Novel formulation of Hamilton-Jacobi equation for higher derivative theory and quantum mechanical correspondence
High Energy Physics - Theory
2021-02-02 v2 General Relativity and Quantum Cosmology
High Energy Physics - Phenomenology
Classical Physics
Quantum Physics
Abstract
For higher derivative theories, using the approach of Caratheodory's equivalent Lagrangian, we show that there exist novel formulations of Hamilton-Jacobi equations, which are different from the formulations derived from Hamilton's canonical approach. The quantum mechanical correspondences of these novel Hamilton-Jacobi equations lead to nonlinear quantum mechanics, which seem being able to avoid the unbounded negative energy problem in the quantum mechanics of higher derivative theories.
Keywords
Cite
@article{arxiv.2009.03200,
title = {Novel formulation of Hamilton-Jacobi equation for higher derivative theory and quantum mechanical correspondence},
author = {Zhi-Qiang Guo},
journal= {arXiv preprint arXiv:2009.03200},
year = {2021}
}
Comments
version2: 30 pages, no figures; largely simplified formulations of critical equations; references added