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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