Parallel Transport and Thomas-Wigner Rotation

2009 ◽  
Vol 116 (5) ◽  
pp. 439-446
Author(s):  
Nieves Alamo ◽  
Carlos Criado
2009 ◽  
Vol 116 (5) ◽  
pp. 439-446
Author(s):  
Nieves Alamo ◽  
Carlos Criado

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser

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.


1987 ◽  
Vol 95 ◽  
Author(s):  
J. P. Conde ◽  
S. Aljishi ◽  
D. S. Shen ◽  
V. Chu ◽  
Z E. Smith ◽  
...  

AbstractWe study the dark conductivity σd, dark conductivity activation energy Ea and photoconductivity σph of a-Si:H,F/a-Si,Ge:H,F superlattices both perpendicular and parallel to the plane of the layers. In parallel transport, both the σph and σd are dominated by the alloy layer characteristics with the superposition of carrier confinement quantum effects. In perpendicular transport, the σd shows an interplay of quantum mechanical tunneling through the barriers and of classical thermal emission over the barrier layer and the σph is controlled by the decreasing absorption by the silicon barrier layer as the optical gap Eopt of the structure decreases.We also found that the multilayer structure allows to grow lower gap a-Si,Ge:H,F alloys than achievable under the same deposition conditions for bulk materials. This stabilizing effect allowed us to study low-gap superlattice structures and extract information about these very low gap (<1.2 eV) a- Si,Ge:H,F alloys.


2010 ◽  
Vol 08 (03) ◽  
pp. 517-528 ◽  
Author(s):  
M. A. JAFARIZADEH ◽  
M. MAHDIAN

This paper is concerned with the spin–momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin and momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not an observer-dependent quantity in the inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and have shown that entanglement decreases with respect to the increase in observer velocity. Finally, we argue that Wigner rotation is induced by Lorentz transformations and can be realized as a controlling operator.


2004 ◽  
Vol 19 (36) ◽  
pp. 2683-2695 ◽  
Author(s):  
A. M. DE M. CARVALHO ◽  
CLAUDIO FURTADO ◽  
FERNANDO MORAES

In this paper we discuss parallel transport of vectors and spinors around circular orbits in Schwarzschild–AdS spacetime. We study the global properties of this spacetime via loop variables or holonomy. A set of paths in this background is considered. We demonstrate that for some special radii there appears the so-called quantized band structure of holonomy invariance. This analysis is also extended to parallel transport of a spinor in this spacetime.


2010 ◽  
Vol 25 (07) ◽  
pp. 511-523
Author(s):  
JUN LIANG ◽  
YI-SHI DUAN

We study localization of various matter fields on a non-Z2-symmetric scalar thick brane in a pure geometric Weyl integrable manifold in which variations in the length of vectors during parallel transport are allowed and a geometric scalar field is involved in its formulation. It is shown that, for spin 0 scalar field, the massless zero mode can be normalized on the brane. Spin 1 vector field cannot be normalized on the brane. And there is no spinor field which can be trapped on the brane for the case of no Yukawa-type coupling. By introducing the appropriate Yukawa coupling, the left or right chiral fermionic zero mode can be localized on the brane.


1992 ◽  
Vol 46 (8) ◽  
pp. 5149-5153 ◽  
Author(s):  
F. Ciocci ◽  
G. Dattoli ◽  
C. Mari ◽  
A. Torre

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