Multivector field formulation of Hamiltonian field theories: Equations and symmetries

Journal of Physics A: Mathematical and General

Volumn 32, Issue 48, 1999, Pages 8461-8484

  Echeverria Enriquez A ^a   Munoz Lecanda M C ^a   Roman Roy N ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038931344     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/32/48/309     Document Type: Article

References (36)

1. Awane A 1992 k-symplectic structures J. Math. Phys. 32 4046-52
2. Binz E, Sniatycki J and Fisher H 1988 The Geometry of Classical Fields (Amsterdam: North-Holland)
3. Cantrijn F, Ibort L A and de León M 1996 Hamiltonian structures on multisymplectic manifolds Rnd. Sem. Math. Univ. Pol. Torino 54 225-36
4. Cantrijn F, Ibort L A and de León M 1999 On the geometry of multisymplectic manifolds Aust. Math. Soc. Ser. 66 303-30
5. Cariñena J F, Crampin M and Ibort LA 1991 On the multisymplectic formalism for first order field theories Diff. Geom. Appl. 1 345-74
6. Dieudonne J 1974 Elements d'Analyse vol IV (Paris: Gauthier-Villars)
7. Echeverría-Enríquez A and Muñoz-Lecanda M C 1992 Variational calculus in several variables: a Hamiltonian approach Ann. Inst. Henri Poincaré 56 27-47
8. Echeverría-Enríquez A, Muñoz-Lecanda M C and Román-Roy N 1996 Geometry of Lagrangian first-order classical field theories Fortschr. Phys. 44 235-80
9. Echeverría-Enríquez A, Muñoz-Lecanda M C and Román-Roy N 1998 Multivector fields and connections setting lagrangian equations for field theories J. Math. Phys. 39 4578-603
10. Echeverría-Enríquez A, Muñoz-Lecanda M C and Román-Roy N 1999 On the multimomentum bundles and the legendre maps in field theories Preprint math-ph/9904007 (to be published in Rep. Math. Phys.)
11. Echeverría-Enríquez A, Muñoz-Lecanda M C and Román-Roy N 1999 Geometry of multisymplectic Hamiltonian first-order field theories Preprint DMAT-UPC
12. García P L 1974 The Poincaré-Cartan invariant in the calculus of variations Symp. Math. Convegno di Geometria Simplettica e Fisica Matematica (INDAM) (Rome, 1973) vol 14 (London: Academic) pp 219-46
13. Giachetta G, Mangiarotti L and Sardanashvily G 1997 New Lagrangian and Hamiltonian Methods in Field Theory (Singapore: World Scientific)
14. Goldschmidt H and Sternberg S 1973 The Hamilton-Cartan formalism in the calculus of variations Ann. Inst. Fourier Grenoble 23 203-67
15. Gotay M J, Isenberg J, Marsden J E, Montgomery R, Śniatycki J and Yasskin P B 1997 Momentum maps and classical relativistic fields I: covariant theory GIMMSY Preprint phisics/9805040
16. Günther C 1987 The polysymplectic Hamiltonian formalism in the field theory and the calculus of variations I: the local case J. Diff. Geom. 25 23-53
17. Hrabak S P 1999 On a multisymplectic formulation of the classical BRST symmetry for first-order field theories (Part I): algebraic structures Preprint math-ph/9901012
18. Hrabak S P 1999 On a multisymplectic formulation of the classical BRST symmetry for first-order field theories (Part II): geometric structures Preprint math-ph/9901013
19. Ibort L A, Echeverría-Enríquez A, Muñoz-Lecanda M C and Román-Roy N 1998 Invariant forms and automorphisms of multisymplectic manifolds Preprint math-dg/9805040
20. Kanatchikov I 1993 On the canonical structure of the De Donder-Weyl covariant Hamiltonian formulation of field theory I. Graded Poisson brackets and equations of motion Preprint PITHA 93/41, hep-th/9312162
21. Kanatchikov I 1995 From the Poincaré-Cartan form to a Gerstenhaber algebra of the Poisson brackets in field theory Proc. 13th Int. Workshop on Geometric Methods in Physics (New York: Plenum)
22. Kanatchikov I V 1997 On field theoretic generalizations of a Poisson algebra Rep. Math. Phys. 40 225
23. Kanatchikov I V 1998 Canonical structure of classical field theory in the polymomentum phase space Rep. Math. Phys. 41 49-90
24. Kijowski J and Tulczyjew W M 1979 A Symplectic Framework for Field Theories (Lecture Notes in Physics vol 170) (Berlin: Springer)
25. de León M, Marín-Solano J and Marrero J C 1995 Ehresmann connections in classical field theories Proc. 3rd Fall Workshop: Differential Geometry and its Applications (Anales de Física, Monografías vol 2) pp 73-89
26. de León M, Marín-Solano J and Marrero J C 1996 A geometrical approach to classical field theories: a constraint algorithm for singular theories Proc. on New Developments in Differential Geometry ed L Tamassi and J Szenthe (Dordrecht: Kluwer) pp 291-312
27. de León M and Martín de Diego D 1996 Symmetries and constant of the motion for singular Lagrangian systems Int. J. Theor. Phys. 35 975-1011
28. de León M, Merino E, Oubiña J A, Rodrigues P R and Salgado M 1998 Hamiltonian systems on k-cosymplectic manifolds J. Math. Phys. 39 876-93
29. López C, Martínez E and Ranada M F 1999 Dynamical symmetries, non-Cartan symmetries and superintegrability of the n-dimensional harmonic oscillator J. Phys. A: Math. Gen. 32 1241-9
30. Marsden J E and Shkoller S 1999 Multisymplectic geometry, covariant Hamiltonians and water waves Math. Proc. Camb. Phil. Soc. 125 553-75
31. Puta M 1988 Some remarks on the k-symplectic manifolds Tensor N. S. 47 109-15
32. Rañada M F 1995 Integrable three particle systems, hidden symmetries and deformations of the Calogero-Moser system J. Math. Phys. 36 3541-3558
33. Rañada M F 1995 Superintegrable n = 2 systems, quadratic constants of motion, and potential of Drach J. Math. Phys. 38 4165-78
34. Sardanashvily G 1995 Generalized Hamiltonian Formalism for Field Theory. Constraint Systems (Singapore: World Scientific)
35. Sarlet W and Cantrijn F 1981 Higher-order Noether symmetries and constants of the motion J. Phys. A: Math. Gen. 14 479-92
36. Saunders D J 1989 The Geometry of Jet Bundles (London Math. Soc. Lecture Notes Series vol 142) (Cambridge: Cambridge University Press)