Stress-energy-momentum tensors in higher order variational calculus

Journal of Geometry and Physics

Volumn 34, Issue 1, 2000, Pages 41-72

  Fernandez A ^a   Garcia P L ^a   Rodrigo, C ^a  

^a UNIVERSITY OF SALAMANCA   (Spain)

Author keywords

58E30; 76M30; 83C40; Classical field theory; Multimomentum maps; Natural Lagrangian densities; Poincar Cartan forms; Stress energy momentum tensors

Indexed keywords

EID: 0042640619     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(98)00063-1     Document Type: Article

References (30)

1. R.J. Alonso, D-modules, contact valued calculus and Poincaré-Cartan form, Cz. Math. J., to appear.
2. Belinfante F.J. On the current and the density of the electric charge, the energy, the linear momentum and the angular momentum of arbitrary fields. Physica. VII:1940;449-474.
3. Dedecker P. Calcul des variations et topologie algèbrique. Mem. Roy. Sci. Liège. 19:1957;1-216.
4. Epstein D., Thurston W. Transformation groups and natural bundles. Proc. London Math. Soc. 38(3):1957;219-236.
5. A. Fernández, Los Fluidos en Relatividad General como teoría de gauge, Tesis Doctoral, Universidad de Salamanca, 1996 (in Spanish).
6. M. Ferraris, Fibered connections and global Poincaré-Cartan forms in higher-order calculus of variations, in: D. Krupka (Ed.), Geom. Meth. Phys., J.E. Purkyně Univ., Brno Cz., 1984, pp. 61-91.
7. M. Ferraris, M. Francaviglia, On the local structure of Lagrangian and Hamiltonian formalisms in higher-order calculus of variations, Proceedings of the International Meeting on Geometry and Physics, Pitagora Editrice, Bologna, 1983, pp. 43-70.
8. García P.L. The Poincaré-Cartan invariant in the calculus of variations. Symposia Mathematica. 14:1974;219-246.
9. P.L. García, A. Fernández, The formalism of Morrison-Greene in relativistic hydrodynamics, Mem. de la Real Acad. de Ciencias Exactas, Físicas y Naturales, Madrid, to appear.
10. P.L. García, J. Muñoz, On the geometrical structure of higher order variational calculus, Proceedings of the IUTAM-ISIMM Symposium on Modern Developments in Analytical Mechanics, vol. I, Tecnoprint, Bologna, 1983, pp. 127-147.
11. P.L. García, A. Pérez-Rendón, Symplectic approach to the theory of quantized fields I, Commun. Math. Phys. 13 (1969) 101-124.
12. Goldschmidt H., Sternberg S. The Hamilton-Cartan formalism in the calculus of variations. Ann. Inst. Fourier. 23:1973;203-267.
13. Gotay M.J. An exterior differential systems approach to the Cartan form. Progr. Math. 99:1991;160-188.
14. Gotay M.J., Marsden J. stress-energy-momentum tensors and the Belinfante-Rosenfeld formula. Contemp. Math. 132:1992;367-392.
15. R. Hermann, Lectures in Mathematical Physics (I, II), Benjamin, New York, 1971.
16. Horák M., Kolář I. On the higher order Poincaré-Cartan forms. Cz. Math. J. 33:1983;467-475.
17. Kijowski J., Pawlik B., Tulczyjew W. A variational formulation of non-gravitating and gravitating hydrodynamics. Bull. Acad. Polonaise des Sciences. XXVII:1979;163-170.
18. Kolář I. A geometrical version of the higher order Hamilton formalism in fibered manifolds. J. Geom. Phys. 1:1984;127-137.
19. J.L. Koszul, Lectures on Fibre Bundles and Differential Geometry, Tata Institute of Fundamental Research, Bombay, 1963.
20. Krupka D. Geometry of Lagrangian structures. Supp. Rend. Circ. Mat. Palermo Ser. II. 14:1987;187-224.
21. T.H.J. Lepage, Sur les champs géodésiques du calcul des variations, I, II Bull. Acad. Roy. Belg., Classe des Sciences 22 (1936) 716-739, 1036-1046.
22. T.H.J. Lepage, Champs stationaires, champs géodésiques et formes intégrables, I, II Bull. Acad. Roy. Belg., Classe des Sciences 28 (1942) 73-92, 247-268.
23. M. Marvan, On global Lepagean equivalents, in: D. Krupka (Ed.), Geometrical Methods in Physics, J.E. Purkyně University, Brno Cz., 1984, pp. 185-190.
24. J. Muñoz, Formes de structure et transformations infinitésimales de contact d'ordre supérieur, C.R. Acad. Sci., Paris, 298, Série I, 8 (1984) 185-188.
25. Muñoz J. Poincaré-Cartan forms in higher order variational calculus on fibred manifolds. Revista Matemática Iberoamericana. 1(4):1985;85-126.
26. J. Muñoz, An axiomatic characterization of the Poincaré-Cartan form for second order variational problems, Lecture Notes in Mathematics, vol. 1139, Springer, Berlin, 1983, pp. 74-84.
27. A. Nijenhuis, Natural Bundles and their General Properties, Diff. Geom. in honour of K. Yano, Kinokuniyo, Tokyo, 1972, pp. 317-334.
28. Palais R., Terng C. Natural bundles have finite order. Topology. 16:1977;271-277.
29. Saunders D.J. An alternative approach to the Cartan form in Lagrangian field theories. J. Phys. 20:1987;339-349.
30. S. Sternberg, Some preliminary remarks on the formal variational calculus of Gel'fand and Dikkii, Lecture Notes in Mathematics, vol. 676, 1977, pp. 399-407.