Novel formulation of Hamilton-Jacobi equation for higher derivative theory and quantum mechanical correspondence

• URL: http://arxiv.org/abs/2009.03200v2
• Date: Mon, 1 Feb 2021 11:15:30 GMT
• Title: Novel formulation of Hamilton-Jacobi equation for higher derivative theory and quantum mechanical correspondence
• Authors: Zhi-Qiang Guo
• Abstract summary: We show that there exist novel formulations of Hamilton-Jacobi equations. The quantum mechanical correspondences of these novel Hamilton-Jacobi equations lead to nonlinear quantum mechanics.
• Score: 2.6778110563115542
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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