Noncommutative and Dynamical Analysis in a Curved Phase-space

Abreu, Éverton M. C.; Rizzuti, B. F.; Mendes, Albert C. R.; Freitas, M. A.; Nikoofard, Vahid

doi:10.5506/aphyspolb.46.879

Cited by 3 publications

(5 citation statements)

References 30 publications

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“…Using the Landau-Lifshitz (1 + 3) -decomposition [8] we observed that, unlike a geodesic equation, the MPTD equations lead to the expression for three-acceleration which contains divergent terms as v → c [9]. Fast test particles are now under intensive investigation [10][11][12][13][14], and represent an important tool in the study, for example, of near horizon geometry of black holes [15][16][17][18][19][20][21][22][23]. So, it would be interesting to find a generalization of MPTD equations with improved behavior in ultra relativistic regime.…”

Section: Introductionmentioning

confidence: 99%

Relativistic effects due to gravimagnetic moment of a rotating body

Ramírez

Дериглазов

2017

Phys. Rev. D

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We compute exact Hamiltonian (and corresponding Dirac brackets) for spinning particle with gravimagnetic moment κ in an arbitrary gravitational background. κ = 0 corresponds to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations. κ = 1 leads to modified MPTD equations with reasonable behavior in the ultrarelativistic limit. So we study the modified equations in the leading post-Newtonian approximation. Rotating body with unit gravimagnetic moment has qualitatively different behavior as compared with MPTD body: A) If a number of gyroscopes with various rotation axes are freely traveling together, the angles between the axes change with time. B) For specific binary systems, gravimagnetic moment gives a contribution to frame-dragging effect with the magnitude, that turns out to be comparable with that of Schiff frame dragging.

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Section: Introductionmentioning

confidence: 99%

Relativistic effects due to gravimagnetic moment of a rotating body

Ramírez

Дериглазов

2017

Phys. Rev. D

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“…Let us discuss the relationship between the structure group and local symmetries of the Hamiltonian action (98). The structure transformation (112) can be identified with the scale transformation (102).…”

Section: Advances In Mathematical Physicsmentioning

confidence: 99%

“…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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“…Here, g αβ = δ αβ + ωαω β a 2 −δ αβ ω a ω b are the metric components over a sphere [19] and this form of Lagrangian has the same very structure as the one presented in S 1 .…”

Section: Classical Spinning Particlementioning

confidence: 98%

“…Since we were working initially on the tangent bundle, we return to it asking that the momenta are functions of x i and ẋi . Thus, (19) reads…”

Section: S 1 : Geometric Point Of Viewmentioning

confidence: 99%

To square root the Lagrangian or not: an underlying geometrical analysis on classical and relativistic mechanical models

Rizzuti¹,

Júnior²,

A.³

2019

Preprint

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The geodesic has a fundamental role in physics and in mathematics: roughly speaking, it represents the curve that minimizes the arc length between two points on a manifold. We analyze a basic but misinterpreted difference between the Lagrangian that gives the arc length of a curve and the one that describes the motion of a free particle in curved space. Although they provide the same formal equations of motion, they are not equivalent. We explore this difference from a geometrical point of view, where we observe that the non-equivalence is nothing more than a matter of symmetry. As applications, some distinct models are studied. In particular, we explore the standard free relativistic particle, a couple of spinning particle models and also the forceless mechanics formulated by Hertz.

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Noncommutative and Dynamical Analysis in a Curved Phase-space

Cited by 3 publications

References 30 publications

Relativistic effects due to gravimagnetic moment of a rotating body

Relativistic effects due to gravimagnetic moment of a rotating body

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

To square root the Lagrangian or not: an underlying geometrical analysis on classical and relativistic mechanical models

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