2020/09/07 by Zhiqiang Guo, Zhi-Qiang 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) #gr-qc #hep-ph #hep-th #physics.class-ph #quant-ph
paper · pdf · doi:10.48550/arxiv.2009.03200
version2: 30 pages, no figures; largely simplified formulations of critical equations; references added
openalex publication_date 2020/09/07 · arxiv created 2021/02/01 · arxiv updated 2021/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.