Jacobi–Maupertuis metric and Kepler equation

Chanda, Sumanto; Gibbons, G. W.; Guha, Partha

doi:10.1142/s0219887817300021

Cited by 18 publications

(19 citation statements)

References 37 publications

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“…The inclusion of an interaction into the geometry of phase-space and the resulting noncommutative geometry is under intensive investigation in various models [55,95,[97][98][99][100][101][102][103][104][105][106][107][108][109][110][111][112][113][114][115].…”

Section: Parametrization Of Physical Time and Physical Hamiltonian Ementioning

confidence: 99%

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Дериглазов

Ramírez

2017

Advances in Mathematical Physics

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We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic fields. The formalism is developed starting from the Lagrangian variational problem, which implies both equations of motion and constraints which should be presented in a model of spinning particle. We present a detailed analysis of the resulting theory and show that it has reasonable properties on both classical and quantum level. We describe a number of applications and show how the vector model clarifies some issues presented in theoretical description of a relativistic spin: (A) one-particle relativistic quantum mechanics with positive energies and its relation with the Dirac equation and with relativistic Zitterbewegung; (B) spin-induced noncommutativity and the problem of covariant formalism; (C) three-dimensional acceleration consistent with coordinate-independence of the speed of light in general relativity and rainbow geometry seen by spinning particle; (D) paradoxical behavior of the Mathisson-PapapetrouTulczyjew-Dixon equations of a rotating body in ultrarelativistic limit, and equations with improved behavior.

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Section: Parametrization Of Physical Time and Physical Hamiltonian Ementioning

confidence: 99%

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Дериглазов

Ramírez

2017

Advances in Mathematical Physics

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“…We thank ProfessorsÁngel Ballesteros and Alexei A. Deriglazov for their correspondence and advice, which were invauable in developing this article, and Prof. Gary Gibbons furthermore for his collaboration in [11,12] and encouragement. Furthermore, we also wish to express special gratitude to the anonymous referee whose valuable advice and questions helped improve and expand the content of this manuscript.…”

Section: Acknowledgementmentioning

confidence: 99%

Geometrical formulation of relativistic mechanics

Chanda

Guha

2018

Int. J. Geom. Methods Mod. Phys.

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The relativistic Lagrangian in presence of potentials was formulated directly from the metric, with the classical Lagrangian shown embedded within it. Using it we formulated covariant equations of motion, a deformed Euler-Lagrange equation, and relativistic Hamiltonian mechanics. We also formulate a modified local Lorentz transformation, such that the metric at a point is invariant only under the transformation defined at that point, and derive the formulae for time-dilation, length contraction, and gravitational redshift. Then we compare our formulation under non-relativistic approximations to the conventional ad-hoc formulation, and we briefly analyze the relativistic Liénard oscillator and the spacetime it implies.

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“…which is the Hamiltonian to be used in the next section. It should be noted that Bohlin transformation is a canonical transformation [57].…”

Section: Two-dimensional Hydrogen Atom In An External Magnetic Fmentioning

confidence: 99%

Zeeman Effect in Phase Space

Paiva

Amorim

Ulhoa

et al. 2020

Advances in High Energy Physics

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The two-dimensional hydrogen atom in an external magnetic field is considered in the context of phase space. Using solution of the Schrödinger equation in phase space the Wigner function related to the Zeeman effect is calculated. For this purpose, the Bohlin mapping is used to transform the Coulomb potential into a harmonic oscillator problem. Then it is possible to solve the Schrödinger equation easier by using the perturbation theory. The negativity parameter for this system is realised.

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Jacobi–Maupertuis metric and Kepler equation

Cited by 18 publications

References 37 publications

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Geometrical formulation of relativistic mechanics

Zeeman Effect in Phase Space

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