The deparametrization problem for parameter-invariant Lagrangian densities
defined over J(1)(N, F), is solved in terms of a projection onto a suitable
jet bundle. The Hamilton-Cartan formalism for such Lagrangians is then int
roduced and the pre-symplectic structure of such Variational problems is pr
oved to be project able through the aforementioned projection. Specific exa
mples with physical meaning are also analyzed.
1998 PACS codes. 02.20.Tw Infinite-dimensional Lie groups, 02.30.Wd Calculu
s of variations and optimal control, 02.40.Ky Riemannian,geometries, 02.40.
Ma Global differential geometry, 02.40.Vh Global analysis and analysis on m
anifolds, 04.20.Fy Canonical formalism, Lagrangians, and variational princi
ples, 11.10.Ef Lagrangian and Hamiltonian approach, 11.10.Kk Field theories
in dimensions other than four, 11.25.Sq Nonperturbative techniques; string
field theory.
1991 Mathematics Subject Classification. Primary: 58E30 Variational princip
les; Secondary: 53B20 Local Riemannian geometry, 58A20 Jets, 58E12 Applicat
ions to minimal surfaces (problems in two independent variables), 58G35 Inv
ariance and symmetry properties, 81S10 Geometric quantization, symplectic m
ethods, 83E30 String and superstring theories.