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Malykin, G. B.

doi:10.1070/pu2006v049n08abeh005870

Cited by 42 publications

(31 citation statements)

References 203 publications

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“…As is known, the Thomas precession happens for a particle with spin, moving along a curved path (where the particle should be considered as a point-like, in order to exclude any relativistic effects emerging for extended bodies [20]), and the frequency of Thomas precession in the laboratory frame is defined by the expression (e.g., [6])…”

Section: Thomas Precession and Its Missed Featuresmentioning

confidence: 99%

The relativistic mechanism of the Thomas–Wigner rotation and Thomas precession

Kholmetskii¹,

Yarman²

2020

Eur. J. Phys.

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We consider the Thomas-Wigner rotation of coordinate systems under successive Lorentz transformations of inertial reference frames and disclose its physical mechanism on the basis of relativistic contraction of moving scale and relativity of simultaneity of events for different inertial observers. This result allows us to understand better the physical meaning of the Thomas precession and to indicate some of the missed points in the physical interpretation of this effect with two particular examples: the circular motion of a classical electron around a heavy nucleus and the motion of a classical electron along an open path, where its initial velocity and acceleration are mutually orthogonal to each other.

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Section: Thomas Precession and Its Missed Featuresmentioning

confidence: 99%

The relativistic mechanism of the Thomas–Wigner rotation and Thomas precession

Kholmetskii¹,

Yarman²

2020

Eur. J. Phys.

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“…There exists a controversy in the evaluation of Thomas precession effect beyond (v/c) 2 as discussed recently [72]. Here, we give relativistic treatment of Thomas precession.…”

Section: Appendix a Thomas Precessionmentioning

confidence: 97%

“…In Refs. [70][71][72][73], T is γ times smaller. The possible reason of the discrepancy might be the noncommutativity of relativistic composition of velocities.…”

Section: Appendix a Thomas Precessionmentioning

confidence: 98%

Decays, contact P-wave interactions and hyperfine structure in exotic atoms

Krivoruchenko

Faessler

2008

Nuclear Physics A

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Contact P -wave interactions connected to the Larmor interaction of a magnetic dipole and Thomas spin precession in the filed of an electric quadrupole are described and their implications for spectroscopy of exotic Ω − -atoms are studied. In order to evaluate the magnitude of the contact P -wave interactions as compared to the conventional long-range interactions and the sensitivity of spectroscopic data to the Ω − -hyperon quadrupole moment, we consider 2P states of Ω − atoms formed with light stable nuclei with spins I 1/2 and atomic numbers Z 10. The energy level splitting caused by the contact interactions is 2-5 orders of magnitude smaller than the conventional long-range interactions. Strong decay widths of pΩ − atoms due to reactions pΩ − → ΛΞ 0 and pΩ − → ΣΞ , induced by t-channel kaon exchanges, are calculated. Ω − atoms formed with the light nuclei have strong widths 5-6 orders of magnitude higher than splitting caused by the contact interactions. The low-L pattern in the energy spectra of intermediate-and high-Z Ω − atoms thus cannot be observed. The Ω − quadrupole moment can be measured by observing X-rays from circular transitions between high-L levels in Ω − exotic atoms. The effect of strong interactions in 208 PbΩ − atoms is negligible starting from L ∼ 10. The contact P -wave interactions exist in ordinary atoms and μ-meson atoms.

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“…One reason for being particularly interested in these issues is due to various attempts to simplify the discussion of the interplay between the Thomas rotation [17][18][19][20][21][22][23][24][25], the relativistic composition of 3-velocities [26][27][28][29][30], and the very closely related Wigner angle [31][32][33][34]. In an earlier article [34], the authors considered ordinary quaternions and found that it was useful to work with the relativistic half velocities w, defined by v = 2w/(1 + w 2 ) so that…”

Section: Introductionmentioning

confidence: 99%

Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Berry

Visser

2021

Physics

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In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

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Untitled

Cited by 42 publications

References 203 publications

The relativistic mechanism of the Thomas–Wigner rotation and Thomas precession

The relativistic mechanism of the Thomas–Wigner rotation and Thomas precession

Decays, contact P-wave interactions and hyperfine structure in exotic atoms

Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

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