Geometric Hamilton-Jacobi Field Theory

TL;DR

This paper proposes an extension of geometric Hamilton-Jacobi theory to higher derivative field theories within the framework of fiber bundles, aiming to deepen the geometric understanding of complex field dynamics.

Contribution

It introduces a novel geometric framework for higher derivative field theories based on Hamilton-Jacobi theory, expanding its applicability to more complex physical models.

Findings

Extended Hamilton-Jacobi theory to higher derivatives

Provided a geometric formulation on fiber bundles

Potential applications in advanced field theories

Abstract

I briefly review my proposal about how to extend the geometric Hamilton-Jacobi theory to higher derivative field theories on fiber bundles.