1998/01/15 by D. R. Grigore, Grigore, Dan Radu
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.math/9801073
openalex publication_date 1998/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present here a possible generalisation of the Poincaré-Cartan form in classical field theory in the most general case: arbitrary dimension, arbitrary order of the theory and in the absence of a fibre bundle structure. We use for the kinematical description of the system the (r,n)-Grassmann manifold associated to a given manifold X, i.e. the manifold of r-contact elements of n-dimensional submanifolds of X. The idea is to define globally a n+1 form on this Grassmann manifold, more precisely its class with respect to a certain subspace and to write it locally as the exterior derivative of a n form which is the Poincaré-Cartan form. As an important application we obtain a new proof for the most general expression of a variationally trivial Lagrangian.