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Parameter invariance in field theory and the Hamiltonian formalism. (English) Zbl 0955.58014

Summary: 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 projectable through the aforementioned projection. Specific examples with physical meaning are also analyzed.

MSC:

58E30 Variational principles in infinite-dimensional spaces
81S10 Geometry and quantization, symplectic methods
81T99 Quantum field theory; related classical field theories
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
58E12 Variational problems concerning minimal surfaces (problems in two independent variables)
58A20 Jets in global analysis
53D50 Geometric quantization
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