scholarly journals Equation of motion of canonical tensor model and Hamilton-Jacobi equation of general relativity

2017 ◽  
Vol 95 (6) ◽  
Author(s):  
Hua Chen ◽  
Naoki Sasakura ◽  
Yuki Sato
Keyword(s):  
General Relativity ◽  
Jacobi Equation ◽  
Equation Of Motion ◽  
Tensor Model ◽  
Hamilton Jacobi Equation

Coherent states, Schrödinger equation, and the Hamilton–Jacobi equation

1995 ◽  
Vol 73 (7-8) ◽  
pp. 478-483
Author(s):  
Rachad M. Shoucri
Keyword(s):  
Schrödinger Equation ◽  
Jacobi Equation ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Hidden Variables ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Phase Variable ◽  
Independent Variable ◽  
Hamilton Jacobi Equation

The self-adjoint form of the classical equation of motion of the harmonic oscillator is used to derive a Hamiltonian-like equation and the Schrödinger equation in quantum mechanics. A phase variable ϕ(t) instead of time t is used as an independent variable. It is shown that the Hamilton–Jacobi solution in this case is identical with the solution obtained from the Schrödinger equation without the need to introduce the idea of hidden variables or quantum potential.

scholarly journals Solving the Hamilton-Jacobi equation for general relativity

1994 ◽  
Vol 49 (6) ◽  
pp. 2872-2881 ◽  
Author(s):  
J. Parry ◽  
D. S. Salopek ◽  
J. M. Stewart
Keyword(s):  
General Relativity ◽  
Jacobi Equation ◽  
Hamilton Jacobi Equation

scholarly journals Dynamic Path in C4 Space-Time

2018 ◽  
Author(s):  
Dimitris Mastoridis ◽  
K. Kalogirou
Keyword(s):  
General Relativity ◽  
Dispersion Relation ◽  
Jacobi Equation ◽  
Space Time ◽  
Complex Time ◽  
Dynamic Path ◽  
Hamilton Jacobi Equation

After developed the formulation of a "general relativity" in C4 [2], we proceed with the formulation of a Hamilton-Jacobi equation in C4. We argue that in this consideration, the usual problems of the ADM formalism, do not exist, due to the complex time as it exists in our consideration. Specically, we can derive a suitable dispersion relation in order to work with and nd a generalised super Hamiltonian

Semiclassical quantization of non-Hermitian multidimensional systems using Hamilton–Jacobi equation

2007 ◽  
Vol 85 (12) ◽  
pp. 1481-1490 ◽  
Author(s):  
A Nanayakkara
Keyword(s):  
Jacobi Equation ◽  
Good Accuracy ◽  
Equation Of Motion ◽  
Multidimensional Systems ◽  
Semiclassical Quantization ◽  
Classical Trajectories ◽  
Action Variables ◽  
Hamilton Jacobi Equation

The Hamilton–Jacobi equation of motion is solved in action variables for non-Hermitian systems. Both real and complex semiclassical eigenvalues are obtained that make action variables into integers. This study shows, regardless of the existence of periodic or quasi-periodic classical trajectories, Hamilton–Jacobi methods can be applied to quantize some complex non-Hermitian systems with a good accuracy. PACS Nos.: 23.23.+x, 56.65.Dy

The Hamilton-Jacobi Equation for a Charged Particle in a Combined Gravitational and Electromagnetic Field

1963 ◽  
Vol 6 (3) ◽  
pp. 351-358
Author(s):  
D. K. Sen
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Jacobi Equation ◽  
Jacobi Form ◽  
Equation Of Motion ◽  
Planetary Motion ◽  
Schwarzschild Metric ◽  
Special Case ◽  
Hamilton Jacobi Equation

The equation of motion of a charged particle in a combined gravitational and electromagnetic field is cast in the classical Hamilton-Jacobi form and then applied to the special case of a Schwarzschild metric, leading to the well established equation of planetary motion.

scholarly journals Kerr–Sen–Taub–NUT spacetime and circular geodesics

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Haryanto M. Siahaan
Keyword(s):  
String Theory ◽  
Equatorial Plane ◽  
Jacobi Equation ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Test Body ◽  
Low Energy ◽  
Energy Limit ◽  
Heterotic String Theory ◽  
Hamilton Jacobi Equation

AbstractWe present a solution obeying classical equation of motion in the low energy limit of heterotic string theory. The solution represents a rotating mass with electric charge and gravitomagnetic monopole moment. The corresponding conserved charges are discussed, and the separability of Hamilton–Jacobi equation for a test body in the spacetime is also investigated. Some numerical results related to the circular motions on equatorial plane are presented, but there is none that supports the existence of such geodesics.

General relativity via complete integrals of the Hamilton–Jacobi equation

2005 ◽  
Vol 46 (3) ◽  
pp. 032502 ◽  
Author(s):  
Enrique Montiel-Piña ◽  
Ezra Ted Newman ◽  
Gilberto Silva-Ortigoza
Keyword(s):  
General Relativity ◽  
Jacobi Equation ◽  
Hamilton Jacobi Equation

On the Hamiltonian and Hamilton–Jacobi equations for metric gravity

2020 ◽  
Vol 98 (4) ◽  
pp. 405-412
Author(s):  
Alexei M. Frolov
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Closed System ◽  
Jacobi Equation ◽  
Hamiltonian Equations ◽  
Jacobi Equations ◽  
Hamilton Jacobi Equation

The closed system of Hamiltonian equations is derived for all tensor components of a free gravitational field gαβ and corresponding momenta πγδ in metric general relativity. The Hamilton–Jacobi equation for a free gravitational field gαβ is also derived and discussed. In general, all methods and procedures based on the Hamiltonian and Hamilton–Jacobi approaches are very effective in actual applications to many problems known in metric general relativity.

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

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