TL;DR
This paper introduces Hamilton-Jacobi diffieties, a new geometric structure that captures the essence of differential equations and their role in the geometric Hamilton-Jacobi theory, especially in field theory.
Contribution
It defines and studies Hamilton-Jacobi diffieties as finite dimensional subdiffieties, highlighting their significance in the geometric formulation of Hamilton-Jacobi theory for field systems.
Findings
Hamilton-Jacobi diffieties are finite dimensional substructures within diffieties.
They play a key role in the geometric Hamilton-Jacobi theory for field theories.
The paper provides a formal framework for these diffieties and explores their properties.
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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Advanced Differential Equations and Dynamical Systems