Legendre transformation for regularizable Lagrangians in field theory

Letters in Mathematical Physics

Volumn 58, Issue 3, 2001, Pages 189-204

  Krupková, Olga ^a   Smetanová, Dana ^a  

^a SILESIAN UNIVERSITY IN OPAVA   (Czech Republic)

Author keywords

Dirac field; Electromagnetic field; Hamilton p2 equations; Hamilton De Donder equations; Lagrangian; Legendre transformation; Lepagean form; Poincar Cartan form; Regularity; Regularizable Lagrangian

Indexed keywords

EID: 0037709861     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014548309187     Document Type: Article

References (19)

1. Betounes, D. E.: Extension of the classical Cartan form, Phys. Rev. D 29 (1984), 599-606.
2. Cantrijn, F., Ibort, L. A. and de León, M.: Hamiltonian structures on multisymplectic manifolds, Rend. Sem. Mat. Univ. Pol. Torino 54 (1996), 225-236.
3. Dedecker, P.: On the generalization of symplectic geometry to multiple integrals in the calculus of variations, In: Lecture Notes in Math. 570, Springer, Berlin, 1977, pp. 395-456.
4. De Donder, Th.: Théorie invariantive du calcul des variations, Gauthier-Villars, Paris, 1930.
5. Giachetta, G., Mangiarotti, L. and Sardanashvily, G.: New Lagrangian and Hamiltonian Methods in Field Theory, World Scientific, Singapore, 1997.
6. Giachetta, G., Mangiarotti, L. and Sardanashvily, G.: Covariant Hamilton equations for field theory, J. Phys. A: Math. Gen. 32 (1999), 6629-6642.
7. Goldschmidt, H. and Sternberg, S.: The Hamilton-Cartan formalism in the calculus of variations, Ann. Inst. Fourier. Grenoble 23 (1973), 203-267.
8. Gotay, M. J.: A multisymplectic framework for classical field theory and the calculus of variations, I. Covariant Hamiltonian formalism, In: M. Francaviglia and D. D. Holm (eds) Mechanics, Analysis and Geometry: 200 Years After Lagrange, North Holland, Amsterdam, 1990, pp. 203-235.
9. Krupka, D.: A geometric theory of ordinary first order variational problems in fibred manifolds, I. Critical sections, II. Invariance J. Math. Anal. Appl. 49 (1975), 180-206; 469-476.
10. Krupka, D.: A map associated to the Lepagean forms of the calculus of variations in fibred manifolds, Czech. Math. J. 27 (1977), 114-118.
11. Krupka, D.: On the higher order Hamilton theory in fibred spaces, In: D. Krupka (ed.) Geometrical Methods in Physics, Proc. Conf. Diffferential Geom. Appl., Mové Město na Moravě, 1983, J. E. Purkyně University, Brno, Czechoslovakia, 1984, pp. 167-183.
12. Krupka, D. and Štěpánková, O.: On the Hamilton form in second order calculus of variations, In: M. Modugno (ed.) Geometry and Physics, Proc. Int. Meeting, Florence, Italy, 1982, Pitagora Ed., Bologna, 1983, pp. 85-101.
13. Krupková, O.: Hamiltonian field theory revisited: A geometric approach to regularity, In: L. Kozma, P. T. Nagy and L. Tamássy (eds.) Steps in Differential Geometry, Proc. Colloq. Differential Geom., Debrecen, July 2000, University of Debrecen, Debrecen, 2001, pp. 187-207.
14. Krupková, O.: Hamiltonian field theory, J. Gconi. Phys., in print.
15. Krupková, O. and Smetanová, D.: On regularization of variational problems in first-order field theory. Rend. Circ. Mat. Palermo, Série II, Suppl. 66 (2001), 133-140.
16. de León, M. and Rodrigues, P. R.: Generalized Classical Mechanics and Field Theory, North-Holland, Amsterdam, 1985.
17. Marsden, J. E. and Shkoller, S.: Multisymplectic geometry, covariant Hamiltonians, and water waves, Math. Proc. Cambridge. Philos. Soc. 125 (1999), 553-575.
18. Saunders, D. J.: The regularity of variational problems, In: Contemp. Math. 132 Amer. Math. Soc., Providence, 1992, pp. 573-593.
19. 2-equations in second order field theory, In: L. Kozma, P. T. Nagy and L. Tamássy (eds) Steps in Differential Geometry, Proc. Colloq. Differential Geom., Debrecen, July 2000, University of Debrecen, Debrecen, 2001, pp. 329-341.