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

2020/09/07 by Zhiqiang Guo, Guo, Zhi-Qiang
Computer Science · Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2009.03200

openalex publication_date 2020/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• STABLE SELF-INTERACTING PAIS–UHLENBECK OSCILLATOR
• Generalized Hamiltonian Dynamics
• Test of the linearity of quantum mechanics by rf spectroscopy of theBe+<mml:mprescripts/>9ground state
• Testing quantum mechanics
• On Gravity's role in Quantum State Reduction

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