2020 journal article

Effect of Thomas Rotation on the Lorentz Transformation of Electromagnetic fields


By: L. Malhotra*, R. Golub n, E. Kraegeloh*, N. Nouri* & B. Plaster*

co-author countries: United States of America 🇺🇸
Source: Web Of Science
Added: September 14, 2020

Abstract A 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 $$\overrightarrow{\beta }+\delta \overrightarrow{\beta }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mo>→</mml:mo></mml:mover><mml:mo>+</mml:mo><mml:mi>δ</mml:mi><mml:mover><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mo>→</mml:mo></mml:mover></mml:math> and successive boosts $$\overrightarrow{\beta }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mo>→</mml:mo></mml:mover></mml:math> and $$\Delta \overrightarrow{\beta }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Δ</mml:mi><mml:mover><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mo>→</mml:mo></mml:mover></mml:math> 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.