Author:
Malhotra Lakshya,Golub Robert,Kraegeloh Eva,Nouri Nima,Plaster Bradley
Abstract
AbstractA relativistic particle undergoing successive boosts which are non collinear will experience a rotation of its coordinate axes with respect to the boosted frame. This rotation of coordinate axes is caused by a relativistic phenomenon called Thomas Rotation. We assess the importance of Thomas rotation in the calculation of physical quantities like electromagnetic fields in the relativistic regime. We calculate the electromagnetic field tensor for general three dimensional successive boosts in the particle’s rest frame as well as the laboratory frame. We then compare the electromagnetic field tensors obtained by a direct boost $$\overrightarrow{\beta }+\delta \overrightarrow{\beta }$$β→+δβ→ and successive boosts $$\overrightarrow{\beta }$$β→ and $$\Delta \overrightarrow{\beta }$$Δβ→ and check their consistency with Thomas rotation. This framework might be important to situations such as the calculation of frequency shifts for relativistic spin-1/2 particles undergoing Larmor precession in electromagnetic fields with small field non-uniformities.
Publisher
Springer Science and Business Media LLC
Reference19 articles.
1. Thomas, L. H. The Motion of the Spinning Electron. Nature 117, 514 (1926); Phil. Mag. 3, 1 (1927).
2. Jackson, J. D. Classical Electrodynamics, 546–548 (John Wiley & Sons, Inc., 1999).
3. Jackson, J. D. Classical Electrodynamics, 550–552 (John Wiley & Sons, Inc., 1999).
4. Ungar, A. A. Thomas rotation and the parametrization of the Lorentz transformation group. Found. Phys. Lett. 1, 57–89, https://doi.org/10.1007/BF00661317 (1988).
5. Ungar, A. A. The relativistic velocity composition paradox and the Thomas rotation. Found. Phys. 19, 1385–1396, https://doi.org/10.1007/BF00732759 (1989).