01)00087-0 |
Reference:
|
[13] Krupková, O.: Hamiltonian field theory revisited: A geometric approach to regularity.Proc. Colloq. Diff. Geom. ``Steps in Differential Geometry", 2001, 187-207, Debrecen University, Zbl 0980.35009, MR 1859298 |
Reference:
|
[14] Krupková, O., Saunders, D. J.: Affine duality and Lagrangian and Hamiltonian systems.Int. J. Geom. Methods Mod. Phys., 8, 3, 2011, 669-697, MR 2807123, 10.1142/S0219887811005336 |
Reference:
|
[15] Miron, R., Anastasiei, M.: The Geometry of Lagrange Spaces: Theory and Applications.1994, Kluwer Academic Publishers, Dordrecht, Zbl 0831.53001, MR 1281613 |
Reference:
|
[16] Miron, R., Hrimiuc, D., Shimada, H., Sabău, S. V.: The Geometry of Hamilton and Lagrange Spaces.Kluwer Academic Publishers, Dordrecht, 2001, Zbl 1001.53053, MR 1839409 |
Reference:
|
[17] Neagu, M.: Riemann-Lagrange Geometry on 1-Jet Spaces.2005, Matrix Rom, Bucharest, |
Reference:
|
[18] Neagu, M.: The geometry of autonomous metrical multi-time Lagrange space of electrodynamics.Int. J. Math. Math. Sci., 29, 1, 2002, 7-16, Zbl 1011.53053, MR 1892327, 10.1155/S0161171202011018 |
Reference:
|
[19] Neagu, M., Udrişte, C., Oană, A.: Multi-time dependent sprays and $h$-traceless maps.Balkan J. Geom. Appl., 10, 2, 2005, 76-92, MR 2235108 |
Reference:
|
[20] Oană, A., Neagu, M.: The local description of the Ricci and Bianchi identities for an $h$-normal $N$-linear connection on the dual 1-jet space $J^{1\ast}(T,M)$.2011, arXiv:1111.4173v1 [math.DG].. MR 3032809 |
Reference:
|
[21] Oană, A., Neagu, M.: From quadratic Hamiltonians of polymomenta to abstract geometrical Maxwell-like and Einstein-like equations.2012, arXiv:1202.4477v1 [math-ph]. MR 3035882 |
Reference:
|
[22] Sachs, R. K., Wu, H.: General Relativity for Mathematicians.1977, Springer-Verlag, New York, Heidelberg, Berlin, Zbl 0373.53001, MR 0503498 |
Reference:
|
[23] Saunders, D. J.: The Geometry of Jet Bundles.1989, Cambridge University Press, New York, London, Zbl 0665.58002 |
Reference:
|
[24] Udrişte, C., Matei, L.: Lagrange-Hamilton Theories (in Romanian).2008, Geometry Balkan Press, Bucharest, |
. |