相关论文: Thomas precession angle and spinor algebra
The Thomas precession is calculated using three different transformations to the rotating frame. It is shown that for sufficiently large values of $v/c$, important differences in the predicted angle of precession appear, depending on the…
Instantaneous derivation of the Thomas precession with only basic vector calculus.
Instantaneous derivation of the Thomas precession.
Using elementary geometric tools, we apply essentially the same methods to derive expressions for the rotation angle of the swing plane of Foucault's pendulum and the rotation angle of the spin of a relativistic particle moving in a…
The new derivation of the equation of the spin precession is given for a particle possessing electric and magnetic dipole moments. Contributions from classical electrodynamics and from the Thomas effect are explicitly separated. A fully…
Exact and simple calculation of Thomas rotation and Thomas precessions along a circular world line is presented in an absolute (coordinate-free) formulation of special relativity. Besides the simplicity of calculations the absolute…
We derive Macfarlane's formula for the Thomas-Wigner angle of rotation using Clifford-algebra methods. The presentation is pedagogical and elementary, suitable for students with some basic knowledge of special relativity; no prior knowledge…
It is demonstrated that the 3--vector $\bs{S}$ currently associated to the spin in an inertial frame does not contract, but rather dilates, in the direction of the velocity. The correct vector $\bs{T}$ is individuated. The equation of…
The problem of spin precession in a time-dependent magnetic field is considered in the adiabatic approximation where the field direction or the angular velocity of its rotation is changing slowly. The precession angles are given by…
We comment on some misunderstandings exhibited in a recent paper by Matolcsi et al. (Gen. Rel. Grav.39 413 (2007)).
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…
This is the first monograph on the geometry of anisotropic spinor spaces and its applications in modern physics. The main subjects are the theory of gravity and matter fields in spaces provided with off--diagonal metrics and associated…
See hep-ph/0304045
Rotation axis variation due to spin orbit resonance: conference report; keywords: planetary precession, rigid body, chaos, KAM, Arnold diffusion, averaging, celestial mechanics, classical mechanics, large deviations
We introduce a notion of planar algebra, the simplest example of which is a vector space of tensors, closed under planar contractions. A planar algebra with suitable positivity properties produces a finite index subfactor of a II_1 factor,…
In this short pedagogical presentation, we introduce the spin groups and the spinors from the point of view of group theory. We also present, independently, the construction of the low dimensional Clifford algebras. And we establish the…
See http://www.math.msu.edu/~abbas or Wiley preprint server.
Part I: The geometric algebra of space is derived by extending the real number system to include three mutually anticommuting square roots of plus one. The resulting geometric algebra is isomorphic to the algebra of complex 2x2 matrices,…
Rejoinder to ``Least angle regression'' by Efron et al. [math.ST/0406456]
The swing-twist decomposition is a standard routine in motion planning for humanoid limbs. In this paper the decomposition formulas are derived and discussed in terms of Clifford algebra. With the decomposition one can express an arbitrary…