Singular Lagrangians: Some geometric structures along the Legendre map

Journal of Physics A: Mathematical and General

Volumn 34, Issue 14, 2001, Pages 3047-3070

  Gràcia, Xavier ^a   Pons, Josep M ^b  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b UNIVERSITY OF BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035853647     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/34/14/311     Document Type: Article

References (47)

1. Anderson J L and Bergmann PG 1951 Constraints in covariant field theory Phys. Rev. 83 1018-25
2. Abraham R and Marsden J E 1978 Foundations of Mechanics 2nd edn (Reading, MA: Addison-Wesley)
3. Abraham R, J Marsden E and Ratiu T 1988 Manifolds, Tensor Analysis and Applications 2nd edn (New York: Springer)
4. Arnol'd VI 1989 Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics vol 60) 2nd edn (New York: Springer)
5. 2 model J. Math. Phys. 30 1345-50
6. Batlle C, Gomis J, J Pons M and Román-Roy N 1986 Equivalence between the Lagrangian and Hamiltonian formalism for constrained systems J. Math. Phys. 27 2953-62
7. Bergvelt M J and de Kerf E A 1986 The Hamiltonian structure of Yang-Mills theories and instantons I Physica A 139 101-24
8. Cariñena J F 1990 Theory of singular Lagrangians Fortschrit. Phys. 38 641-79
9. Cariñena J F and López C 1987 The time-evolution operator for singular Lagrangians Lett. Math. Phys. 14 203-10
10. Cariñena J F, López C and Martínez E 1989 A new approach to the converse of Noether's theorem J. Phys. A: Math. Gen. 22 4777-86
11. Cariñena J F, López C and Martínez E 1991 Sections along a map applied to higher-order Lagrangian mechanics Noether's theorem Acta Appl. Math. 25 127-51
12. Cariñena J F, López C and Román-Roy N 1988 Origin of the Lagrangian constraints and their relation with the Hamiltonian formulation J. Math. Phys. 29 1143-9
13. Dieudonné J 1970 Élements d'Analyse vol 3 (Paris: Gauthier-Villars)
14. Dirac PAM 1950 Generalized Hamiltonian dynamics Can. J. Math. 2 129-48
15. Dirac PAM 1964 Lectures on Quantum Mechanics (New York: Yeshiva University)
16. Dominici D, Longhi G, Gomis J and Pons J M 1984 Hamilton-Jacobi theory for constrained systems J. Math. Phys. 25 2439-52
17. Ferrario C and Passerini A 1990 Symmetries and constants of motion for constrained Lagrangian systems: a presymplectic version of the Noether theorem J. Phys. A: Math. Gen. 23 5061-81
18. Gotay M J and Nester J M 1979 Presymplectic Lagrangian systems I: the constraint algorithm and the equivalence theorem Ann. Inst. H Poincaré A 30 129-42
19. Gotay M J, Nester J M and Hinds G 1978 Presymplectic manifolds and the Dirac-Bergmann theory of constraints J. Math. Phys. 19 2388-99
20. Godbillon C 1969 Géometrie Différentielle et Mécanique Analytique (Paris: Hermann)
21. Gràcia X and Pons J M 1988 Gauge generators, Dirac's conjecture and degrees of freedom for constrained systems Ann. Phys., NY 187 355-68
22. Gràcia X and Pons J M 1989 On an evolution operator connecting Lagrangian and Hamiltonian formalisms Lett. Math. Phys. 17 175-80
23. Gràcia X and Pons J M 1992 A generalized geometric framework for constrained systems Diff. Geom. Appl. 2 223-47
24. Gràcia X and Pons J M 1992 A Hamiltonian approach to Lagrangian Noether transformations J. Phys. A: Math. Gen. 25 6357-69
25. Gràcia X and Pons J M 1994 Noether transformations with vanishing conserved quantity Ann. Inst. H Poincaré A 61 315-27
26. Gràcia X and Pons J M 1995 Gauge transformations for higher order Lagrangians J. Phys. A: Math. Gen. 28 7181-96
27. Gràcia X and Pons J M 2000 Canonical Noether symmetries and commutativity properties for gauge systems J. Math. Phys. 41 7333-51
28. (Gràcia X and Pons J M 2000 Preprint math-ph/0007037)
29. Gràcia X, J Pons M and Román-Roy N 1991 Higher-order Lagrangian systems: geometric structures, dynamics and constraints J. Math. Phys. 32 2744-63
30. Gràcia X and Roca J 1993 Covariant and noncovariant gauge transformations for the conformal particle Mod. Phys. Lett. A 8 1747-61
31. Gràcia X 2000 Fibre derivatives: some applications to singular Lagrangians Rep. Math. Phys. 45 67-84
32. (Gràcia X 2000 Preprint math-ph/0007038)
33. Goldschmidt H and Sternberg S 1973 The Hamilton-Cartan formalism in the calculus of variations Ann. Inst. Fourier 23 203-67
34. José J V and Saletan E J 1998 Classical Dynamics: a Contemporary Approach (Cambridge: Cambridge University Press)
35. Kolář I, Michor P W and Slovák J 1993 Natural Operations in Differential Geometry (Berlin: Springer)
36. Marmo G and Mukunda N 1986 Symmetries and constants of the motion in the Lagrangian formalism on TQ: beyond point transformations Nuovo Cimento B 92 1-12
37. Marmo G, Mukunda N and Samuel J 1983 Dynamics and symmetry for constrained systems: a geometrical analysis Riv. Nuovo Cimento 6 no 2
38. Muñoz M C and Román-Roy N 1992 Lagrangian theory for presymplectic systems Ann. Inst. H Poincaré A 57 27-45
39. Menzio M R and Tulczyjew W M 1978 Infinitesimal symplectic relations and generalized Hamiltonian dynamics Ann. Inst. H Poincaré A 28 349-67
40. Pons J M 1988 New relations between Hamiltonian and Lagrangian constraints J. Phys. A: Math. Gen. 21 2705-15
41. Pons J M, Salisbury D C and Shepley L C 1999 Reduced phase space: quotienting procedure for gauge theories J. Phys. A: Math. Gen. 32 419-30
42. (Pons J M, Salisbury D C and Shepley L C 1998 Preprint math-ph/9811029)
43. Pugliese F and Vinogradov A M 2000 On the geometry of singular Lagrangians J. Geom. Phys. 35 35-55
44. Saunders D J 1989 The Geometry of Jet Bundles (London Math. Soc. Lecture Note Series vol 142) (Cambridge: Cambridge University Press)
45. Siegel W 1988 Conformal invariance of extended spinning particle mechanics Int. J. Mod. Phys. A 3 2713-8
46. Tulczyjew W M 1975 Sur la différentielle de Lagrange C. R. Acad. Sci., Paris A 280 1295-8
47. Tulczyjew W M 1976 Les sous-varietés lagrangiennes et la dynamique Lagrangienne C. R. Acad. Sci., Paris A 283 675-8