2002/08/26 by Manuel de León, Michael A. McLean, de León, Manuel +9
Mathematics · Physics and Astronomy · #53D05 #70S05 #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG) #math-ph #math.MP #math.SG #msc:53D05 #msc:70S05
paper · pdf · doi:10.48550/arxiv.math-ph/0208036
arxiv created 2002/08/26 · openalex publication_date 2002/08/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This review paper is concerned with the generalizations to field theory of the tangent and cotangent structures and bundles that play fundamental roles in the Lagrangian and Hamiltonian formulations of classical mechanics. The paper reviews, compares and constrasts the various generalizations in order to bring some unity to the field of study. The generalizations seem to fall into two categories. In one direction some have generalized the geometric structures of the bundles, arriving at the various axiomatic systems such as k-symplectic and k-tangent structures. The other direction was to fundamentally extend the bundles themselves and to then explore the natural geometry of the extensions. This latter direction gives us the multisymplectic geometry on jet and cojet bundles and n-symplectic geometry on frame bundles.