Parameter invariance in field theory and the Hamiltonian formalism.

Abstract

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 introduced and the pre-symplectic structure of such Variational problems is proved to be project able through the aforementioned projection. Specific examples with physical meaning are also analyzed. 1998 PACS codes. 02.20.Tw Infinite-dimensional Lie groups, 02.30.Wd Calculus of variations and optimal control, 02.40.Ky Riemannian,geometries, 02.40.Ma Global differential geometry, 02.40.Vh Global analysis and analysis on manifolds, 04.20.Fy Canonical formalism, Lagrangians, and variational principles, 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 principles; Secondary: 53B20 Local Riemannian geometry, 58A20 Jets, 58E12 Applications to minimal surfaces (problems in two independent variables), 58G35 Invariance and symmetry properties, 81S10 Geometric quantization, symplectic methods, 83E30 String and superstring theories.