Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics and Spectroscopy

A Method of É. Borel for calculation of the Thomas precession: The geometric phase in relativistic kinematic velocity space and its applications in optics

Grigorii B. Malykin

Published Feb 1, 2013• 0 citations
Publisher

Abstract

In 1913, É. Borel (1871–1956) considered the relativistic kinematic rotation of a body that arises in the course of its orbital motion. In order to determine the angular velocity of this rotation, Borel introduced the notion of a kinematic space and applied the Gauss-Bonnet formula for a sphere of a unit radius. However, at that time, his results did not find practical applications and, soon, were forgotten. After the discovery of electron spin by S.A. Goudsmit and G.E. Uhlenbeck in 1925, real interest in this phenomenon was rekindled, and it was considered once again by L.H. Thomas in 1926–1927, being termed the Thomas precession. The Thomas precession manifests itself mostly in optical phenomena.

DOI
10.1134/s0030400x13020197

Related papers

Spin-orbital motion and Thomas precession in the classical and quantum theories

The motion of a magnetic spin particle in electromagnetic fields is considered on the basis of general principles of the classical relativistic theory. Alternative approaches in derivation of the equations of charge motion and spin precession, the problem of noncollinearity of the momentum and velocity of a particle with spin, the origin and the meaning of Thomas precession in dynamics of the spin particle are also considered. The correspondence principle in the spin theory is discussed. 1

•Jan 1, 2001•0 citations

Thomas precession, spin-orbit interaction, and Berry’s phase

Harsh Mathur

The spin-orbit interaction is shown to arise as a Berry phase term in the adiabatic effective Hamiltonian for the orbital motion of a Dirac electron. This approach makes explicit the intimate connection of the spin-orbit interaction and Thomas precession.

Physical Review Letters•Dec 9, 1991•87 citations

Nonlinear effects in Thomas precession due to the interplay of Lorentz contraction and Thomas–Wigner rotation

Antonio Di Lorenzo

It is demonstrated that the 3-vector [Formula: see text] currently associated to the spin in an inertial frame does not contract, but rather dilates, in the direction of the velocity. The correct vector [Formula: see text] is individuated. The equation of motion for the two vectors is shown to contain two terms, a common linear rotation, identified with Thomas precession, and also a nonlinear rotation depending on the direction of the spin itself.

arXiv:2210.10635•Scientific Reports•Oct 6, 2022•0 citations

On the difference between Wigner's and Møller's approaches to the description of Thomas precession

V. I. Ritus

An account is given of the Wigner concept of particle spin and velocity rotations and of the variation of the angle between them under Lorentz transformations with noncollinear velocities. It is shown that Moller's description of spin rotation can be reduced to the Wigner rotation, and Moller's formula for the angle of spin rotation in the curvilinear motion of a particle is corrected. The permutation asymmetry of the relativistic velocity addition law distinguishes the Wigner sequence of Lorentzian boosts by its applicability to the description of spin and velocity rotations in curvilinear motion.

Physics-Uspekhi•Jan 31, 2007•23 citations

SPIN-ORBITAL MOTION AND THOMAS PRECESSION IN THE CLASSICAL AND QUANTUM THEORIES

Vladimir A Bordovitsyn, A. N. Myagkii

The motion of a magnetic spin particle in electromagnetic fields is considered on the basis of general principles of the classical relativistic theory. Alternative approaches in derivation of the equations of charge motion and spin precession, the problem of noncollinearity of the momentum and velocity of a particle with spin, the origin and the meaning of Thomas precession in dynamics of the spin particle are also considered. The correspondence principle in the spin theory is discussed.

arXiv:quant-ph/0102107•Lomonosov Conference on Elementary Particle Physics•May 1, 2001•0 citations

Thomas Precession

Abraham Albert Ungar

Thomas precession is a physical effect predicted by Einstein’s theory of special relativity [97, 108, 109, 110], and is related to the so-called mixed state geometric phase of quantum mechanics [69]. It possesses angular velocity, given by the vector equation (13.58), p. 577, which is written as a gyrovector equation in (13.59).

CRC Press eBooks•Dec 17, 2014•0 citations
In 1913, É. Borel (1871–1956) considered the relativistic kinematic rotation of a body that arises in the course of its orbital motion. In order to determine the angular velocity of this rotation, Borel introduced the notion of a kinematic space and applied the Gauss-Bonnet formula for a sphere of a unit radius. However, at that time, his results did not find practical applications and, soon, were forgotten. After the discovery of electron spin by S.A. Goudsmit and G.E. Uhlenbeck in 1925, real interest in this phenomenon was rekindled, and it was considered once again by L.H. Thomas in 1926–1927, being termed the Thomas precession. The Thomas precession manifests itself mostly in optical phenomena.
An account is given of the Wigner concept of particle spin and velocity rotations and of the variation of the angle between them under Lorentz transformations with noncollinear velocities. It is shown that Moller's description of spin rotation can be reduced to the Wigner rotation, and Moller's formula for the angle of spin rotation in the curvilinear motion of a particle is corrected. The permutation asymmetry of the relativistic velocity addition law distinguishes the Wigner sequence of Lorentzian boosts by its applicability to the description of spin and velocity rotations in curvilinear motion.