Hamilton-Jacobi Diffieties

Abstract

Diffieties formalize geometrically the concept of differential equations. We introduce and study Hamilton-Jacobi diffieties. They are finite dimensional subdiffieties of a given diffiety and appear to play a special role in the field theoretic version of the geometric Hamilton-Jacobi theory.

31 pages, to appear in Journal of Geometry and Physics, slight changes in the presentation to match the version accepted by the journal

References in corpus (9)

• Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
• Geometric Hamilton-Jacobi Theory
• Geometric Hamilton-Jacobi Theory for Nonholonomic Dynamical Systems
• The Lagrangian-Hamiltonian Formalism for Higher Order Field Theories
• A Geometric Hamilton-Jacobi Theory for Classical Field Theories
• Secondary Calculus and the Covariant Phase Space
• The Hamilton-Jacobi Formalism for Higher Order Field Theories
• Partial Differential Hamiltonian Systems
• Hamilton-Jacobi theory and the evolution operator

Cited by in corpus (10)

• Geometric Hamilton-Jacobi theory for higher-order autonomous systems
• Characteristics, Bicharacteristics, and Geometric Singularities of Solutions of PDEs
• Complex Path Integrals and the Space of Theories
• Geometric Hamilton-Jacobi Field Theory
• Structural aspects of Hamilton-Jacobi theory
• Hamilton-Jacobi theory in multisymplectic classical field theories
• A Hamilton-Jacobi formalism for higher order implicit systems
• An overview of the Hamilton--Jacobi theory: the classical and geometrical approaches and some extensions and applications
• On Koszul-Tate resolutions and Sullivan models
• Classical and relativistic fluids as intermediate integrals of finite dimensional mechanical systems