Distinguished Riemann-Hamilton geometry in the polymomentum electrodynamics

 Access to full text

 Full (PDF)

1. Asanov, G. S., 10.1002/prop.2190380802, Fortschr. Phys., 38, 8, 1990, 571-610, (1990) Zbl0744.53035MR1076500DOI10.1002/prop.2190380802
2. Atanasiu, Gh., Neagu, M., Canonical nonlinear connections in the multi-time Hamilton geometry, Balkan J. Geom. Appl., 14, 2, 2009, 1-12, (2009) Zbl1186.53038MR2539737
3. Christodoulou, D., Francaviglia, M., Tulczyjew, W. M., 10.1007/BF00757208, J. Gen. Relativ. Gravit., 10, 1979, 567-579, (1979) Zbl0448.58006MR0541653DOI10.1007/BF00757208
4. Chruściński, D., 10.1016/S0034-4877(98)80181-X, Rep. Math. Phys., 41, 1, 1998, 13-48, (1998) Zbl0932.70016MR1617898DOI10.1016/S0034-4877(98)80181-X
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, (1998) 
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.. (1991) MR1147643
7. Eells, J., Lemaire, L., 10.1112/blms/10.1.1, Bull. London Math. Soc., 10, 1978, 1-68, (1978) Zbl0401.58003MR0495450DOI10.1112/blms/10.1.1
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, (2002) MR1978795
9. Giachetta, G., Mangiarotti, L., Sardanashvily, G., Covariant Hamiltonian field theory, 1999, arXiv:hep-th/9904062v1. (1999) 
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]. (2004) MR1188431
11. Kanatchikov, I. V., 10.1063/1.57105, AIP Conf. Proc., 453, 1, 1998, 356-367, (1998) Zbl0982.81028MR1765516DOI10.1063/1.57105
12. Krupková, O., 10.1016/S0393-0440(01)00087-0, J. Geom. Phys., 43, 2002, 93-132, (2002) Zbl1016.37033MR1919207DOI10.1016/S0393-0440(01)00087-0
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, (2001) Zbl0980.35009MR1859298
14. Krupková, O., Saunders, D. J., 10.1142/S0219887811005336, Int. J. Geom. Methods Mod. Phys., 8, 3, 2011, 669-697, (2011) MR2807123DOI10.1142/S0219887811005336
15. Miron, R., Anastasiei, M., The Geometry of Lagrange Spaces: Theory and Applications, 1994, Kluwer Academic Publishers, Dordrecht, (1994) Zbl0831.53001MR1281613
16. Miron, R., Hrimiuc, D., Shimada, H., Sabău, S. V., The Geometry of Hamilton and Lagrange Spaces, Kluwer Academic Publishers, Dordrecht, 2001, (2001) Zbl1001.53053MR1839409
17. Neagu, M., Riemann-Lagrange Geometry on 1-Jet Spaces, 2005, Matrix Rom, Bucharest, (2005) 
18. Neagu, M., 10.1155/S0161171202011018, Int. J. Math. Math. Sci., 29, 1, 2002, 7-16, (2002) Zbl1011.53053MR1892327DOI10.1155/S0161171202011018
19. Neagu, M., Udrişte, C., Oană, A., Multi-time dependent sprays and $h$-traceless maps, Balkan J. Geom. Appl., 10, 2, 2005, 76-92, (2005) MR2235108
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 $J^{1*}(T,M)$, 2011, arXiv:1111.4173v1 [math.DG].. (2011) MR3032809
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]. (2012) MR3035882
22. Sachs, R. K., Wu, H., General Relativity for Mathematicians, 1977, Springer-Verlag, New York, Heidelberg, Berlin, (1977) Zbl0373.53001MR0503498
23. Saunders, D. J., The Geometry of Jet Bundles, 1989, Cambridge University Press, New York, London, (1989) Zbl0665.58002
24. Udrişte, C., Matei, L., Lagrange-Hamilton Theories (in Romanian), 2008, Geometry Balkan Press, Bucharest, (2008)