The geometrization of quantum mechanics, the nonlinear Klein-Gordon equation, Finsler gravity and phase spaces

DOI10.1016/j.geomphys.2020.104068zbMath1461.81026OpenAlexW3118761376MaRDI QIDQ2662731

Carlos Castro Perelman

Publication date: 14 April 2021

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2020.104068

zbMATH Keywords

nonlinear wave equationquantum mechanicsgravitationFinsler geometryMoyal star products

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Gravitational interaction in quantum theory (81V17) NLS equations (nonlinear Schrödinger equations) (35Q55) Geometry and quantization, symplectic methods (81S10) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Covariant wave equations in quantum theory, relativistic quantum mechanics (81R20) Noncommutative geometry in quantum theory (81R60) Deformation quantization, star products (53D55) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40) Alternative quantum mechanics (including hidden variables, etc.) (81Q65)

Related Items (1)

Geometric phase of quantum wave function and singularities of Bohm dynamics in a one-dimensional system

Cites Work

• Unnamed Item
• Unnamed Item
• Novel remarks on point mass sources, firewalls, null singularities and gravitational entropy
• Bohmian trajectories and quantum phase space distributions
• On the geometrization of quantum mechanics
• Cayley graphs and complexity geometry
• Born's reciprocal relativity theory, curved phase space, Finsler geometry and the cosmological constant
• The transition of energy and bound states in the continuum of fractional Schrödinger equation in gravitational field and the effect of the minimal length
• Can Bohmian mechanics be made relativistic?
• MAKING NONLOCAL REALITY COMPATIBLE WITH RELATIVITY
• Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle
• The Schrödinger–Newton equation and its foundations
• The Schrödinger–Newton equation as a non-relativistic limit of self-gravitating Klein–Gordon and Dirac fields
• Regular black holes from semi-classical down to Planckian size

This page was built for publication: The geometrization of quantum mechanics, the nonlinear Klein-Gordon equation, Finsler gravity and phase spaces